003621 EARTH SCIENCES LIBRARY THE STRENGTH OF THE EARTH'S CRUST JOSEPH BARRELL Reprinted for private circulation from THE JOURNAL OF GEOLOGY, Vol. XXII, Nos. 1-8, 1914 Vol. XXIII, Nos. 1,5, and 6, 1915 * t * THE STRENGTH OF THE EARTH'S CRUST VQL xxn PAGES PART I. Geologic Tests of the Limits of Strength .... 28- 48 PART II. Regional Distribution of Isostatic Compensation . . 145-165 PART III. Influence of Variable Rate of Isostatic Compensation 209-236 PART IV. Heterogeneity and Rigidity of the Crust as Measured by Departures from Isostasy 289-314 PART V. The Depth of Masses Producing Gravity Anomalies and Deflection Residuals: Section A, Development of Criteria for Spheroidal Masses 441-468 Section B, Applications of Criteria to Determine the Limits of Depth, Form, and Mass 537~555 PART VI. Relations of Isostatic Movements to a Sphere of Weak- ness the Asthenosphere 655-683 PART VII. Variation of Strength with Depth, as Shown by the Nature of Departures from Isostasy: Section A, Presentation of Theory 729-741 VOL. XXIII PAGES Section B, Applications of the Theory 27-44 PART VIII. Physical Conditions Controlling the Nature of the Lithosphere and Asthenosphere: Section A, Relations between Rigidity, Strength, and Igneous Activity .-* . . . 424-443 Section B, Relations with Other Fields of Geophysics 499-515 Detailed outlines will be found on the first page of each part, followed by an introduction to and summary of the part. THE STRENGTH OF THE EARTH'S CRUST I. GEOLOGIC TESTS OF THE LIMITS OF STRENGTH JOSEPH BARRELL Reprinted for private circulation from THE JOURNAL OF GEOLOGY, Vol. XXII, No. i, January-February 1914 STRENGTH OF THE EARTH'S CRUST JOSEPH BARRELL New Haven, Connecticut PREFACE PART I. GEOLOGIC TESTS OF THE LIMITS OF STRENGTH INTRODUCTORY AND SUMMARY 29 MOUNTAINS BUILT BY COMPRESSION OR IGNEOUS ACTIVITY ... 32 SHIFTINGS OF LOAD DUE TO CLIMATIC CHANGE 33 THE EVIDENCE FROM EROSION CYCLES 34 THE EVIDENCE FROM DEPOSITION 36 Preliminary Statement . 36 The Deltas of the Nile and Niger 39 Discussion of Results 43 PREFACE The publication of a series of papers on " Diastrophism and the Formative Processes" by T. C. Chamberlin was begun in the Journal of Geology in October, 1913. The second part, on "Shelf- Seas and Certain Limitations of Diastrophism," is nearly identical in substance with a portion of a paper read by Professor Chamberlin on August 13, 1913, at the Twelfth International Geological Con- vention at Toronto, Canada. In this part particularly it is pointed out that the parallel surface and bottom of the shelf-seas, also their occasional extension as shallow water bodies over considerable por- tions of the continent at certain times, indicate a relation to sea- evel and wave base rather than to a delicate isostatic adjustment. The implications of this and other lines of argument given by Chamberlin are toward crustal rigidity, not crustal mobility. The first four parts of the present article on "The Strength of the Earth's Crust" had been completed before the writer read Pro- fessor Chamberlin's paper, or knew that he was at work upon the subject; but the conclusions are so closely in accord with his, though reached by other lines of attack, that this article may be 28 THE STRENGTH OF THE EARTH'S CRUST 29 regarded as a continuation of the same subject, an added contri- bution in the large field of diastrophism and the formative pro- cesses, following out certain of its ramifications. A somewhat general survey is given here of the problem of the strength of the crust, beginning with the lines of evidence which tear upon it and following out to some degree the conclusions drawn from it. It has in this way been cast into the form of those articles published by the Journal of Geology from time to time, under the caption of "Studies for Students." PART I. GEOLOGIC TESTS OF THE LIMITS OF STRENGTH INTRODUCTION AND SUMMARY The capacity of the outer crust to resist vertical stresses is an important field in the theory of dynamical and structural geology. On the one hand, it is known that the larger segments, those of continental and oceanic proportions, rest to a large degree in isostatic equilibrium, the subcrust of the continental areas being lighter than that of the oceanic areas in proportion to the regional elevation. On the other hand, the minor features, those which enter into the composition of the landscape, are known to have been sculptured by external forces and are to be explained there- fore as sustained by reason of the rigidity of the crust. Between these two extremes in magnitude of terrestrial relief lie mountain ranges, plateaus, and basins; made in part by tangential forces, modified by erosion and sedimentation. To what extent can these constructional and destructional forces work in oppo- sition to those other forces which by producing vertical movement make for isostatic equilibrium ? The method of attack is from two directions. The geologist examines the structures imposed by tangential forces, the mountains built by igneous extrusion, the surfaces made by erosion, the strata consequent upon sedimenta- tion. From them he may determine the amount of strain which the crust can endure before periodic movements occur in the 'direc- tion of relief from strain. The geodesist, by means of the plumb- line and pendulum, determines the subcrustal densities and notes the degree to which these are balanced against the relief, pointing 30 JOSEPH BARRELL therefore to a relation of flotational equilibrium within the solid earth. Most geologists in former years have utilized but little the prin- ciples of isostasy, as may be seen by reference to the standard manuals. On the one hand, the weight of sediments may be spoken of as the cause of downsinking with such equal pace that the condi- tion of a shallow sea prevails for a geologic period, though perhaps accompanied by the deposition of thousands of feet of sediment. On the other hand, and without argumentation to explain the apparent inconsistency, the same geologist may state that tangen- tial forces have built folded mountains miles in height which may be subsequently largely removed by erosion before marked vertical warping of the crust occurs. In contrast to the geologists, certain geodesists have argued in recent years for a high degree of isostatic adjustment; isostasy being regarded by Hayford, for example, as largely complete in areas probably between one square mile and one square degree in size, the mean departure of these unit areas from the level of com- plete compensation being stated by him as ranging from 250 to 570 ft. These figures he does not regard, however, as of a high order of accuracy, the latter being probably the more reliable of the two. He states that their significance is mainly in showing that isostatic compensation is nearly perfect. It has even been argued by Button, Willis, and Hayford, as an outflow of geodetic studies, that those vertical movements of the outer crust which tend to give isostatic equilibrium are the ultimate causes of the periodic great compressive movements. There is here between geologists and geodesists a tendency to a fundamental difference of opinion, resulting from the emphasis upon one or the other of those opposing forces which work in the outer crust. The truth must lie within the broad zone between these two extremes of theory. To try to bring them together in harmony is the problem before us. The first part of the paper, on the geologic tests of the limits of strength, opens with a brief review of the lines of geologic evidence which may be used as tests of the degree of resistance or response by the crust to vertical stresses, having regard to both area and THE STRENGTH OF THE EARTH'S CRUST 31 intensity. Deltas built into deep seas seem best adapted to give quantitative measurements. Those of the Nile and the Niger therefore are subjected to detailed study. They indicate that the earth is competent over those regions to sustain stresses due to sedimentation which are measured by the weight of several thou- sand feet of rock, even where the load is continuous over tens of thousands of square miles. Whatever response there may be is so slow that the deposition is able to keep pace with subsidence and maintain the load as a permanent stress of this magnitude upon the crust. By analogy the conclusion may be applied to other parts of the earth, and to those negative loads created by the erosion to base-level of regions previously unwarped to an elevation pre- ( ' sumably near to that which would give isostatic equilibrium. Consequently, also, the crust should be able to bear in consider- able degree the folded and overthrusted structures piled up by the tangentially compressive forces which periodically operate to such large degree within its outer shell. Deeper changes, involving changes of density, are involved, however, in orogenic processes and express themselves in vertical warpings associated with, and following after, folding. This association of vertical and tangential forces complicates the problem of the crustal strength needed to support mountain range?. The measures derived from the study of deltas are more in accord with those larger estimates of the strength of the crust obtained by Putnam and Gilbert in 1895 fr m a transcontinental series of gravity measurements in which was developed and em- ployed for the first time the conception of local rigidity but regional isostasy. 1 Their conclusions have been thought to be superseded and controverted, however, by much more elaborate and complete geodetic studies, first by Hayford, and later by Hayford and Bowie, which went to show that the crust was very much weaker and in much more perfect static equilibrium. The calculations of Hoskins tended to show also that the crust within the zone of isostatic compensation could not bear perma- nently loads as great as those apparently imposed by these deltas. If, however, the great hydrostatic pressures within the deeper crust 1 Bull. Phil. Soc. Wash., XIII (1895), 31-75; Jour. GeoL, III (1895), 331-34. 32 JOSEPH BARRELL give to it an added resistance to stress differences as great as indi- cated by the experiments of Adams, then the strains imposed by the deltas may be permanently borne. This confrontation of the conclusions drawn from various paths of approach raises the problems which are treated in the second part. MOUNTAINS BUILT BY COMPRESSION OR IGNEOUS ACTIVITY Mountain ranges made by folding or extravasation must be independent to some degree from vertical forces, but these are not suitable geologic tests of the rigidity of the crust, since it is known, as noted in the introduction, that they are secondarily connected with diminutions of density in the zone of isostatic compensation and in many cases are rejuvenated after partial erosion by later up warping. The individual mountains or plateau remnants left standing by circumdenudation, or piled up as volcanic cones are clearly burdens upon the earth. The volume which rises above the average level is a measure of the stress. Gilbert has so used them and obtained values ranging from 40 to 700 cubic miles. 1 These volumes, how- ever, might be called minimum estimates, as may be seen upon examination of their nature. If a certain broad upwarping reduces the vertical stresses to a minimum and erosion follows without further adjustment, it is the volume of the valleys rather than the mountains which soon comes to measure the larger possible departures from equilibrium. The remaining mountains by their weight produce local downward stresses, but the more regional stresses are upward and are due to the breadth of the field of erosion. These regional stresses will become larger ultimately than the local stresses due to the residual masses. Volcanic cones do not continue to be built up until their base begins to sink into the crust as fast as the upward growth takes place. On the contrary, their growth ceases when the hydrostatic pressure of the high column of lava or a decadence of pressure in the reservoir below leads finally to a shifting of the vents. 1 "The Strength of the Earth's Crust," Bull. Geol. Soc. Am. (1889), I, 25. THE STRENGTH OF THE EARTH'S CRUST 33 Regional igneous activity has poured out lavas and breccias, burying previous mountainous topography and adding thousands of feet to the outer crust. Lack of simultaneous erosion, as in the Miocene flows of the Columbia plateau, shows that subsidence progressed, perhaps with approximately equal pace. The present altitude of the Columbia plateau is youthful, as shown by the steep canyon walls and undissected interfluvial areas. The initial sub- sidence accompanying igneous outpouring and the distinctly later upwarping without compression suggest that here isostasy has pre- vailed. But in such regions the geologic evidence points toward a minimum strength of the crust. The wide area of activity, the nu- merous vents, the general absence of localization, all are suggestive of widespread fluid rock beneath, magmas which are probably far above the level where the accompanying temperatures are normal. Such conditions would seem to imply the impossibility of the outer crust carrying over such regions the stresses which are possible in regions long free from igneous activity. More reliance as maxi- mum measures of the strength of the crust should be placed there- fore upon those external changes which are entirely independent in origin from the interior of the earth locally beneath them. SHEETINGS OF LOAD DUE TO CLIMATIC CHANGE Some of the most striking examples of loading and unloading of the crust are those connected with the climatic fluctuations of the Pleistocene. The continental ice sheet formed, advanced, and retreated rather rapidly, as viewed from the geologic standpoint. As it retreated, the lacustrine and estuarine shores show that the land was rising with the melting of the ice. The upwarping accom- panying deglaciation was limited to the approximate region of maximum glaciation and was greatest in the direction where the ice was thickest, in the St. Lawrence valley the maximum uplift being more than 600 ft. These relations suggest strongly an iso- static response to the relief of load. It is not known, however, to what degree the previous downwarp compensated for the burden of the continental ice sheet and what degree of regional stress the crust was able to bear. The lack of close response is seen in that the up warp continued as a residual movement after the ice departed. 34 JOSEPH BARRELL The movement of the crust could not keep pace with the climatic change but it shows by means of these fossil water planes its incom- petency to bear without at least partial yielding a burden as broad and as heavy as the Pleistocene climates placed upon it. Gilbert, in 1889, was led by reflection upon the changes of load imposed by the waters of extinct Lake Bonne ville to use them as a measure of the strength of the earth's crust to resist isostatic adjustments, 1 and as previously stated, tested the conclusions drawn therefrom by comparisons with the volumes of mountains made by extravasation, or circumdenudation, or their combination, and of valleys of erosion. Of Lake Bonneville he states: Considering the main body of Lake Bonneville, it appears from a study of the shorelines that the removal of the water was accompanied, or accompanied and followed, by the uprising of the central part of the basin. The coinci- dence of the phenomena may have been fortuitous, or the unloading may have been the cause of the uprising. Postulating the causal relation, and assuming that isostatic equilibrium, disturbed by the removal of the water, was restored by viscous flow of crust matter, then it appears (from observational data) that the flow was not quantitatively sufficient to satisfy the stresses created by the unloading. A stress residium was left to be taken up by rigidity, and the measure of this residuum is equivalent to the weight of from 400 to 600 cubic miles of rock. From these phenomena and theoretic considerations arises the working hypothesis that the measure of the strength of the crust is a prominence or a concavity about 600 cubic miles in volume. THE EVIDENCE FROM EROSION CYCLES Erosion base-levels folded and uplifted tracts, leaving for a time during the process mountains of circumdenudation whose local stresses have previously been discussed. The development of peneplains implies a rigidity of the crust sufficient to prevent responsive vertical movement until after the completion of the cycle of denudation. It may be difficult to determine the original average elevation and the degree of progressive uplift pari passu with erosion which preceded the peneplanation, but the fact that broad areas become flat and are controlled until the next deforma- tive movement by the level of the sea suggests that they cannot ' Bull. Geol. Soc. Am., I (1889), 23-27. THE STRENGTH OF THE EARTH'S CRUST 35 lie after erosion in close isostatic equilibrium ; that whatever stress this implies can be carried by the earth for long periods of time. The ancient peneplains are now broadly warped and uplifted. The rivers, as a rule, are intrenched in youthful valleys; or their seaward courses are drowned and not yet reclaimed by delta build- ing. These features testify to the recency of world-wide crustal unrest, marked chiefly by movements of a vertical nature; move- ments which presumably diminished the vertical stresses in the outer portions of the earth and has produced at the present time, as Willis has argued, a higher degree of isostatic compensation than has been customary through the long periods of quiet which sepa- rate the epochs of movement. There are difficulties, however, in using ancient base-leveled surfaces now upwarped as measures of the previous stress. It is known that a region like the Colorado plateaus which now stand markedly high tended to lie near sea-level from the beginning of the Paleozoic to the end of the Mesozoic. Presumably a decrease of density within the zone of isostatic compensation has taken place here during the Cenozoic and the uplift has accompanied or followed the internal change. Furthermore, if there are stages in the uplift, a considerable volume of rock is removed during each stage, so that at no one time has the average elevation of the region been as high as the residual masses might be thought to imply. Allowing for these qualifi- cations, however, there seems no doubt that the study of erosion cycles will throw light upon the limits of stress due to unloading which the crust can resist, and also upon progressive changes in subcrustal densities through geologic times. This evidence of considerable crusted rigidity, shown by freedom from compen- sating movements during a cycle of erosion, or by warpings not in sympathy with isostatic stresses during cycles of crust movements, has been pointed out before. Hayford has sought to explain it away by invoking, first, the slight crustal cooling which would occur in regions of erosion because of removal of the upper rock, heating in regions of deposition. Second, he assumes as probable the existence of a high coefficient of compressibility sufficient to make eroded regions rise in appreciable ratio to the thickness of 36 JOSEPH BARRELL the load eroded. Third, he assumes a crustal undertow from heavy toward high areas which would not only fold the surface rocks and heat them in the region of undertow but restore the equilibrium of mass in the regions of erosion and deposition. 1 It may be said of all of these factors that when they are subjected to quantitative statement they appear so trifling as to fail wholly to explain the magnitude and breadth and periodicity of crust move- ments. The inadequacy of the temperature effects has been pointed out clearly by Harmon Lewis. 2 The assumption of the high coefficient of compressibility involves more instead of less difficulty for the high isostasist. The inadequacy of isostatic undertow to account for folding has been discussed briefly by the present writer elsewhere. 3 On the other hand, the control of the level of the earth's surface during epochs of quiet by the forces of planation and not by forces making for close isostatic adjustment has been discussed convincingly by Chamberlin in his present series of articles. It seems clear, then, that in the study of cycles of erosion and deposition much may be determined in regard to the limits of terrestrial rigidity. The subject could be developed further, but it is preferred to place the emphasis of this paper upon the more readily estimated loads produced by the building of deltas. THE EVIDENCE FROM DEPOSITION Preliminary statement. -The waters deposit sediment upon the depressed areas of the crust. To what extent may such areas be loaded before yielding of the base and resultant subsidence take place? The geologic record makes it clear that subsidence and deposition are necessarily related. It has been stated often that deposition was the cause and subsidence the effect, the two being regarded as in delicate isostatic adjustment. But this is in reality an assumption, for such a supposed relationship overlooks the extent to which subsidence might have gone forward without deposition and ignores the external load which may have been necessary to 1 "The Relations of Isostasy to Geodesy, Geophysics, and Geology," Science, N.S., XXXIII (1911), 199-208. 2 "The Theory of Isostasy," Jour. Geol., XIX (1911), 622, 623. s Joseph Barrell, Science, N.S., XXIX (1909), 259, 260. THE STRENGTH OF THE EARTH'S CRUST 37 perpetuate and add to a crust movement initiated by internal causes. Sedimentation is dependent upon the rate and continuity of subsidence as well as upon the rate of deposition. Thus, although the sediments give the most complete record of crustal movements, for the distant past it is not easy to separate cause and effect and ascribe to each its part. Where the thickness of sedi- ments, however, is small, as over much of the continental interior, the cause of submergence is presumably almost wholly independent of the local load. Where the sediments are thick and subsidence rapid, as within the geosynclines, the load imposed by sedimenta- tion may on the contrary become the controlling force. It is a particular phase of deposition, however, which will be considered in this article, a study of the load imposed upon the crust by certain deltas. As long as the water plane lies at a constant level the delta builds out at its front. Upon subsidence of the supporting crust the shore retreats inland; less sediment reaches the now sub- merged front, and the delta in consequence grows chiefly by addi- tions to the shoreward part of its upper surface. The two methods of growth not uncommonly alternate upon the same delta, showing the discontinuity of subsidence. In building outward a delta acquires a convex shoreline. This form is clearly related to aggra- dation, not to isostatic uplift, and its volume is a measure of a load inclined to further sinking, the larger rivers tending to drain toward and into the downwarps of a continent. To what degree, then, can a region of the crust which is possibly already resisting down- ward strain bear this added burden ? A preliminary examination will be made of several classes of deltas in order to choose those best adapted to test this question. Most of the deltas of Eurasia and South America are at present advancing rapidly into shallow embayments and the faunas of the continental islands show that the latter were recently a part of the land. The physical and organic evidence thus concur in showing that a very recent subsidence has taken place. It is to be con- cluded that a submergent phase in the Cenozoic crustal oscillations has marked the short interval since the last retreat of the Pleisto- cene ice. The great deltas constructed during the late Tertiary and in the Pleistocene are consequently now in great part drowned. 38 JOSEPH BARRELL Their location, volume, and limits in most cases are not known. Their modern and smaller representatives, as they build out into shallow water, do not greatly increase the load upon the crust. Deltas recently drowned are therefore not well adapted to serve as tests of the strength of the crust. Deltas which lie in re-entrant angles of the continents are also poorly adapted to be used as a test. Those of the Indus, the Ganges, and the Colorado are illustrations. As they fill up the heads of gulfs and are without the typical convex outline, it is not only difficult to compute their volume but their situation is such as to suggest that even without the construction of the delta the region might be far out of isostatic adjustment. Certain rivers, which face the open ocean, such as the Columbia, do not build deltas because of the power of the waves and currents which sweep laterally the fine detritus. Many rivers, however, build considerable submarine deltas even where the in-planing forces of the ocean prevent a terrestrial outward growth. Such submarine deltas, owing probably to the power of the waves rather than to recent submergence, are marked by convexities in the bathymetric contours opposite the river mouths. The Congo, the Orange, and the Zambesi are examples. These hidden deltas which are built out into deep waters cannot reach more than a certain distance from the shore and part of their detritus is carried laterally along shore by the waves, but never- theless they possess a very considerable volume and the convexity which they make upon the ocean floor shows to that degree the rigidity of the crust. The maximum test is found where great rivers have carried forward subaerial topset beds of their deltas over what was pre- viously deep ocean. Fluviatile construction in such examples has dominated over marine destruction, giving a convex outline to the shore; but the subaqueous deposits may still make up the greater part of the volume. Even in these cases the question may be raised whether the deltas have attained the maximum possible size per- mitted by the strength of the crust. Their size may, on the con- trary, be limited even here by the balance of the surface agencies and the limited time during which the river has dominated over THE STRENGTH OF THE EARTH'S CRUST 39 the sea. It is a fair presumption, however, that the largest deltas have reached a size where subsidence keeps pace with added volume. The deltas of the Nile and Niger. Only the most powerful rivers, laden with abundant waste and protected by their situation from the heavier wave and current action, can build deltas of this last class directly into ocean basins. Perhaps the two best of the few good examples are those of the Nile and the Niger. Both have built out great deltas from regularly curving shores of the Atlantic type the type where recent folded mountains do not mark the line between continent and ocean, the type where tangential forces FIG. i. Delta of the Nile. Scale i: 10,000,000. From Andree's Allgemeiner Handatlas, vierte Auflage. cannot be supposed to have disturbed recently the isostatic balance of continent and ocean. To determine the areas, depths, and volumes of the deltas from the standpoint of isostasy, a smooth curve, as shown in Figs, i and 3, was continued through them from the shore beyond. The sub- marine contours were also projected in dotted lines, giving the form of the bottom as it presumably would now be if no rivers at these places had entered the sea. The volume of the deltas may then be determined by computing the volume included between these two sets of contour lines. In both cases, in so far as the positions of the hypothetical bottom contours are open to doubt, they have been located some- what above a most probable position, so as to tend to throw the error of computation in the direction of too small rather than too 40 JOSEPH BARRELL large a volume. For instance, the easterly drift of the water facing the Nile delta may have carried considerable mud in suspension to beyond the line assumed here as its limits. In consequence, the hypothetical 2,ooo-meter contour should be drawn perhaps much closer to the coast of Palestine than has been done. Beneath the Niger delta the contours lie close together on the west but have been drawn as spreading apart toward the east. It would perhaps be nearer the truth to project the steep character of the coastal slopes to the east of the Niger delta under it to where the contours meet the chain of volcanic island mountains extending from the Cameroons out to sea. This appears to be especially probable, since Buchanan has shown that the gentle slopes of the Guinea coast even beyond the limits of the deltas, and extending from 2 soKm. 200 ,00 Seolevel FIG. 2. Vertical section of the delta of the Nile on A- A, Fig. i. Horizontal scale i: 5,000,000. Vertical scale 1:200,000. Area of section, 295 kilometers. long. 23o' E. to lat. 8 S., are mantled throughout by very soft, black, oozy mud, characteristic of river estuaries. All the way down the coast as far as Loanda, lat. 8 S., the same gentle gradients and the same very soft river mud were found. It appears that the land debris brought down by the Niger and Congo, and by other less impor- tant rivers, is collected and concentrated in this district. The prevailing current past the mouth of the Congo is a northerly one, while all along the coast from Cape Palmas to the Niger an easterly current sets. These help to confine the drainage matter of both rivers to a comparatively small extent of littoral. If from the soundings west of Cape St. Paul we compute the mean continental slope, we find that the 5oo-fathom line is at a mean distance of 4.1 miles, the i,ooo-fathom line at 11.7 miles, and the i,5oo-fathom line at a distance of 17 miles from the loo-fathom line. If it is assumed that in the absence of the Niger and the Congo the continental slope would be much the same as the average found in the profiles west of Cape St. Paul, it may be concluded that the excess of mud forming the flatter talus along the coasts affected by these rivers is due to the mud brought down by them. 1 1 J. Y. Buchanan, "On the Land Slopes Separating Continents and Ocean Basins, Especially Those on the West Coast of Africa," Scottish Geographical Magazine, May, 1887, pp. 7, 8. THE STRENGTH OF THE EARTH'S CRUST Buchanan states that this gentle bottom slope extends for 1,100 miles along the coast, and computes the volume contained between the steep gradient presumably once existing and the flatter gradient of the present bottom. This represents a deposit of 66,- ooo cubic nautical miles of detritus due principally to the Niger and the Congo. 1 This great volume cannot be used safely, however, as the measure of a load upon the crust, since a believer in the theory of close isostatic compensation could claim with some degree FIG. 3. Delta of the Niger. Scale i : 10,000,000. From Andree's Allgemeiner Handatlas, vierte Auflage. of reason that the initial slope of the concave shores of the Gulf of Guinea need not have been as steep as the bold convexity of Africa to the west, or that the load may have depressed the bottom so as to have equalized the pressures. Furthermore, Buchanan does not include any of the land area of the Niger delta. The following estimates will give the volume only of the clearly constructional part of the Niger delta, including both the land and 1 Op. cit., p. 8 and Fig. 3. The volume stated by Buchanan appears to be correct if the two profiles have a common point taken upon the shoreline. In his figure, how- ever, the common point A is shown as upon the loo-fathom contour. From this error in the diagram given by Buchanan the volume estimated from the diagram would be much less than 66,000 cubic nautical miles. 42 JOSEPH BARRELL the sea portion. But it will be seen, from Buchanan's statements, that this is a minimum estimate of the areal load imposed by the rivers, for a more or less continuous burden on the crust would appear to stretch for a thousand miles along this African coast, reaching a maximum unit value, however, in the great delta of the Niger. The outer limits of the deltas were taken where the convex slopes fade out into the general ocean bottom. The results of computing the volumes shown between the two sets of contour lines are as follows: TABLE I DELTA or THE NILE Area within i,ooo-m. contour 71,000 sq. km. (27,400 sq. mi.) Area within 2,ooo-m. contour 106,000 sq. km. (38,800 sq. mi.) Radius of equivalent circle 175 km. (no mi.) Equivalence in equatorial square degrees 8.6 sq. degr. Average thickness within assumed limits 0.84 km. (2,800 ft.) Equivalence in rock upon land 0.46 km. (1,540 ft.) Ratio to 76 miles of crust i to 260 = 0. 0038 Maximum thickness 2 . 0-2 . 3 km. (6,600-7,600 ft.) Equivalence in rock upon land i . i-i . 3 km. (3,600-4,200 ft.) Volume within assumed limits (extending on the east to somewhat below 2,000 m.) 89,000 cu. km. (21,300 cu. mi) Equivalence in rock upon land 50,000 cu. km. (11,700 cu. mi.) TABLE II DELTA OF THE NIGER Area within the assumed limits 195,000 sq. km. (75,300 sq. mi.) Radius of equivalent circle 250 km. (155 mi.) Equivalence in equatorial square degrees 15.8 sq. degr. Average thickness within assumed limits i . i km. (3,600 ft.) Equivalence in rock upon land 0.6 km. (1,980 ft.) Ratio to 76 miles of crust i to 200= .005 Maximum thickness 3.0 km. (9,900 ft.) Equivalence in rock upon land i . 65 km. (5,450 ft.) Volume within assumed limits 217,000 cu. km. (52,000 cu. mi.) Equivalence in rock upon land 120,000 cu. km. (27,000 cu. mi.) The deltas in their growth had displaced their volume of water. The added loads which they throw upon the crust are measured by THE STRENGTH OF THE EARTH'S CRUST 43 subtracting the weight of the water from that of the sediments. A specific gavity of 2. 67 has been taken by geodesists as the aver- age for the outer shell of the earth. The degree of consolidation of the deeper parts of the deltas is not known, but for present pur- poses the specific gravity of their sediments as a whole may be assumed as 2.50. This will be near the truth if the composition is that of the average shale, if 10 per cent of pore space be assumed and this is wholly filled with water. The specific gravity of sea water is i . 03 , leaving an effective specific gravity for the sediments of 1.47. The ratio of 1.47 to 2.67 is 0.55. The thicknesses given for the deltas should therefore be multipled by this factor for estimating the equivalent burdens of rock of specific gravity of 2.67 above sea-level. 4Ookm. FIG. 4. Vertical section of the delta of the Niger on A-A, Fig. 3. Horizontal scale i : 5,000,000. Vertical scale i : 200,000. Area of the section, 645 kilometers. It is seen that the deltas are in the form of inclined double convex lenses. Thicknesses approaching the maximum are found over considerable areas in the middle. The load imposed by this thickness is equivalent in the Nile delta to 3,600-4,200 ft. of rock above sea-level; in the Niger delta to 5,000-5,500 ft. Discussion of results. The region of the southeastern Mediter- ranean is held by Suess to be geologically of very recent origin, downfaulted from the continent. The delta of the Nile, much smaller than that of the Niger, is therefore to be regarded as young and may be still increasing in volume. The great size of the Niger delta suggests, on the other hand, that it may have reached the limit permitted by the strength of the crust. Subsidence may now intermittently keep pace with deposit. If the i,ooo-meter contour has been located correctly, as shown in Fig. 3, it suggests that such may be the case, since it is 44 JOSEPH BARRELL seen that in contrast to the Nile delta the slopes are much steeper between the 1,000- to 2,ooo-meter than between the 200- to 1,000- meter contours. This can be explained by assuming that the steep slope lying below and beyond a flatter slope was once a foreset slope just below wave base, whereas it now lies at least 800 meters below. If such a subsidence has occurred, it appears, however, to have been confined to within the limits of the delta; since a peripheral overdeepening of the ocean floor is not evident. On the other hand, it is noted by Penck, but probably too sweepingly, that all bathy- metric curves have their steepest slopes between 1,000 and 2,000 meters in depth. 1 Such a phenomenon might be due to lateral flow of sediment under a certain depth of load and without relation to subsidence of the base. The question whether the load of the Niger delta is as great as the crust can bear is therefore an open one. The Gulf of Guinea, where now the delta is built, is regarded by many geologists as having originated since the Middle Mesozoic by a breaking-down from the continent of Gondwana, but the presence of Middle Cretaceous marine beds skirting much of the coast of West Africa suggests perhaps that the delta in its con- struction does not go back of the Tertiary. In fact it would seem possible from the youthful relief of the continental plateau that the delta built from its waste is of Upper Tertiary and Pleistocene growth. A single delta might happen to be a mere veneer of sediment upon an originally slightly submerged projecting part of the coast. Such a fortuitous coincidence of unrelated circumstances may, however, be dismissed as highly improbable in the case of two great rivers draining in opposite directions from the same continent. The conclusion that these deltas are really externally constructive features and measure a real strain upon the crust is strengthened by noting the submarine deltas opposite the other great rivers of Africa, built into the ocean, even though the waves and currents have limited them by preventing their subaerial seaward growth. In the mechanics of the relation of the delta to the stresses in the crust an important factor is the nature of the marginal land. Shores of the Pacific type have great mountain systems marginal 1 Morphologic der Erdoberflache, I (1894), 146. THE STRENGTH OF THE EARTH'S CRUST 45 to the continents. Parallel to them the sea has great fore-deeps. It appears as though the mountain ranges had been piled too high by tangential forces, and, by virtue of the partial rigidity of the crust, had depressed the neighboring ocean bottoms. Erosion of the coastal mountains and deposition of their waste in the fore- deep would tend, up to a certain limit, to equalize the strain in the crust. In that case it might happen that, although the mass of the delta measures a stress, this might be opposite in character to pre-existing stresses, with the result that the strain upon the crust beneath the delta before the infilling might be as great or greater, but in an opposite direction. The greatest remaining strain within the sea-bottom could conceivably be an upward strain under the parts of the fore-deep not filled. Such relations are not found around abyssal slopes of the Atlantic type. These are regarded by many geologists following the lead of Suess as made by marginal downbreaking of the con- tinents. They have but little or no relation to the older folded structures and no excessive deeps parallel to the continental mar- gins. If these relations of the Atlantic and Indian oceans to the continents are rightly interpreted as to cause, it is probable that the stresses which make for downsinking extend beyond the parts already foundered. The margin of continents and ocean basins are not likely to be depressed too low, but if remaining out of isostatic adjustment they would tend rather to stand too high. There is no theoretic reason to believe, therefore, that the Nile and Niger deltas have neutralized pre-existing strains. They are best regarded as real and present burdens sustained by the rigidity of the crust. Whether or not, however, the building of deltas produced stresses of a character identical with, or opposite to, those previously existing in the region, the stress gradient between the areas of the delta and the surrounding areas would be measured by the weight of the sediments, and this would tend to produce differential flexure. It would seem to be a logical conclusion, therefore, from these tests, that certain parts of the earth's outer crust can resist for considerable periods of time vertical stresses at least equivalent to the weight in air of 10,000-25,000 cubic miles of rock in lenslike 46 JOSEPH BARRELL forms spread over areas of 40,000-75,000 square miles and reaching thicknesses in air over considerable areas of 4,000-5,000 feet. The tabulation of the data regarding the deltas shows the area of the Niger delta to be equivalent to a circle 310 miles in diameter and that over this area the load of the delta is one two-hundredths the weight of the crust to a depth of 76 miles, this being the depth of the zone of isostatic compensation given by the latest determi- nation of Hay ford. According to Hoskins, in a calculation made for Chamberlin and Salisbury, 1 a dome corresponding perfectly to the sphericity of the earth and formed of firm crystalline rock of the high crushing strength of 25,000 pounds to the square inch, and having a weight of 180 pounds to the cubic foot, would, if unsupported below, sustain only ^\^ of its own weight. This result is essen- tially independent of the extent of the dome, and also its thickness, provided the former is continental and the latter does not exceed a small fraction of the earth's radius. The delta, though large, is so limited in size in comparison with continental areas that it would be somewhat more effectively sup- ported, but its externally convex form can hardly be supposed to give it added domal strength, since it consists of more or less uncon- solidated material piled upon a concave floor. The theory of isostasy holds that at a certain depth in the crust there is an approach to equal pressures, the larger relief of the sur- face being balanced in large part by subsurface variations in density. The larger segments of the crust tend to rise or sink until the elevations are in adjustment to the density beneath. A corol- lary of this theory is that unbalanced surface loads are largely sustained by the strength of the crust above this level of equal pressures; in other words, but little of the load is transmitted to the deeper earth below. For purposes of discussion it may then be assumed that the load of the Niger delta is supported by the outer 76 miles of crust. This depth is one-fourth of the diameter of the circle equivalent in area to the delta. The load over this area, as stated, is one two-hundredths of the weight of the supporting crust. Allowing something for the limited area of the delta, it is seen never- 1 Geology, I, 555, 1904. THE STRENGTH OF THE EARTH'S CRUST 47 theless to imply a strength of the crust about twice that assumed as a maximum by Hoskins as a basis for his calculation. There are several contributing factors which may explain the disagree- ment between the figures obtained by observation of the deltas and the calculation given by Hoskins and others: First, part of the stress is transmitted laterally to some extent into the deeper layers, but as the diameter of the loaded area is four times its depth this can be a partial explanation only and has, furthermore, been allowed for. Second, part of the stress may be transmitted into the deeper earth below the yb-mile zone of isostatic compensation. This is about equivalent to third, that the zone of isostatic compensation may extend deeper, at least locally, and fade out more after the suggestion made by Chamberlin. 1 Fourth, a consideration which the writer regards as most important is that the crust may in reality possess greater crushing strength than the 25,000 pounds per inch postulated by Hoskins. At the time that Hoskins made this cal- culation it seemed that this figure was the highest which could be chosen, since it is higher in fact than the crushing strength of the average surface rock when subjected for even a short time to com- pression in a testing machine, and in the earth the stresses must be carried for indefinite periods. The experiments by Adams 2 have shown, however, that under the conditions of cubic compression which exist in the earth the rocks are capable of sustaining for indefinite times far higher stress differences than they could bear even for a short time when subjected to stress in one direction only, as at the surface of the earth. These experiments showed that: At ordinary temperatures but under the conditions of hydrostatic pressure or cubic compression which exist within the earth's crust, granite will sustain a load of nearly 100 tons to the square inch, that is to say, a load rather more than seven times as great as that which will crush it at the surface of the earth under the conditions of the usual laboratory test. Under the conditions of pressure and temperature which are believed to obtain within the earth's crust empty cavities may exist in granite to a depth of at least n miles. 3 . 1 Jour. Geol., XV (1907), 76. 2 "An Experimental Contribution to the Question of the Depth of the Zone of Flow in the Earth's Crust," Jour. GeoL, XX (19^2), 97-118. *0p. cit., p. 117. ' I 4 8 JOSEPH BARRELL It appears then that, even allowing for the great increase in tem- perature within the earth's crust at depths greater than can be reached by the limitations of experiment, the demands made upon the strength of the crust by the load of the Niger delta are not greater than can be explained by the theory of the mechanics of materials as now understood. This theory rests, however, even after Adams' experiments, upon only a limited range of laboratory observation, and extending over but limited periods only, thus demanding extrapolation both of stress and of time when applied to the whole thickness of the outer crust and over hundreds of thousands of years. Therefore the study of the direct evidence supplied by geologic observation is more convincing in regard to the limits of crustal strength. These deltas point toward a measure of crustal rigidity capable of sustaining to a large degree the downward strains due to the piling-up and overthrusting of mountains built by tangential forces, or those resulting from the load of sediments in areas of deposition, or those upward strains produced by the erosion of plateaus previously uplifted toward isostatic equilibrium. A final conclusion must, however, await a further discussion in the later parts. [To be continued} THE STRENGTH OF THE EARTH'S CRUST JOSEPH BARRELL New Haven, Connecticut PART II. REGIONAL DISTRIBUTION OF ISOSTATIC COMPENSATION INTRODUCTION AND SUMMARY 145 GEODETIC MEASUREMENTS OF ISOSTASY BY HAYFORD AND BOWIE . 149 Hayford's Conclusions from Deflections of the Vertical . . . 149 Hayford and Bowie on Variations of Gravity 152 REGIONAL VERSUS LOCAL DISTRIBUTION OF COMPENSATION . . . 156 Conclusions on This Topic by Hayford and Bowie . . . . 156 Review and Analysis of the Evidence 157 The Test by Adjacent Stations at Different Elevations . . . 160 The Test by Areas of Grouped Residuals 162 INTRODUCTION AND SUMMARY The strength of the crust has been tested in the first part of this paper by those geologic changes which alter the surface of the earth, but not the density of its interior. If these changes in load initiate rather than merely coincide with vertical movements which serve to diminish the stress, they are thereby shown to be greater than the earth can permanently endure. If, on the other hand, the constructional forms persist, as in the two great deltas studied, then the movements which may exist in the crust due to those loads must be slower at least than the process of surface construction. Such loads consequently, unless counterbalanced by some factor not apparent, are within the limits of crustal strength. But surface changes and the loads implied can be measured only in special cases. The previous attitude of the crust and the degree and direction of strain then existing in it are complicating factors which it is difficult quantitatively to evaluate. For these reasons the evidence yielded by geodetic investigation promises, in the end, more general and more accurate results. 145 146 JOSEPH BARRELL It is an important conclusion, established by geodetic evidence, that the ocean basins are underlain by heavier matter than that beneath the continental platforms; the tendency through geologic time for the continents to rise relatively to the oceans may be correlated with this difference in density and the lightening of the land areas by the progressive erosion of the land surfaces. It is believed that the rejuvenative movements are in the direction of isostatic equilibrium. Fortunately for land-dwelling vertebrates, the crust is too weak for readjustment to be deferred until after the erosion of the lands, begun by the subaerial forces, shall have been completed by the sea. But the power of geodetic research does not cease with the establishment of this cause of the maintenance of the differential relief between land surface and ocean floors. Beneath the surface of the continents it reveals heterogeneities of density and measures them against the more or less local relief above. To the extent to which areas of lighter or denser matter do not correspond to pro- portionately higher or lower relief, real strains either upward or downward are shown to exist through the crust. Over areas of plains which have not suffered much change for geologic ages, geodesy may thus reveal the existence of large crustal strain. On the contrary, in regions of mountainous relief, although the individual mountains are sustained by rigidity and bring local strains upon the supporting basement, geodetic study may show that there is close regional compensation of density balanced against relief, obliterat- ing with depth the stress differences due to topography, l&ese methods of research are thus capable of attacking the problem of the amount and direction of vertical strain existing in the crust under any part of the land surface and, to a lesser degree of accuracy, the crust beneath the sea. The breadth of the individual areas which depart from equilibrium in one direction may constitute also a vital part of the problem. But although these are fields of research open to the geodesist, they are cultivated with much labor. The position of many sta- tions on the surface of the earth must be determined by astronomic observations to within a fraction of a second of arc. Then a triangulation network, continent-wide, ties these together and shows THE STRENGTH OF THE EARTH'S CRUST 147 at each station, after allowing for the small errors of observation, what are the deflections of the vertical produced by the variations of relief and density. But this deflection for each station is the net result of all the relief from mean level and all the subsurface departures from the densities necessary to. sustain that relief for distances of hundreds and, to a diminishing extent, even thousands of miles. The problem is made more soluble, however, by another and independent mode of attack. Observations on the intensity of gravity, when corrected for latitude, for elevation, for the sur- rounding relief and the density theoretically needed to sustain that relief, show the vertical component of those outstanding forces whose horizontal component was measured by astronomic determi- nations. It is seen that if the topography is known and its influence evaluated, and sufficient observations are reduced, the distribution of subcrustal densities and consequently the amount of crustal strains form soluble but complex problems. The mathematical mode of investigation of such problems has, however, both its advantages and disadvantages. The advantages lie in giving quantitative results and in the test of the accuracy of the trial hypotheses by means of the method of least squares. A disadvantage lies in the necessity of erecting simple hypotheses in place of the complex realities of nature, in order to bring the data within the range of mathematical treatment. The precision of mathematical analysis is furthermore likely to obscure the lack of precision in the basal assumptions and through the apparent finality of its results tends to hide from sight other possibilities of the solution. It is because of the geologic nature of the hypotheses on which the calculations concerning isostasy rest, and the geologic bearing of the results, that it is no act of presumption for the geologist to enter into this particular field of the geodesist. The measurements of isostasy have been placed most fully on a quantitative basis by Hayford, and the science of geology is in- debted to him in large measure. In the following consideration of the geodetic evidence attention will be confined almost entirely to his work, supplemented by that of Bowie. Hayford was the first to consider the influence of the topography and its compensation 148 JOSEPH BARRELL to very great distances from each station, the first to make a con- siderable number of trial solutions upon various assumptions as to the depth of the zone of isostatic compensation, with the result that the reduction of the observations gave the dimensions of the earth with a considerably smaller probable error than any previous computations. 1 But the conclusions in regard to the strength of the crust, drawn in the first part of this article from the study of deltas, stand in strong contrast to certain statements by Hayford and later by Hayford and Bowie. This second part must therefore outline the results reached by them and show what reconsiderations are neces- sary in order to bring into harmony their conclusions and the evidence derived from the previous geologic study. A preliminary review without criticism is given of their work in order to bring out their methods and results, and the geologic conclusions which they draw from those results. It is followed by a re-examination of the subject of regional versus local compensation. This is the problem of the size of the area over which, by virtue of the rigidity of the crust, irregularities of density and topography do not have individual relationships but do largely compensate each other over the region as a whole. It is a measure, therefore, of the areal limits of crustal strength. The tests employed by Hayford and Bowie are, as they note, indeterminate up to radii above 58.8 but less than 166.7 km- m length. Consequently Hayford did not change his opinion, based upon previous investigations, that regional com- pensation was limited to areas of less than one square degree. In 1 The final publications have been issued by the United States Coast and Geodetic Survey and are as follows: Hayford, "The Figure of the Earth and Isostasy from Measurements in the United States (up to 1906)," 1909; referred to in this paper as Hayford, 1906; Hayford, "Supplementary Investigation in 1909 of the Figure of the Earth and Isostasy," 1910; referred to in this paper as Hayford, 1909; Hayford and Bowie, "The Effect of Topography and Isostatic Compensation upon the Intensity of Gravity," 1912; referred to in this paper as Hayford and Bowie, 1912; Bowie, "Effect of Topography and Isostatic Compensation upon the Intensity of Gravity" (second paper), 1912; referred to in this paper as Bowie, 1912. In addition Bowie has published in the American Journal of Science, "Some Relations between Gravity Anomalies and the Geologic Formations in the United States," (4) XXXIII (1912), 237-40. The following discussion of their geodetic measurements and results will be con- fined to the work in these five papers. THE STRENGTH OF THE EARTH'S CRUST 149 this article, however, two other tests are applied which indicate that although in some areas compensation does not extend to 166 . 7 km. radius, in other areas it extends farther. It is concluded that the United States shows regional departures from isostasy over areas many times larger than Hay ford thought to exist, as broad and in some regions probably somewhat broader than the areas of the Nile and Niger deltas, the breadth depending in considerable part upon the magnitude of the loads per unit of surface. 1 GEODETIC MEASUREMENTS OF ISOSTASY BY HAYFORD AND BOWIE Hayford's conclusions from deflections of the vertical. The posi- tions of many stations over the United States were determined with great accuracy by geodetic measurements from other stations, thus making a closed network. The positions were also determined by astronomic observation. The differences in latitude and longitude between the geodetic and astronomic positions give the observed deflections of the vertical due to the attraction of the surface irregularities and internal heterogeneities of the geoid. To account for these deflections the gravitative attraction upon the plumb-line at each station of all the topography from ocean bottoms to moun- tain tops within 4,126 km. was computed. The influence of the topography alone upon the direction of the vertical is known as the topographic deflection and averages a little over 30". The average of the actually observed deflections are, however, but a fraction of this value. Consequently the excesses of volume represented by continents above oceans, and by plateaus on continents must be very largely balanced and neutralized by corresponding deficiencies of density in the crust beneath, which in turn explains how the larger relief is sustained. This is the theorem of isostasy. Various hypotheses in regard to the magnitude and distribution of these deficiencies in density under the continents, of excesses under the oceans, may be made, and the deflections recomputed on these successive suppositions and compared with the observed deflections. *At the recent meeting of the Geological Society of America, December 30, 1913, to January i, 1914, Professor W. H. Hobbs gave a paper on "A Criticism of the Hayfordian Conception of ' Isostasy Regarded from the Standpoint of Geology." The writer did not have the pleasure of hearing this paper, but it is clear that Professor Hobbs has attacked independently the same problems as here discussed. 150 JOSEPH BARRELL The difference is the residual error due to the partial incorrectness of a hypothesis. The exactly correct hypothesis would reduce all residual errors to zero except for the errors of observation and computation. A hypothesis which approximates to the truth will give small residual errors. In a large mass of data the sum of the squares of the residuals as derived from different hypotheses serves as a test of the relative agreement of the hypotheses with nature, that hypothesis applying best for which the sum of the squares is a minimum. In all of the complete solutions a uniform distribution of compensation was assumed to exist from the surface to the bottom of the zone of isostatic compensation. That is, if the column under a certain portion of land was 3 per cent lighter than under a certain portion of water, then it was assumed that at any and every depth the two columns differed in density by 3 per cent. The differences abruptly terminate at the level where the two columns, the long but light land column and the short but heavy sea column, become of equal weight. At the level of this surface isostatic compensation is complete and there is hydrostatic equilibrium. A tabulation of the probabilities of these hypotheses as applied to the whole of the United State is as follows: TABLE III Hypothesis Sum of Squares of 765 Residuals Solution B (extreme rigidity; depth of compensation infinite) 107,385 Solution E (depth of compensation 162. 2 km.) 105297 Solution H (depth of compensation 120. 9 km.) 10,063 Solution G (depth of compensation 113. 7 km.) 10,077 Solution A (depth of compensation zero) 18,889 The first investigation, that of 1906, favored Solution G, the final, that of 1909, as shown in this table, favored H. The most probable depth on the hypothesis of uniform compensation with depth and of equal depth of compensation for the whole United States was a little greater, being 122.2 km., 76 miles. It is seen, however, that there is but little change in the sum of the squares for a considerable range in the assumed depth. Further, Hayford states that the hypothesis of all compensation being attained in a lo-mile stratum whose bottom is at a depth of 35 miles is about as probable as the solution which he adopted. 1 Other variations in the hypothesis are also possible with about the same probable error. 2 1 1906, p. 151. a 1906, p. 153. THE STRENGTH OF THE EARTH'S CRUST 151 A distribution suggested by Chamberlin, of compensation greatest a little below the surface and diminishing to nothing at 178.6 miles, is also about as probable. Hayford therefore does not claim that his geodetic studies determine with precision the nature or depth of the distribution of compensation. The figure of 76 miles should therefore be used always with this reservation. The residuals were classified into fourteen geographic groups. The most probable depths of compensation indicated for the several groups range from 66 to 305 km. According to Hayford, the evidence from these groups is, however, so weak and conflicting that he sees no indication that the depth of compensation is not constant over the whole area investigated. 1 He notes that, so far as the evidence goes, it indicates the depth of compensation to be greater in the eastern and central portions of the United States than in the western portion. 2 The subject is one which will be taken up later in the discussion of geodetic results. In regard to the completeness of compensation, Hayford states: From the evidence it is safe to conclude that the isostatic compensation is so nearly complete on an average that the deflections of the vertical are thereby reduced to less than one-tenth of the mean values which they would have if no isostatic compensation existed. One may properly characterize the isostatic compensation as departing on an average less than one-tenth from completeness or perfection. The average elevation of the United States above mean sea-level being about 2,500 feet, this average departure of less than one-tenth part from complete compensation corresponds to excesses or deficiencies of mass repre- sented by a stratum only 250 feet (76 meters) thick on an average.3 It is not intended to assert that every minute topographic feature, such, for example, as a hill covering a single square mile, is separately compensated. It is believed that the larger topographic features are compensated. It is an interesting and important problem for future study to determine the maximum size, in the horizontal sense, which a topographic feature may have and still not have beneath it an approximation to complete isostatic compensation. It is certain, from the results of this investigation, that the continent as a whole is closely compensated, and that areas as large as states are also compensated. It is the writer's belief that each area as large as one degree square is generally largely compensated. The writer predicts that future investigations will show that the maximum horizontal extent which a topographic feature may have and still escape compensation is between i square mile and i square degree. This prediction is based, in part, upon a consideration of the mechanics of the problem.4 1 1909, pp. 55-59. 3 19 o9, p. 59. 2 1906, pp. 143, 146. 4 1906, p. 169. 152 JOSEPH BARRELL These conclusions imply a weakness of the crust surprising to the geologist and stand in marked contrast to those figures derived from the study of the deltas of the Nile and Niger. This subject also will be discussed later, as here it is desired to give only a summary state- ment of the methods and conclusions. Hay ford and Bowie on variations of gravity. Regarding the rela- tions of variations in gravity to isostasy, Hayford and Bowie state: As soon as it was evident that the proper recognition of isostasy in connec- tion with computations of the figure and size of the earth from observed deflections of the vertical would produce a great increase in accuracy, it appeared to be very probable that a similar recognition of isostasy in connection with computations of the shape of the earth from observations of the intensity of gravity would produce a similar increase of accuracy. Logically the next step to be taken was therefore to introduce such a definite recognition of isostasy into gravity computations. Moreover, it appeared that if this step were taken it would furnish a proof of the existence of isostasy independent of the proof furnished by observed deflections of the vertical, and would therefore be of great value in supplementing the deflection investigations and in testing the conclusions drawn from them. In other words, the effects of isostasy upon the direction of gravity at various stations on the earth's surface having been studied, it then appeared to be almost equally important to investigate the effects of isostasy upon the intensity of gravity. 1 In order to make the computations, the isostatic compensation was assumed to be complete under every topographic feature and uniformly distributed to a depth of 114 km. below sea-level, pro- ducing hydrostatic equilibrium at this depth. The mean density of 2 . 67 was taken as applying to the whole zone to this depth. Under land 3 km. high this gives a density of 2 . 60 from sea-level to a depth of 114 km.; under ocean 5 km. deep a density of 2.74 from ocean bottom to 114 km. below the bottom. 2 The authors show that the topography and its compensation for the whole earth must be taken into consideration. On these assumptions the theoretic value of gravity was computed for every station, 124 in the final publication. This computed value is sub- tracted from the observed value and gives the " new-method" anomaly for each station. The results are shown in Fig. 5. 1 Hayford and Bowie, 1912, p. 5. 2 Hayford and Bowie, 1912, pp. 9, 10. THE STRENGTH OF THE EARTH'S CRUST 154 JOSEPH BARRELL Of the two other principal methods of gravity reduction which have been previously used, the Bouguer reduction takes no account of isostatic compensation, postulating a high rigidity of the earth's crust, and neglects all curvature of the sea-level surface. The "free-air" reduction assumes that each piece of topography is compensated for at zero depth. These two reductions correspond thus to the limiting solutions tried for deflections of the vertical. The sum of the squares of the new method anomalies, when com- pared respectively with the similar sums derived from the hypothesis of rigidity and the hypothesis of compensation at depth zero, shows that the assumption of isostatic compensation uniformly dis- tributed to a depth of 114 km. gives on the average smaller anomalies; is therefore much more probable and yields a more accurate value for the intensity of gravity. The mean anomaly of all stations in the United States without regard to sign, omitting the exceptionally large anomalies of the Seattle stations, is as follows: New method o. 018 dyne 1 Bouguer o. 063 Free air o. 028 The value of gravity for the United States Coast and Geodetic Survey office at Washington was determined as 980 .112 dynes per gram. The mean new-method anomaly is consequently about o . 00002 of the value of gravity. The probable error of observation and computation is about 0.003 dyne. The errors may, however, frequently exceed o . 004 dyne and in rare cases may be as great as o.oio dyne. 2 The fact that these measures of gravity are the forces acting on one gram will be understood through the rest of the paper. Of the 124 stations, 32 have anomalies between o. 020 and o. 030, 12 have anomalies between 0.030 and 0.040. 3 Still smaller num- bers of stations have higher anomalies. These anomalies measure departures in the earth's crust from the conditions of isostasy which were postulated. In the interpretation of the anomalies in terms of mass it is shown that a small excess of mass immediately below 1 Bowie, 1912, p. 12. 'Hayford and Bowie, 1912, p. 79; Bowie, 1912, p. 13. 3 Bowie, 1912, p. 13. THE STRENGTH OF THE EARTH'S CRUST 155 the station or a large excess at great depth or to one side may have the same effect. Therefore it is necessary to speak of the net effective excess or deficiency of mass. 1 A table is given showing these relations, and as a mean working hypothesis it is assumed that ordinarily each 0.0030 dyne of anomaly is due to an excess or deficiency of mass equivalent to a stratum 100 ft. thick. In the final paper it is concluded : From the evidence given by deflections of the vertical the conclusion has been drawn that in the United States the average departure from complete compensation corresponds to excesses or deficiencies of mass represented by a stratum only 250 feet thick on an average. The gravity determinations indicate this average to be 630 feet instead of 250 feet. In neither case is the average value determined or defined with a high grade of accuracy. The difference between the two determinations of the average value is therefore of little importance. The determination given by the gravity observations is probably the more reliable of the two. Each determination is significant mainly as showing that the isostatic compensation is nearly perfect. The average elevation in the United States above mean sea level is about 2,500 feet. Therefore, from gravity observations alone the compensation may be considered to be about 75 per cent complete on an average for stations in the United States. 8 This conclusion implies a somewhat greater rigidity to the crust than that which is stated for the deflections of the vertical, but in regard to the maximum horizontal extent which a topographic feature may have and still escape compensation the authors still express the belief that the limit is between one square mile and one square degree. "It appears from the inconclusive evidence fur- nished by the gravity observations that the radius of this area is probably less than 18.8 kilometers." 3 This review of the work of Hay ford on deflections of the vertical, and of Hayford and Bowie on the gravity anomalies has been given in order that the methods of the work, its bearings on the strength of the crust, and the conclusions which were reached, may be per- ceived. It is seen that a large difference of view as to the strength of the crust exists between this interpretation from the geodetic evidence and that from the geologic. In the following pages will be 1 Hayford and Bowie, 1912, pp. 108-12; Bowie, 1912, p. 22. 2 Bowie, 1912, pp. 22, 23. 3 Hayford and Bowie, 1912, p. 102. 156 JOSEPH BARRELL given a discussion which it is thought brings out certain errors in the conclusions drawn from the geodetic work and thereby reconciles the two lines of evidence. REGIONAL VERSUS LOCAL DISTRIBUTION OF COMPENSATION Conclusions on this topic by Hay ford and Bowie. Under this heading Hayford and Bowie state: The question whether each topographic feature is completely compensated for by a defect or excess of mass exactly equal in amount directly under it, or whether the topographic feature is compensated for by a defect or excess of mass distributed through a more extensive portion of the earth's crust than that which lies directly beneath it, is a very important one. The theory of local compensation postulates that the defect or excess of mass under any topographic feature is uniformly distributed in a column extending from the topographic feature to a depth of 113.7 kilometers below sea level. The theory of regional compensation postulates, on the other hand, that the individual topographic features are not compensated for locally, but that compensation does exist for regions of considerable area considered as a whole. In order to have local compensation there must be a lower effective rigidity in the earth's crust than under the theory of regional compensation only. In the latter case there must be sufficient rigidity in the earth's crust to support individual features, such as Pikes Peak, for instance, but not rigidity enough to support the topography covering large areas. Certain computations have been made to ascertain which is more nearly correct, the assumption of local compensation or the assumption of regional compensation only. In making such computations it is necessary to adopt limits for the areas within which compensation is to be considered complete. A reconnoissance showed that the distant topography and compensation need not be considered, for their effect would be practically the same for both kinds of distribution. As a result of this reconnoissance it was decided to make the test for three areas, the first extending from the station to the outer limit of zone K (18. 8 kilometers), the second from the station to the outer limit of zone M (58.8 kilometers), and the third, to the outer limit of zone O (166.7 kilometers) .* The average anomaly with regard to sign by the new method with local compensation, and the average anomaly by each of the three new-method reductions with regional distribution of the compensation are respectively 0.002, o.ooi, o.ooi, and 0.002 dyne. The means without regard to sign for the different distributions of the compensation are respectively, 0.020, 0.019, 0.019, and 0.020 dyne. These mean anomalies give only negative evidence. 2 1 Hayford and Bowie, 1912, p. 98. 2 Bowie. 1912, p. 22. THE STRENGTH OF THE EARTH'S CRUST 157 The problem may be tested in another way. If local compensation be true, an unusually high mountain is underlain by unusually light matter and the intensity of gravity at a station on its top is less than if the mountain was supported by regional compensation and had matter of the mean regional density below it. If the station is much below the average level of a mountainous region, local compensation implies, on the contrary, denser matter beneath and a higher value of gravity than would be given by regional compensation. These relations result in the following principle : For stations above the mean level, if local compensation be nearer the truth the hypothesis of regional compensation would tend to show its error by large negative anomalies. If regional compensation be nearer the truth, the hypothesis of local compensa- tion would tend to show its error by giving large positive anomalies. For stations below the mean level the reverse would be true. But for any individual station other departures from the truth of that hypothesis of isostasy which gives the basis for the calculations may have greater influences and give larger anomalies than the question to be tested. Following this principle it is stated: There are 22 stations in the United States in mountainous regions and below the general level and the means, with regard to sign, of the anomalies by the four methods of distribution are o.ooo, +0.001, +0.003, an d +0.005 dyne, while the means without regard to signs are respectively 0.017, 0.017, o .018, and o . 019 dyne. For the 18 stations in the United States in mountain- ous regions and above the general level the means, with regard to sign, of the anomalies by the several methods of distribution of the compensation are +0.003, +0-003, o.ooo, and o.io dyne. The means, without regard to sign, are respectively 0.018, 0.018, 0.017, and 0.020 dyne. The mean, with regard to sign, of the anomalies for the stations at each of the two mountain groups, indicates that the theory of regional distribution of compensation to the outer limit of zone O, 166.7 kilometers is far from the truth. So far as may be judged from the other average anomalies no one method seems to have any decided advantage (see pp. 98-102 of Special Publication No. lo). 1 Review and analysis of the evidence. -The present writer does not see in these computations any support for the hypothesis of local 1 Bowie, 1912, p. 22. 158 JOSEPH BARRELL compensation of the topography to between limits of one square mile and one square degree with the added suggestion of a radius less than 1 8. 8 km., which has been advanced on other pages by the authors. 1 These figures merely show that, to the outer limit of zone M, radius 58.8 km., and probably to outer limit of zone N, radius 99 km., one method is as good as another for purposes of computation, which is not true in nature. The errors introduced by observation and computation, the errors introduced by the lack of recognition necessary in the preliminary hypothesis regarding the irregularities in the depth and distribution of compensation -these produce effects which overshadow the small systematic differences due to the hypotheses of local versus regional compensation. For the outer limit of zone 0, radius of 166.7 km., a real distinction does, however, begin to appear in the data for the two groups of mountain stations. It is, however, very small and based upon a rather too limited number of stations to give quantitative reliability to the mean. Furthermore, as discussed in detail under a later heading, there is quite possibly a real difference between the limits of regional compensation and depth of compensation in the moun- tain regions of the West compared to other parts of the continent. Evidence drawn from the Cordillera cannot, therefore, be applied safely to the other portions of the United States. Let the assumption be introduced that the limits of regional compensation are variable, ranging from 100 to 500 km. in radius. Such variable limits may well exist because of several factors; first* because of a real variability in the strength of the crust; second, because the greater vertical stresses could be carried only by smaller areas. In regions of mountainous relief due to folding, or of high anomalies due to great irregularities of density, the mean size of unit areas should therefore be less. On the whole the anomalies as well as the relief appear to be somewhat greater over the western United States. Third, in regions of recent block faulting or warping the stresses have presumably been lessened from what they were immediately before the movement. Such diminution of strain could take place by the breaking-up of a large unit area of crust into smaller units with differential movement among them, as 1 Hayford and Bowie, 1912, p. 102. THE STRENGTH OF THE EARTH'S CRUST 159 well as by vertical movement of the whole area to a level best satisfying the stress. The western United States is known to be such a region, which in the late Tertiary and up to the present has been markedly affected by block faulting and differential vertical movements. Suppose, then, that the mean radius of regional compensation in a mountainous region is 300 km. but that unit areas exist ranging in radius from 100 to 500 km. Of mountain stations located at random, a fraction of the total number would be situated within or near areas where regional compensation did not extend to 166 . 7 km. Let the stations be divided into one group consisting of those below the mean regional elevation and another group above the mean regional elevation. Let the anomalies be computed successively according to hypotheses of regional compensation to successive limits and the mean of the group for each limit be taken. This is the test applied by Hayford and Bowie. It has been seen that for radii of 18.8 and 58.8 km. the results are indeterminate. For a larger radius the group anomaly might be expected to show an increase as soon as the assumed radius exceeded the actual radii of a part of the areas. Consequently, if the hypothesis be true that the areas of regional compensation are variable in size, the mean anomalies of the two groups of 22 and 18 stations, found with regard to sign to be +0.005 an d o.oio respectively for radius of 166.7 km., do not show that regional compensation on the whole does not exist to those limits. It may indicate only that some areas are less than that radius. The mean radius of regional compensation may be 166.7 km. or possibly even larger. Other tests must therefore be sought which will give a more conclusive answer. Further, it is to be noted that the mean anomalies with regard to sign for the hypothesis of regional compensation to radius of 166.7 km., although somewhat greater than for the other hypoth- eses, are yet of the same order of magnitude; and in all cases are but a fraction of the mean anomaly without regard to sign. Appar- ently, then, the assumption of regional compensation to 166.7 km. introduces a smaller error than the assumption of uniform and com- plete compensation with an average specific gravity of 2.67 to a constant depth of 114 km. 160 JOSEPH BARRELL The test by adjacent stations at different elevations. -There is, however, another way of using the data given for stations situated well above and below the mean elevation of mountainous regions. If a pair of stations be taken close together, one far above the mean elevation, the other far below, they will presumably, because of their juxtaposition, be affected in much the same way by the errors incident to the hypothesis of uniform compensation through a depth of 114 km., with complete compensation at that depth. In order that good results may be obtained, however, the specific gravity of the local rocks should be carefully determined in order to have a correction for the mass between the stations. The parts of the anomalies due to the irregularities and incompleteness of compensa- tion will ordinarily have the same sign and be of nearly the same value at the adjacent stations. This is indicated by the contour lines of Fig. 5, which show 'that in the same region the anomalies are of sufficiently regular gradation in magnitude to make the drawing of contour lines possible. The parts of the anomalies at the high and low stations due to errors in the hypothesis of local or regional compensation will, however, be of opposite sign. If, then, the algebraic difference of the anomalies for such a pair of stations be computed for successive hypotheses of broader regional com- pensation, the part of the anomalies due to vertical imperfection of the hypothesis will be largely eliminated. The algebraic difference measures the horizontal imperfection of the hypothesis. That hypothesis is favored whose assumed radius of regional compensa- tion gives a minimum value to this algebraic difference. This test may be made by combining data given on p. ico, Hayford and Bowie, with p. 15, Bowie; although, because of incompleteness of the tables, this combination gives the data for only a few of the properly situated mountain stations. The best couple of stations for the application of this test consist of 42, Colorado Springs, and 43 Pikes Peak. Somewhat more distant stations -44, Denver, and 45, Gunnison may also be added to the group. The tabulation is shown on p. 161 (Table IV). It is seen that for three of the four Colorado stations the absolute value of the anomaly is least with regional compensation to 166.7 km. For the fourth station it remains practically constant for THE STRENGTH OF THE EARTH'S CRUST 161 all the cases. The anomalies were not computed for greater radii. The more convincing argument, however, for regional compensation to at least 166 . 7 km. radius in the vicinity of Pikes Peak is the fact that the algebraic difference of the anomalies between the top and bottom of the mountain, stations 43 and 42, is less than one-half for regional compensation to 166. 7 km. radius than for the correspond- ing value given by the hypothesis of local compensation. The decrease in the difference is furthermore progressive with each TABLE IV NUMBER AND NAME OF STATION ELEVATION OF STATION IN METERS DISTANCE FROM MEAN ELEVATION IN METERS WITHIN 100 MILES ANOMALY WITH REGIONAL COMPENSATION WITHIN OUTER LIMIT OF Local Com- pensation. Radius o.o Km. Zone K, Radius 18.8 Km. ZoneM, Radius 58.8 Km. Zone O, Radius 166.7 Km. COLORADO 42 . Colorado Springs 1,841 4,293 1,638 2,340 420 + 2,035 -574 -380 -458 0.009 + -019 .018 + .018 - .009 0.009 + .Oil .Ol6 + .O2I .004 o.oio + .006 - .009 + .026 + .007 O.OIO + .002 .001 + .016 + .005 43. Pikes Peak 44. Denver 45. Gunnison Mean of 42, 44, and 4C . Algebraic Difference 4342 + .028 + .028 + .020 + .015 + .016 .001 + .012 - -003 43 (mean of 42, 44, 45) ARIZONA 68. Yavapai 69. Grand Canyon. . 2,179 849 + 512 824 .001 .OI2 .001 .on .001 .Oil - .009 .021 Algebraic difference 68-60 +O.OII +O.OIO +O.OIO +0.012 assumed widening of the zone. The result of adding the more distant stations, 44 and 45, favors regional compensation more markedly but is indeterminate between M and O. It would seem, then, that the front range of the Rocky Mountains in Colorado is upheld above the surrounding plains and parks by virtue of the rigidity of the earth. The two stations in Arizona at 68 and 69 are well situated also to test the question of local versus regional compensation, but the 162 JOSEPH BARRELL difference in the anomalies in this case is so nearly constant as to give an indeterminate answer. In the absence of more detailed statements by Hay ford and Bowie the reason why the anomaly at the Grand Canyon station 69 reaches a larger negative value for regional compensation to 166.7 km. than for more limited com- pensation is not evident. The usual rule is that the progressive change in the anomaly for stations below the regional level for successive assumptions of wider regional compensation is by increments with a plus sign. Here, on the contrary, the change in the limits from zone M to zone involves a minus increment of o.oio in the anomaly. The cause of this reversal of sign, which the writer does not understand, seems in this case to be the cause of the indeterminate result. Another line of evidence as to the effective limits over which the rigidity of the earth may extend is derived from a study of the grouping of the deflections of the vertical shown in illustrations 2, 3, 5, 6, Hayford, 1909, and the lines of equal anomaly for the new method of reduction, illustration No. 2, Bowie, 1912, the latter giving the basis for Fig. 5 of this article. The test by areas of grouped residuals. Illustration No. 5, Hayford, 1909, shows the grouping of the residuals of solution H for the north and south components of the deflections. An area with a plus sign corresponds to an excess of density to the south, or deficiency to the north. An area with a minus sign corresponds to a deficiency of density to the south, or excess to the north. A north-south chain of stations is therefore best for ascertaining the limits of the areas of north-south deflection of like sign. Such a belt extends across the United States between long. 97 and 98, showing 9 areas covering 1,620 miles. The mean intercept is therefore 180 miles. This mean intercept must be somewhat less than the mean diameter. Illustration No. 6, Hayford, 1909, shows the grouping of the residuals of solution H for the east and west components of the deflections. An area with a plus sign corresponds to an excess of density to the east, or deficiency to the west. An area with a minus sign corresponds to a deficiency of density to the east, or excess to the west. An east-west chain of stations is therefore best THE STRENGTH OF THE EARTH'S CRUST 163 for ascertaining the limits of the areas of like sign. Such a belt extends across the United States between lat. 38 and 39. The following adjustments in groups seem, however, fair to make, considering the lack of exact accuracy in any one station. At Cincinnati is a station showing small residuals opposite in sign to the stations on each side. If this is overlooked, three small groups become one of average size. In central Kansas a small minus area depending on a single observation may be likewise omitted. In western Colorado several small areas depending each upon two observations had their number diminished by one. The same was done in California. This gave 14 areas extending over 2,580 miles, a mean individual intercept of 184 miles. If 16 areas be taken, a mean value is derived of 161 miles. More weight, it is thought, is to be attached to the determination of 184 miles, and this is supported by the 180 miles shown by the north-south chain of stations. The areas of like sign are between centers of excess and defect of mass. They are not, therefore, coincident with the areas of excess and defect, but in discussing the average size of areas, the one may be used as a measure of the other. It may be concluded, therefore, that the deflections of the verti- cal show areas with departures from isostatic equilibrium in one direction and these areas average about 180 miles, 290 km., in mean intercept. The mean diameters of the areas of like sign are pre- sumably somewhat greater. This would make the mean radius of areas of regional compensation, as indicated by similarity of sign among residuals, at least 166.7 ^ m - the radius of the outer limit of zone O used in the discussion of the gravity anomalies. If we turn now to the anomalies shown by the determinations of gravity, Fig. 5, adapted from Bowie, shows their segregation into areas of like sign. The mean value without regard to sign for all stations excluding Seattle is 0.018 dyne per gram. Including the two Seattle stations the mean is 0.020 dyne. Between the con- tours for 0.020 and +0.020 lie tracts where the anomalies are within the mean limits. The areas of exceptionally large anomalies are above those limits. It is only these which form on this illus- tration well-defined inclosed areas, but even these are far from 164 JOSEPH BARRELL regular in outline. The areas showing positive anomalies of more than 0.020 dyne were estimated roughly to average 130 by 240 miles across, a mean diameter of 175 miles. The areas showing negative anomalies of more than 0.020 dyne were found to average roughly about 190 by 250 miles, a mean diameter of 220 miles. The long narrow connections were neglected in making this estimate. Unit areas of more than mean anomaly may therefore be taken to average about 200 miles or 320 km. in diameter. The mean radius is therefore approximately that of the outer limits of zone O, 166.7 km- The figures, although they correspond fairly closely to those derived from the deflections of the vertical, cannot in reality be very well compared, since these are areas selected because the anomaly rises above a certain magnitude; the others represent, on the con- trary, a succession of contiguous areas between centers of excess and defect in mass without reference to magnitude. Apparently some influence blurs out the limitations of areas of. small gravity anomaly. This will be discussed in a later part. Now assume for the moment that isostatic compensation is uni- form to the bottom of the zone, as postulated by the hypothesis; that is, that the residuals and anomalies are due to excesses or defects of mass which are uniformly distributed. Then, over any one area of excess or deficiency of mass, the deflections around it and anomalies within it signify a departure from compensation in one direction. This is a regional departure. If the strength of the crust was so small that it was able to support notable departures from compensation over areas of only one square degree or less, then these large unit areas could not exist. A vertical warping up or down would immediately take place until the broad region as a whole lay so close to complete compensation that its surface irregularities became subdivided into subordinate positive and negative areas of the limiting size. The sum of the excesses and defects of mass would approach zero in broad areas containing many unit departures. It would seem, therefore, that the geodetic results shown in Fig. 5, instead of indicating local compensation to limits of less than one square degree, show on the contrary a ready THE STRENGTH OF THE EARTH'S CRUST 165 capacity of the crust under the United States to carry over areas of from 5 to 10 or 15 square degrees, and exceptionally over even larger areas, departures from equilibrium greater than the mean. This agrees in order of areal magnitude with the Nile and Niger deltas. However, the influence of irregularity in the distribution of com- pensation with depth, and the magnitude of stress per unit area remain to be investigated. [To be continued] THE STRENGTH OF THE EARTH'S CRUST JOSEPH BARRELL New Haven, Connecticut PART III. INFLUENCE OF VARIABLE RATE OF ISOSTATIC COMPENSATION INTRODUCTION AND SUMMARY 209 THE SPECIFIC GRAVITY OF ROCKS 211 INTERPRETATION OF ANOMALIES IN TERMS OF MASS AND DEPTH . 216 RELATIONS OF ANOMALIES TO EXPOSED GEOLOGIC FORMATIONS . 221 LARGE OUTSTANDING ANOMALIES NOT RELATED TO GEOLOGY OR TOPOGRAPHY 227 CRITERIA FOR SEPARATING VERTICALLY IRREGULAR COMPENSATION FROM REGIONALLY INCOMPLETE COMPENSATION . . . . 228 GRAVITY ANOMALIES CAUSED LARGELY BY REGIONAL DEPARTURES FROM ISOSTASY 234 INTRODUCTION AND SUMMARY The work of Hayford on the deflections of the vertical, and of Hayford and Bowie on the anomalies of gravity, has supplied the geodetic data from which future work must start. As an initial basis to guide their work, it was desirable to assume the hypothesis that isostatic compensation was complete for each topographic irregularity, giving local compensation, and that it was uniformly distributed to a constant depth. The actual results may then be compared to this ideal of local, uniform, and complete isostasy and the degree of departures noted, as given by residuals and anomalies. In Part II the subject of the regional distribution of compensa- tion was examined and the conclusion was reached that the crust was sufficiently rigid to bear such mountains as Pikes Peak without requiring special compensation below. In general it is thought compensation in mountain regions extends to more than 200 km. and in some regions to more than 400 km. In this part are considered the effects of variations in the vertical distribution of 209 210 JOSEPH BARRELL compensation and the degree to which such variability may give rise to anomalies and residuals without signifying incompleteness of compensation in the column as a whole or regional departures from isostasy. In order to show the limits of variation in density which are to be expected, the specific gravity of rocks is first considered. Figures are computed for the mean specific gravity of igneous rocks and the three types of sediments. It is shown that the range of varia- tion is an important factor. Under the subject of th- relations between mass and the distance of mass upon anomahV , the effects are computed of unit masses at various depths ai.u extorting various distances. 1 This lays the basis for considering the Influence of the specific gravity of the surface geologic formations upon th p> difference between the mean anomalies for stations on pre-Cambrian and those on Cenozoic areas. It is found that the greater density of the older rocks accounts for a part and another part is accounted for by their resistance to erosion. This still leaves, however, large outstanding regional variations not related to surface geology or topography and requiring some other explanation. To that end criteria are discussed for the recognition and separation of the effects of mere variable vertical distribution of compensation on the one hand, from partial regional absence of isostasy on the other. It is concluded from the application of these criteria that the anomalies are in large part caused by real regional departures from isostasy extending over broad areas. The results are thus 1 A paper by Gilbert has recently appeared entitled "Interpretation of Anomalies of Gravity" (Part C, Professional Paper 85, U.S. Geological Survey, 1913). This did not reach the present writer until after Parts III and IV of this article were in galley proof, so that his results cannot be as fully interwoven into the discussion as would otherwise have been the case. On pp. 30, 31, Gilbert considers the interpre- tation of anomalies on the assumption of vertical heterogeneity of the crust and shows clearly that moderate variations of density in a vertical direction could explain them. From this he infers that the anomalies may be due in part to such irregularities. This is the topic which is treated in Part III of the present article under the title "Inter- pretation of Anomalies in Terms of Mass and Depth." The method of reasoning is somewhat different, but although the conclusion reached is the same, the calculations given here are intended to bring out in addition the limitations of area and mass within which that principle applies. It is concluded as a result of the following examination of the evidence that although vertical variations of density are a real cause they are not the major cause of anomalies. THE STRENGTH OF THE EARTH'S CRUST 211 confirmatory of those reached in Parts I and II. In addition, how- ever, it appears that there is a regional departure from isostasy of two orders of magnitude. Loads under the mean value, giving anomalies below 0.018 to 0.020 dyne and estimated to be equiva- lent to about 750 feet of rock, can be carried over regions of irregu- lar boundaries ranging up to from 1,000 to 2,000 km. across. Over such a broad region the anomalies are of one sign except for some smaller well-defined sub-areas of high anomaly within them which may or may not have the same sign. These smaller areas give a higher order of stress magnitude and are of more restricted dimen- sions, being measured in hundreds of kilometers. They range in magnitude of anomaly to several times the value of the mean and the equivalent radii of their areas probably average 100 to 200 km. The deflection residuals show by the limits of the areas of like sign that the regional variations of gravity anomalies of this areal magnitude extend over the whole country, but where the amounts of the local anomalies are less in value than the mean they are largely masked on the contour map of gravity anomalies (Fig. 5), because of their superposition upon the broader areas. Presumably a multiplication of the gravity stations would bring them to light as undulations in the contours which show the regional departures. A final conclusion on the subject of the variable vertical distri- bution of mass must, however, be deferred until consideration has been given to a hypothesis advanced by Gilbert in his recent paper, that heterogeneities of mass below the zone of compensation may be the cause in major or minor part of the apparent departures from isostasy. This is a subject too large to be considered in this third part of the present article, but it is planned to investigate it in Part V by a method of graphic analysis devised for determining the depth of excesses or deficiencies of mass. THE SPECIFIC GRAVITY OF ROCKS For a knowledge of the variations of density likely to occur in rocks it is important to know the range in specific gravities shown by the common rock types. The following figures, except those for shale, are taken from Pirsson's Rocks and Rock Minerals: 212 JOSEPH BARRELL TABLE V Rock Specific Gravity Granite 2 . 63-2 . 75 Syenite 2.6 -2.8 Diorite 2.8 -3.1 Dolerite 3.0-3.3 Limestone 2.6-2.8 Sandstone 2.5-2.7 Shale 2.4 -2.8 Slate About 2 . 8 [The specific gravity of shale, although the most abundant of sedimentary rocks, is not given in any of the manuals of geology, but Professor Hobbs, who has read much of this manuscript and to whom the writer is indebted for a number of suggestions, has called attention to the above figure as given by Trautwine. In general, Trautwine and Kent give a somewhat greater range in specific gravities and they average a little lower than those here given. The figures from Pirsson, however, probably express more closely the relation of the petrologic type and the more compact states of rocks to their density. They are, therefore, thought to be better representative of the lithosphere.] These figures show that notable departures may occur from the mean density of the outer crust and suggest furthermore that 2.67, the mean density used by Hayford, is lower than the actual mean. A more thorough analysis of the subject is therefore needed. The abyssal igneous rocks and metamorphic rocks are almost without pore space. The sedimentary rocks, on the other hand, possess abundant pore space in their unconsolidated states, very little in their compact states. The latter is the usual mode of occurrence in the older geological formations. The density is therefore a function of both mineral composition and porosity. The chemical compositions of the several rock types and also of the average sediment and the average igneous rock are well known. The mineral compositions are less well known but may be computed with a fair degree of accuracy; the densities, on the contrary, are least commonly reported and the mean densities of the rock types cannot in consequence be closely determined by averaging numerous determinations, as is done for the chemical compositions. It seems desirable, therefore, to compute the densities of the rock types from the chemical and mineral compositions, combining this with the densities of the individual minerals, making a separate correc- THE STRENGTH OF THE EARTH'S CRUST 213 tion for the porosity factor. The data, assembled from various sources 1 and subjected to computation, give the following results: TABLE VI COMPOSITION OF AVERAGE IGNEOUS ROCK Mineral Percentage Quartz . 12.0 Feldspars Orthoclase molecule 22.0 Albite molecule 29.5 Anorthite molecule 8.0 Hornblende and pyroxene 16. 8 Mica 3.8 Accessory minerals 7.9 100. o TABLE VII COMPOSITION OF AVERAGE SEDIMENTS Mineral Shale Sandstone Limestone Quartz 22.3* 66.8* 2.O Feldspars Orthoclase 18 o 7 o ? Labradorite Clay 12. 2< of 4-5 6 6f O. I 2 Ol Limonite S 6 i 8 o 6 Calcite 1 {cc .0 Dolomite/ 5-7 ii. i 33 35 -O Other minerals ii .4 2. 2 c.o IOO.O IOO.O IOO.O * The total percentage of free silica. t Probably sericite in part; in that case the feldspar figure becomes lower. J Two per cent clay takes o . 79 of AUOj. Thb requires that most of alkalies form non-aluminous hydrous silicates or that 0.81 AhOj as given by Clarke is too low. It is thought that the densities without porosity are figures of some value for geodetic computations. The chief error in making the final estimates is in connection with the lack of accurate knowl- edge regarding the pore space of those sedimentary rocks not used 1 For data on the mean chemical and mineral composition of rocks see F. W. Clarke, "Data of Geochemistry," Bull. 491, U.S. Geol. Surv., 1911, pp. 30, 31. For specific gravities of minerals see Pirsson, Rocks and Rock Minerals, 1908, p. 31; also Dana, Mineralogy. For a discussion of pore space see Fuller, "Total Amount of Free Water in the Earth's Crust," Water Supply Paper No. 160, U.S. Geol. Surv., 1906, pp. 59-72. 214 JOSEPH BARRELL as building stones, but this affects appreciably the density of only a superficial layer and chiefly of the youngest deposits. The ratio of shale, sandstone, and limestone in the average sediment in percentage is, according to Mead, 1 shale 80, sandstone n, limestone 9. The ratio of average porosities in percentage is, according to Fuller, 2 crystalline rocks 0.2, shales 4, sandstones 15, limestones 5. The figure given by Fuller for shale rests upon a single determination of 7.8 per cent by Delesse, and is averaged in by Fuller with slate. Eight per cent porosity will here be assumed as probably a better estimate. This gives the porosity of the average sedimentary rock as 8 . 5 per cent. The pore space may be taken, following Fuller's estimate, as half filled with water. From these data the specific gravities are computed to be as follows: TABLE VIII SPECIFIC GRAVITIES COMPUTED FROM MINERAL COMPOSITIONS Rock No Pore Space Allowed Pore Space Half Filled with Water Average igneous rock. . Shale Sandstone 2.80 2.6 9 2.67 2.80* 2-51 2.35 Limestone Average sedimentary rock 2. 7 6 2.70 2.64 2.50 *The same figure as used by Chamberlin and Salisbury, Geology, I (1904), 538; also by Pirsson, Rocks and Rock Minerals; also by G. H. Darwin as the density of the outer crust. Where Cenozoic deposits occur in thickness, they are consider- ably compacted except at the surface, but still the mean specific gravity, owing to the abnormal pore space and deficiency in lime- stones, is doubtless less than 2.50; 2.45 may be taken. It is probable, on the other hand, that the Paleozoic rocks on the whole have somewhat less pore space than this average, especially as the porosity figure for sandstone rests mainly upon determinations for browns tone, a rather porous type; 2.55 may then be taken as the average for Mesozoic and Paleozoic formations. The pre-Cambrian '"Redistribution of the Elements in the Formation of Sedimentary Rocks," Jour. Geol., XV (1907), 238-56. 3 Loc. tit. THE STRENGTH OF THE EARTH'S CRUST 215 rocks contain both igneous and sedimentary formations, but the considerable iron ore and metamorphic nature would bring the specific gravity of the sediments somewhat above the average of 2 . 70 for non-porous sediments. Broad areas of pre-Cambrian probably range therefore between 2 . 75 and 3 .00 in specific gravity. More limited areas, because of a predominance of granite and quartzite, may range as low as 2 . 70. About 2 . 67, however, would be a minimum. As these are merely averages it is better in basing calculations upon them to assume a certain range in density for each figure and to obtain thus a knowledge of the influence of reasonable variations upon the results. The data may then be tabulated as follows: TABLE IX ESTIMATED MEAN SPECIFIC GRAVITIES OF GEOLOGIC FORMATIONS Pre-Cambrian 2 . 75-2 . 80 Paleozoic and Mesozoic 2 . 50-2 . 60 Cenozoic 2 . 40-2 . 50 The range in these specific gravities shows the necessity of con- sidering them in all refined calculations on the anomalies of gravity. In place, however, of using a mean density figure for all stations on formations of a certain geologic age, it would be of much more value to have measurements of the actual surface densities occurring in each area; also estimates by geologists, based on geologic structure and these surface measurements, of the densities extend- ing to the base of the sedimentary rocks of each locality. It seems probable from the mean density of 2 . 80 obtained for igneous rocks that the density of 2.67 used by geodesists for the mean density of the zone of compensation is too low. If any variation from the average composition takes place with depth within the limits of 76 miles, it is likely to be a variation toward more basic and heavier rocks. Assuming, however, an average uniformity of chemical composition, the opposing effects of tem- perature and pressure remain to be considered. Using the coeffi- cient of expansion of the average igneous rock computed by W. H. Emmons, 1 0.000,019,9 for iC., and a temperature gradient of 1 Chamberlin and Salisbury, Geology, I (1904), 547. 2i6 JOSEPH BARRELL i F. for 60 ft. in depth, gives an aggregate expansion of 3 . 6 per cent to the outer 76 miles. Using 6,500,000 as the modulus of cubic compressibility of the average rock in pound-inch units 1 gives a total compression of 3 . 7 per cent to the outer 76 miles due to pressure; that is, the volume effects of heat and pressure prac- tically offset each other within the zone of isostatic compensation. Therefore 2 . 80 appears to be the lowest mean figure which should be taken. The use of 2 . 67 as a mean figure requires for isostatic equilibrium a density of but 2.60 extending to a depth of 76 miles under land 3 km. high, a figure lower than the specific gravity of granite. INTERPRETATION OF ANOMALIES IN TERMS OF MASS AND DEPTH Suppose that the zone of isostatic compensation is not ol uniform density under any one station, but contains masses of variable density irregularly distributed. Let these masses be of considerable thickness and area as compared to the depth of the zone of compensation. Suppose that the topography is so adjusted to the aggregate density that the pressures are everywhere equal at the bottom of the zone of compensation. Abnormally light masses would then have to be balanced by abnormally heavy masses in the same column. There would still be deflections of the vertical and anomalies of gravity because gravitation varies inversely with the square of the distance, the upper and adjacent masses of abnormal density affecting the station more than those more distant ones of opposite abnormality lying vertically below the upper. The residuals from deflection and gravity measure- ments would under such an arrangement measure strains within the outer crust but not upon its bottom. The strains, if produced by abnormalities in the upper parts of the crust, would further be proportionately smaller and yet give rise to residuals of a certain magnitude than if produced by abnormalities in the lower parts of the crust. This aspect of the problem must be investigated before any final significance regarding the strength of the crust can be attached to the grouping of residuals discussed under the 1 F. D. Adams and E. G. Coker, An Investigation into the Elastic Constants of Rocks, More Especially with Reference to Cubic Compressibility, 1906, p. 67. THE STRENGTH OF THE EARTH'S CRUST 217 last part of Part II. It leads to a consideration of the relations between mass, distance, and anomaly. Under the title of " Interpretation of Anomalies in Terms of Masses "* Hayford and Bowie show that the excesses and deficiencies of mass to a great distance have an effect upon the gravity anomalies and that therefore the guarded expression "net effective excess (or deficiency) of mass" is necessary for correctness. They give the following tabulation to show the influence of uncompensated masses in the crust in giving gravity anomalies when the gravity is computed on the assumption of isostasy: 2 TABLE X Each tabular value is the vertical attraction in dynes produced at a station by a mass equivalent to a stratum 100 ft. thick, of density 2 .67, and of the horizontal extent indicated in the left-hand argument, if that mass is uniformly distributed from the level of the station down to the depth indicated in the top argument and from the station in all directions horizontally to the distance indicated in the left-hand argument. DEPTH RADIUS OF MASS i.ooo Ft. 5,000 Ft. 10,000 Ft. 15,000 Ft. 113.7 Km. i,28om. (the outer radius of zone E) o 0029 0.0018 O.OOII 0.0008 o.oooo 166.7 km. (the outer radius of zone O) 0.0037 o . 0034 o . 0034 0.0034 0.0024 i, 190 km. (or io4o', the outer radius of zone 10) o 0040 o 0037 o 0037 o 0037 o 0034. On p. in it is concluded by these authors that the best working hypothesis is to take each o . 0030 dyne of anomaly as due to an excess (or deficiency) of mass equiva- lent to a stratum 100 ft. thick. This working hypothesis is equivalent, as may be seen by inspection of the table just given, either to the assumption that the excess (or deficiency) of mass is uniformly distributed to a depth of 113. 7 kilometers and extends to a distance of more than 166. 7 kilometers and less than 1,190 kilometers from the station, or that it extends to a distance of 166. 7 kilometers from the station and is distributed to an effective mean depth of more than 1 5,000 feet and less than 113.7 kilometers, or the working hypothe- sis may be considered to be a combination of these two assumptions. The mean anomaly of 0.018 dyne, interpreted on this basis of 0.030 dyne being taken as equivalent to 100 ft. of mass, gives a Hayford and Bowie, p. 108. 'Ibid., 1912, p. 109. 2i8 JOSEPH BARRELL mean departure from isostatic compensation amounting to 600 ft.; given more exactly by Bowie as 630 ft. It is seen from the quoted statement that the authors accept, first, as one alternative a very widespread regional net excess (or deficiency) of mass uniformly distributed in depth; or, second, a somewhat broad regional distribution but confined to the outer part of the zone of compensation; or, third, some combination of the two assumptions. The first assumption would throw a real strain upon the bottom of the zone of compensation and signifies regional compensation to limits very far beyond those stated elsewhere by the authors. It is therefore inconsistent from that standpoint, but gives a smaller vertical load and consequently a smaller vertical departure from the level giving isostatic equilibrium than would a more limited area. If, for example, it be assumed that the radius of the zone limiting regional compensation is 58.8km., which is about the maximum limit for regional compensation which Hayford allows elsewhere; then it may be computed that for uniform distribution of the excess (or deficiency) of mass to a depth of 114 km., a mass equivalent to 100 ft. of density 2.67 corresponds to an anomaly of but 0.0013 dyne instead of 0.0030. This would, for a mean anomaly of 0.018, signify an average departure over the United States of 1,380 ft. from the level giving isostatic equilibrium, instead of 600 ft. The second assumption, that the excess (or deficiency) is in the outer part of the crust, gives also a much higher anomaly for a unit mass than would an equally permissible assumption that the excesses or deficiencies occurred at various levels and on the average were at a depth of one- third or one-half of the zone of compensation. The relationship of anomalies to geologic formations, to be dis- cussed later, shows certain variations in density in the outer crust, but the greater parts of the anomalies are not due to this cause. From the previous discussion on the limits of regional compensa- tion it would seem that, on the assumption that the excesses or deficiencies of mass are on the whole uniformly distributed, 0.0024 would be an appropriate figure to use as the mean anomaly for unit thickness of mass. The highest anomalies, however, are THE STRENGTH OF THE EARTH'S CRUST 219 probably better interpreted by o . 0030 as a divisor, since as a class they must be assumed as due to excesses or deficiencies of mass which are both near and large. This does not mean, however, that the larger masses are not assumed as scattered uniformly, according to the laws of chance, through the crust. It is seen, then, that Hayford and Bowie have favored those interpretations which gave a large anomaly per unit mass and have ascribed the total anomaly as on the average to be interpreted on this basis, obtaining there- by a smaller figure as the mean departure in feet from the level for perfect compensation. They have not discussed, furthermore, in the text the influence of deeper-seated variations of density, which might give considerable residuals, nor the possibility that departures from the mean density in opposite directions might balance each other so as to give equal pressures at the bottom of the zone of compensation. The latter case will not seem improbable to the geologist. The great batholiths of the Archean appear to make a universal floor in the crust. They range in composition from granites to gabbros and have come to rest at various levels. Light and heavy masses may well be irregularly distributed in the same vertical cylinder. If at the time of origin the whole were too heavy, a tendency would have arisen for the column to sink until equilibrium was attained. If the whole, on the con- trary, were too light, the column would have tended to rise until a heavier base balanced the lighter mass above. Thus, if irregular distribution of density arose as the result of vertical igneous intrusion, the whole region would tend to seek that level where the irregularities would balance. In order to gain quantitative ideas as to this possibility of partly explaining the anomalies, the writer has made calculations on the following assumptions. A station is situated upon the axis of a vertical cylinder extending from the station to a depth of 1 14 km. The radius is taken successively at -58. 8, 166.7, an d 1,190 km. Let such a cylinder be divided into five equal cylinders by horizontal planes. Let each of the five be equivalent in mass to a cylinder of the same radius but only 100 ft. in depth and of density 2 . 67 ; in other words, the unit mass as used by Hayford and Bowie. What will be the attraction in dynes per gram pro- 22O JOSEPH BARRELL duced at the station by each cylinder respectively? 1 The results are as follows: TABLE XI VERTICAL ATTRACTION IN DYNES ON ONE GRAM AT STATION BY CYLINDER 22.8 KM. THICK, DENSITY 0.00357, EQUIVALENT IN MASS TO THICKNESS OF 100 FT. AT DENSITY 2.67 No. of Cylinder Depth in Km. from Station to Top of Cylinder Attraction for Radius of 58.8 Km. Attraction for Radius of 166.7 Km. Attraction for Radius of noo Km. I II Ill O.o 22.8 4^ 6 0.0031 0.0017 O OOIO 0.0032 O.OO28 o 0024 O . 0036 0.0035 O OO3< IV 68.4 o 0007 O OO2O o 003 ^ v QI . 2 o 0005 o 0017 O OO34. The results for radius 58.8 km. show that masses of this size situated near the bottom of the zone of compensation exert but a fraction of the influence given by equivalent masses near the sur- face. A balancing of light and heavy masses in a column of this radius would give isostasy at the base and yet produce notable anomalies. For radius 166.7 km. the importance of depth is much diminished. For radius 1,190 km. it practically disappears. This means that a wide regional variation in depth with plus and minus departures from the uniform density, the light and heavy layers balancing, would not produce anomalies provided, as stated, there was isostatic equilibrium at the base. To give a somewhat extreme illustration; suppose that the upper cylinder, I, is 2 per cent lighter than the mean density of 1 The formula for making these computations was kindly worked out for me by Professor H. S. Uhler, checking it as given by B. O. Pierce, Newtonian Potential Func- tion, p. 8. It is as follows: in which F = force in dynes per gram. p = density, in this case =0.003,5 7. Y =constant of gravitation = o .000,000,066,58. o = radius of cylinder. c = distance on axis from station to top of cylinder. A=depth of cylinder; in this case 22 .8 km. For radii of 58.8 and 166.7 km. no correction need be made for curvature of the earth's surface. For = 1190 km. an empirical correction was obtained by comparing the results with Hayford's computations. The writer overlooked until later the fact that Hayford and Bowie also give this formula with a different notation on p. 1 7 of their work. . THE STRENGTH OF THE EARTH'S CRUST 221 2.67 and the lower cylinder, V, is 2 per cent heavier. Let these abnormalities be limited areally to the cylinder. This is a departure in density of o. 054, 15.1 times the density o . 00357. The anomalies will be as follows: TABLE XII ANOMALIES DUE TO IRREGULAR VERTICAL DISTRIBUTION OF DENSITY DENSITY 2 PER ANOMALIES No. oy CYLINDER FROM TABLE CENT FROM MEAN Radius 58. 8 Km. Radius 166.7 Km. Radius IIQO Km. I.. 2 616 o 047 o 048 o 0^4. V. 2. 724 +o 008 -j-o 026 H-O 051 Resultant anomaly o O3Q O O22 o 003 It is seen from this tabulation that, first, irregular superposed but balanced positive and negative distributions of density up to distances as large as the radii of the areas of grouped residuals could produce at least a considerable part of the anomalies; or, second, actual departures from isostatic equilibrium with the resultant strain on the crust could produce them; or, third, a combination of the two. In the second case, as Hay ford and Bowie show, 1 the anomalies could result from a layer a few miles thick adjacent to the station and of very abnormal density; or from deep and regional masses of great volume, but departing only slightly from the mean density. The choice between these several alternatives, or the degree to which they co-operate, must be investigated under the following topics. RELATIONS OF ANOMALIES TO EXPOSED GEOLOGIC FORMATIONS The latest data given by Bowie on this subject are shown in Table XIII (p. 222 ): 2 These figures of course are not to be regarded as of high pre- cision, as may be seen by comparing the earlier and later results. *0p.cit., Pp. 108-11. 2 " Some Relations between Gravity Anomalies and the Geologic Formations in the United States," Am. Jour. Sci. (4), XXXIII (1912), 237-40. 222 JOSEPH BARRELL Hayford and Bowie in their successive publications give the follow- ing for the pre-Cambrian and Cenozoic stations, the two groups TABLE XIII Geologic Formation Number of Stations Mean with Regard to Sign Mean without Regard to Sign Pre-Cambrian IO -J-O 016 o 026 Paleozoic 21 o 003 O OIO Mesozoic 20 -j-o 002 O OI ? Cenozoic . . 20 o 008 O O2I Intrusive and Effusive Unclassified. . II 22 0.007 -J-O OI I 0.015 O O2O All stations 123 o ooo O OIO to which the attention will be confined. A few stations of high anomaly must have considerable influence on the result, as most of the stations are used in common in all of the estimates. TABLE XIV Geologic Formation Number of Stations Mean with Regard to Sign Mean without Regard to Sign Hayford and Bowie, U.S.C.J Pre-Cambrian 7 +0.019 0.026 and G.S \ Cenozoic 20 O Oil O O2I Bowie, U.S.C. and G.S { Pre-Cambrian Cenozoic & +0.024 0.007 0.024 O.O2I Bowie, Am. Jour. Scl < Pre-Cambrian Cenozoic IO 29 +0.016 0.008 O.026 O.O2I * Fifteen stations have plus anomalies, 1 7 have minus anomalies. Bowie's figures in the American Journal of Science will be used in the following discussion. Bowie favors the explanation that these relations of anomalies to geologic formations are due to slight changes of density extend- ing more or less through the zone of compensation and leading to departures from perfect isostasy. The writer, however, is led to favor the view that about one-half of the contrasted anomaly for these two groups is due to a lesser density within the outer mile of crust beneath the Cenozoic stations, as contrasted to the outer mile of crust beneath the pre-Cambrian stations. The remainder of the anomaly it is thought is explained by the ease of erosion of Cenozoic formations, the resistance to erosion of the pre-Cambrian THE STRENGTH OF THE EARTH'S CRUST 223 rocks. The latter consequently tend to stand above the regional levels. They therefore possess surficial excess both of density and volume. The average thickness of sedimentary rocks if spread uniformly over the globe is thought to be between 2,000 and 2,500 ft. 1 Over the pre-Cambrian areas it must average much less; over the areas of later formations much more. Under the Cenozoic stations assume: i ,000 ft. of sediments at density 2 . 40 to 2 . 50 4,000 ft. of sediments at density 2 . 50 to 2 . 60 Giving a total of 5,000 ft. at density 2 . 48 to 2 . 58 With a deficiency of density of o. 19 to o. 09 Under the pre-Cambrian stations assume: 5,000 ft. of crystalline rock at density 2 . 75 to 2 . 80 An excess of density of o. 08 to o. 13 This does not involve the improbable assumption that below the outer 5,000 feet of crystalline rock of density 2 . 75 to 2 . 80 the den- sity suddenly decreases to 2.67 and then remains constant through- out the zone of compensation. The vertical density gradient, if uniform for all points, has but little effect, it being the horizontal variations of density which enter into the problem of isostasy. To maintain conformity with Hayford's figures, therefore, the density 2.67 will be frequently assumed as the mean density of the litho- sphere, although the previous discussion shows that it cannot be assumed as the density of the outer mile of crystalline rocks when comparing these to the mile of sedimentary rocks taken as the mean depth underlying the Cenozoic stations. In comparison with this thickness of 5,000 ft. the average area of formations is very great. A plane sheet of rock 100 ft. thick and of density 2.67, if of indefinite extent, will produce an anomaly of 0.0034 dyne upon a point outside of it, irrespective of the distance to that point. This theory may be applied without gross error to the relation of surface geologic formations to anomalies. If this unit mass be expanded from 100 to 5,000 ft. thickness, the 1 F. W. Clark, "Data of Geochemistry," Bull 491, U.S. Geol. Surv., 1911, p. 30. 224 JOSEPH BARRELL density will be decreased to 0.053 that of water. The data may then be tabulated as follows: TABLE XV COMPUTED ANOMALIES DUE TO DENSITIES OF SURFACE FORMATIONS Deficiencies or Excesses of Density Anomalies in Dynes per Gram Due to Thickness of 5,000 Ft. Unit mass .... O CK"? O 0034 Cenozoic. O IQ O OI2 Pre-Cambrian 0.09 +0.08 0.006 -f-o 005 +0.13 +0.008 These mean anomalies of the pre-Cambrian due to the greater density of the outer 5,000 ft. of rock, when compared to the Cenozoic anomalies, are, as shown by this tabulation, at a minimum o.on greater, at a maximum 0.020 greater, at a mean 0.0155 greater. The difference of the means shown by geodetic measurement was 0.024. The specific gravities seem to have been taken as far apart in limits as is allowable and the assumed mean thickness of sediments as 5,000 ft. beneath the Cenozoic stations is a generous figure; the mean thickness is more likely to be less, rather than greater. The means for the geodetic anomalies as related to geologic formations are perhaps subject to about the same degree of error as the determinations of the anomalies from the specific gravities and thickness. The result, although not of a high order of accuracy, shows that although the range in specific gravities accounts for a considerable part, perhaps one-half or two-thirds, of the relation of anomalies to geologic formations, it can hardly account for the whole. To find the cause for the remaining portion of the anomaly, two hypotheses may be considered: first, that it is due to a slight regional excess of density extending to a depth of 114 km., the hypothesis favored by Bowie; or, second, that the Archean areas on the average stand higher than the Cenozoic by virtue of resistance to erosion. The geologic evidence as it is at present understood is against the first hypothesis and in favor of the second. This statement THE STRENGTH OF THE EARTH'S CRUST 225 is based on the view that Archean and Proterozoic areas have tended to be rising elements of the continent. Erosion instead of sedimentation has been dominant in later geologic time, which is the reason why these rocks are now exposed as surface formations. If there is any deep-seated departure of density from the mean this tendency to rise should correspond, however, to a deficiency of density persisting through the geologic ages, extending through much of .the zone of compensation and offsetting the more than average surface density. Such a regional deficiency is opposite in character to the excess which is postulated by Bowie as an explanation of the positive anomalies. Assume then as the next step in the argument that the density of the zone of compensation beneath the pre-Cambrian areas to a depth of 114 km. is the same as under Cenozoic areas except for the outer 5,000 ft., both having a mean density of 2.75 to 2.80, but taken here as 2.67. The outstanding anomaly in that case is due to a longer mean column for the pre-Cambrian areas and conse- quently greater mass above the level of complete compensation. If the mean radius of these longer pre-Cambrian and shorter Ceno- zoic columns is as great as 166.7 km., then the unit excess or deficiency of mass of 100 ft. at density 2.67 when spread over these columns will correspond to an anomaly of 0.0024. If the mean effective areas of the pre-Cambrian and Cenozoic formations affecting individual stations are less, the unit mass will give a smaller unit anomaly. If the mean effective areas are greater, the unit anomaly will not, however, rise above 0.0035. Assume then in conclusion a mean radius of 166.7 km., an anomaly of 0.0024 dyne as resulting from 100 ft. of added mass of mean density, and the outstanding anomaly not accounted for by the surficial densities but due to an outstanding difference in volume as between 0.008 and 0.012. These figures correspond to a differential mean elevation of 330 to 500 feet of the pre-Cambrian above the Cenozoic, due to erosion. To physiographers such a conclusion will seem quite in accord with the geologic evidence testifying to the resistance of pre-Cambrian formations. The character of the Archean and Proterozoic anomalies enters into the problem of crustal rigidity in the following way. If there 226 JOSEPH BARRELL were local and close compensation, then as erosion removed the softer surrounding rocks there should be isostatic upwarping of such areas of denudation and relative downwarping of the uneroded crystalline areas. Such warping of the Mohawk, St. Lawrence, and Champlain valleys with respect to the Adirondacks has not been noted, though the problem from the standpoint of field evidence has not been fully studied. The physiographic evidence that residual mountain masses known as monadnocks or unakas have not been shown, however, to be marked by local downwarping and, on the contrary, certainly stand in relief due to circumdenuda- tion, combines with the geodetic evidence of the average excess of gravity for the resistant areas of pre-Cambrian formations, to suggest effective rigidity against the stresses produced by erosion. The evidence, however, as developed thus far from the geodetic standpoint shows that there are more important factors than that of the surface geologic formation, since the larger anomalies are much greater than these figures which have been discussed and hold but little relation to either relief or surface geology. In fact Hayford and Bowie do not find any discoverable relation between the anomalies in general and the topography. It is thought by the writer, however, that if stations were located especially to test the intensity of gravity over various broad plateaus remaining by circumdenudation and the intensity compared with that over adjacent broad areas of lower level, the mean differential anomalies due to the surface excess of mass in the plateau over the lowlands would rise to a larger figure than the 0.008 to 0.012 dyne which has remained to be explained in the present discussion. These figures are low because certain pre-Cambrian areas, like those in the vicinity of Baltimore and Washington, have been lowered by prolonged denudation and do not stand markedly above the level of younger formations. Further- more, the tendency of broad pre-Cambrian areas to stand above sea-level is very probably of an isostatic nature. This implies under such areas a slightly lower mean density to the whole zone of compensation which would diminish the anomaly due to the surface elevation. In individual areas of 100 to 200 km. radius, however, such a relation of positive anomaly to pre-Cambrian THE STRENGTH OF THE EARTH'S CRUST 227 formations and plateaus of circumdenudation may not be found, since it is clear that the anomaly from this cause may be much more than neutralized by other causes. A large number of stations covering broad areas would therefore be required adequately to eliminate these other influences from the means. LARGE OUTSTANDING ANOMALIES NOT RELATED TO GEOLOGY OR TOPOGRAPHY In Fig. 5, of Part II, the anomalies are shown for all stations in the United States. It is seen that they possess an areal grada- tion in magnitude which permits the drawing of anomaly contours. The excessive anomalies of both signs cover oval areas in various parts of the country and show a common disregard of physio- graphic provinces, structural provinces, and geologic formations. Looking at Fig. 5, one cannot see in either the distribution of anomalies or trends of contours a reflection of Atlantic Coastal Plain, or Appalachian Mountains, or Mississippi Valley. Typical examples of the lack of necessary relation of the large anomalies to geologic formations are seen in the following tabula- tion: TABLE XVI No. Station Geologic Formation Anomaly 123 74 96 Albany, N.Y St. Paul, Minn Mena, Ark Cambro-Ordovician Cambro-Ordovician Pennsylvanian . . -0.043 +0.059 O O?2 IOI Helen wood, Tenn. . Pennsylvanian .... ~f~O O4.O c-2 e;6 Seattle Wash Quaternary O OO3. 112 Olympia Wash Quaternary -L-O OT.'i The lack of relation of these anomalies to topography is equally striking. It is clear then that internal conditions in the crust, not expressed on its surface, must be the principal cause of these larger departures from isostasy. The large anomalies show their relation- ship to internal causes most clearly, but the smaller anomalies may also by analogy be ascribed in part to such hidden causes. The results, however, of surface activities -circumdenudation, sedi- mentation, tangential pressure, or extravasation must show in large ratio over regions where the internal variations from uniform density are small; but over the greater part of the United States 228 JOSEPH BARRELL the distribution of anomalies appears to depend more upon the internal than upon the external departures from regional uni- formity and complete isostasy. The internal heterogeneities of mass are therefore presumably greater than the shiftings of mass due to external activities. CRITERIA FOR SEPARATING VERTICALLY IRREGULAR COMPENSATION FROM REGIONALLY INCOMPLETE COMPENSATION Suppose the topography smoothed out to a mean level over areas as large as the limits for regional isostasy. The deflection residuals and gravity anomalies would then be due to one or more of three internal causes; first, vertically irregular or laterally displaced compensation; second, regionally incomplete compensa- tion above the bottom of the zone of compensation because of the effective rigidity of the crust above that level; third, regionally incomplete compensation above a certain level because the zone of compensation may be deeper in places, transferring stresses into a deeper rigid earth. The existence of a general approach toward compensation and away from absolute rigidity suggests that the last is not so important as the first two causes. Under this section then will be considered these two causes, their effects upon the deflections of the vertical and the intensity of gravity, with the purpose of drawing criteria by which the action of the two causes may be recognized and separated. To do this it will be necessary to discuss here to some extent the theory of the attraction of underground masses upon stations at the surface of the earth. It has been shown that balanced irregularities in the vertical distribution of densities through the zone of compensation could give pronounced anomalies without disturbing the isostatic equilib- rium at the bottom of the zone, since the total weight of the column could still be normal. To show the effect of such balanced irregu- larities upon a point outside of the column: Take a vertical line and a horizontal line which intersect. The masses whose effects are to be investigated will be distributed on the vertical line. The effects are to be determined for points on the horizontal line. To express the trigonometric relations between any point on the vertical and any point on the horizontal line, let a point on the vertical line at depth D be defined as at a vertical THE STRENGTH OF THE EARTH'S CRUST 229 angle 6 below a point on the horizontal line; the latter to be denned as at distance R from the intersection. Let the gravitative attraction of unit masses along this vertical line upon any other point either in or outside of this line be repre- sented by F. The horizontal component will be the force produ- cing deflection of the vertical and may be represented by Fh. The vertical component will give the acceleration of gravity due to the unit mass and may be represented by Fv. Taking the unit mass such that the constants will have a value of unity, the following relations are deduced: Attraction of unit mass at depth D, upon a point at R: VL cos3 e g- = tan cos 3 R 2 For the intersection point, R and 0=O and Fk=o Let the depth of the zone of compensation, 114 km., be taken as unit distance, i . oo, and for purposes of discussion let points I, II, III, IV be located on a vertical line at depth of 0.25, 0.50, 0.75, and i. oo as shown on Fig. 6. Solving the equations for these points and for various values of R gives the following tabulation: TABLE XVII TABLE OF RELATIVE ATTRACTIONS (Not in dynes per gram) ATTRACTION BY UNIT MASSES AT ATTRACTION AT STATIONS FOR VARIOUS VALUES OP R No. Depth Angle below /? = I.OO R=o R=0.2$ R=o.$o R = i.oo = 2.00 Fh Fv Fh Fv Fh Fv Fh Fv Fh Fv o 0.25 0.50 0-75 I.OO O I 4 02' 26 3 4' 3652' 45 o o o o o O 16.00 4.00 1.78 I.OO 16.00 S.6o 1.44 o-5i O. 21 o S.6o 2.88 1-52 0.91 4.00 2.88 1.40 0.68 0.36 o 1.44 1.40 1.04 0.72 I.OO 0.91 0.72 0-51 o-35 o 0.23 0.36 0.38 0-35 0.25 o. 24 0.23 O.2I 0.18 o 0.03 0.06 0.08 0.09 I II Ill IV 230 JOSEPH BARRELL Fig. 6 shows the curves for R=i. For any other value of R the curves would be the same in form, but the scales of ordinates and abscissas would be changed. These curves may be used therefore in a general way. Attraction on A by points on vertical line, shoam by abscissas on the vertical line. Horizontal Vertical component F> component F v R^2S R--.50 R.LOO Combined attractions of I and IH upon points on the horizontal line.shoiun by ordinates on the horizontal line Scale of distance. t.oo Horizontal component Sum of I and HI Diff. of 1 and IH Vertical component f- Sum of I and HI Diff. of I and 1U FIG. 6 FIG. 7 FIG. 6. -Curves showing relative attraction of all points on the vertical line upon a point at distance R=i. FIG. 7. Combined attractions upon all points on the surface by unit masses of like and unlike signs at I and III of Fig. 6. The table shows that if unit masses at II and III have the same sign the horizontal component, Fh, for the sum of their attractions at o. 2$R will be i .95, at R it will be i . 23, which is 63 per cent of the value at 0.25^. If the unit masses have unlike signs the horizontal component of their difference at o.2$R will be 0.93, at R it will be 0.21, which is but 23 per cent of the value at o.2$R. The vertical component, Fv, due to the sum of the masses at o. 25^ is 4.40; at .R is o. 74. The vertical component due to the difference at o.2$R is i .35; at R is o. 02 and of opposite sign. It is noticed that the gravity anomaly diminishes rapidly with increasing horizontal distance from these two masses and passes through zero. The deflection of the vertical first increases sharply and THE STRENGTH OF THE EARTH'S CRUST 23 1 then diminishes, but less rapidly than the gravity anomaly. It is important to notice that in both cases the total influence due to masses of opposite sign diminishes much more rapidly, and where their distance apart is 0.25 their influence is small at distance R and negligible at 2R. This gives a means of determining whether, in the crust, anomalies and deflections are due to regional departures from isostasy or to balanced irregularities in density without absence of isostasy at the base of the zone. To give a further illustration of balanced departures in density spread over a greater vertical distance, and representing in that way perhaps a more average case, assume that an excess or deficiency equivalent to a unit mass is at depth 0.25 and another at depth 0.75. The following tabulation shows their influence upon the surface of the earth at increasing horizontal distances. TABLE XVIII ATTRACTION BY UNIT MASSES AT I AND III UPON POINTS ON THE HORIZONTAL LINE Position Horizontal Distance on Surface of Earth from Vertical Line of Mass o 0.25 0.50 I .OO 2.OO 4.00 Fh HI O -6. ii -3.56 -1.42 -0-55 O. 121 +m f O -5-09 2. 2O O.4O -0.03 0.003 Fv 1 I -m r -17.78 -7.12 -2.48 0.61 o. ii .0.015 +HI / 14.22 -4.08 O.4O +0.15- +0.05 +0.007 The data in this table are represented by the curves of Fig. 7. It shows that for this arrangement of masses the influence on the surface falls off rapidly at a horizontal distance between 0.25 and 0.75, which are also the vertical depths to I and III. When the masses are of opposite sign the anomaly passes through zero at a horizontal distance of about 0.6, and the deflection force for opposite sign decreases to half the value of the sum at about o. 75. The ratio between the effects of like and unlike masses becomes more marked the greater the distance of the point, although the actual magnitudes of the forces decrease. . 232 JOSEPH BARRELL Now assume the unit masses at I and III to be parts of masses of like density extending to the left of o to a distance N. Consider the aggregate effect upon a given point, as that at 0.50, or in general at point R. The effect of each unit at distance x to the left of o upon the point at o. 50 will be measured by an ordinate at a distance x to the right of o . 50. This will give the same aggregate result as concentrating the masses at o and summing up the area of the curve to the right of the point at o . 50 to a distance of o . 50+ N. Stated in general terms, masses at depths I and III extending linearly to distance N to the left of o will have an aggregate effect upon a point R equal to the area of the curve between R and R-{-N. As to the aggregate effect on Fv, the gravity anomaly: If the two sheets are of negative density, it is seen that the result will be an increased negative anomaly over the effect of the separate unit masses. If the lower mass is, however, of positive density, the result for ordinarily limited sheets will be a change between o and 0.50 from a large negative to a small positive anomaly. This may be compared with the effects of other possible distribu- tions of mass upon the gravity anomaly. If the anomaly due to the adjacent departure from uniform distribution is of the mean value or greater, the more distant abnor- mal masses will have but relatively small influence. This is because the higher anomalies, with the exception of Seattle, are but two or three times the mean. Further, in a zone of large radius there are a greater number of positive and negative departures. Their aggregate effect, according to the laws of chance distribution would increase but slowly and this effect is diminished by distance accord- Ffl=tan 0cos 3 ing to the formula - ~ 2 . A reversal from a large anomaly of one sign to a large anomaly of opposite sign, rather than a small one of opposite sign, marks then in general a passage from an area of excess or deficiency of mass to the opposite. A gradual change in the anomaly is the reflection of a change in the subsurface abnormalities nearly as gradual. If the areal variations show that the passages of the anomaly through zero are not frequent, they go to show that limited notable irregularities of density of opposite sign in the THE STRENGTH OF THE EARTH'S CRUST 233 same column are rare. Furthermore, it has been shown under the topic "The Variable Rate of Compensation upon Gravity Anomalies" that a variable distribution of balanced densities has more effect if in areas of between 100 and 200 km. radius and has but little effect on anomalies if the balanced densities extend over much larger areas. As to the aggregate effects produced upon Fh, giving deflection residuals, by these sheets I and III: If the sheets have like sign the deflection force, as shown in Fig. 7, will die out somewhat gradually and extend to considerable distances. If they have unlike sign the deflection force will fall off sharply between 0.25 and i . oo. If, however, the abnormalities of density should dis- appear gradually, that is, if the sheets did not terminate sharply at o, this rate of falling off would be slower. Reversals of sign of the deflection residuals would require areal, not vertical, irregu- larities of mass. They could not take place as an effect of dis- tance from a single mass or of two masses of unlike sign and vertically over^each other. Where sharp reversals of sign take place in the deflection residuals the presence of areally contiguous areas of unlike departures in mass is shown. A mere difference in magni- tude of excess of mass but of the same sign may, however, produce changes in the sign of the deflection residuals. In the irregular areal distribution of abnormal masses not balanced by being over each other, the deflection areas of like sign would thus tend to be smaller than the anomaly areas of like sign. A gradual fading-out of the deflection residuals would be the mark of gradual fading-out of the abnormal mass or the increasing influence of distant masses. Various special combinations of three or more masses could at any one point simulate the relations indicated, but such special relations would not be of common occurrence and could not give a generah'ty of relation of this sort. There have thus been drawn up a set of criteria by which balanced irregularities within the zone of compensation may be distinguished from regional departures from isostasy. It remains to apply those to the areal distribution of gravity anomalies and deflection residuals as given by Hayford and Bowie. It must be recognized, however, that the stations, although numerous as 234 JOSEPH BARRELL compared to previous measurements, are yet very scattered for the precise application of these tests and can at best give but qualitative results. It is thought, nevertheless, that the general nature of the answer is determinative. GRAVITY ANOMALIES CAUSED LARGELY BY REGIONAL DEPARTURES FROM ISOSTASY The first question is: To what degree do the areas of excess (or deficiency) of mass as indicated by gravity anomalies coincide with areas of excess (or deficiency) as shown by the deflection residuals ? In Fig. 5 1 there are indicated a number of ovals shown in dot-and-dash outline and marked + or . These are the definitely bounded areas of excess or deficiency of mass indicated by the deflection residuals. The entire surface of the crust must be constituted of such areas, but only a few are surrounded by sufficient observations to permit a boundary to be drawn at present. Even this boundary must not be regarded as sharply definite. Beside these ovals there are shown in illustrations 5 and 6, Hayford, 1909, areas of residuals characterized by like sign, referred to in the present paper as ''areas of grouped residuals." They are not definitely bounded on all sides and are not shown in Fig. 5 of this article. The areas of grouped residuals show the intercepts across areas of like sign, but at least two intercepts at an angle to each other are necessary to define well the limits of the area of which they are a part. As the deflection stations are situated largely in lines or zones across the country and not surrounding the areas of like sign, it is seen why the boundaries of relatively few areas are well determined. In so far, however, as the relations of the areas of positive and negative anomaly to positive and negative deflections of the vertical are apparent, Hayford and Bowie state: "The gravity anomalies corroborate the evidence given by the deflections. In no important case are the anomalies and deflections contradictory." 2 It is seen by inspection of the illustrations by Hayford, and also by the discussion in Part II of this article, that the areas of 'P. 153, Part II. 2 Hayford and Bowie, 1912, p. 112. THE STRENGTH OF THE EARTH'S CRUST 235 like sign of deflection residuals are more sharply bounded and smaller in size than the areas of like sign of gravity anomalies. The latter occur commonly in areas so broad that a vertically bal- anced irregularity in the distribution of density would have but little effect. Yet the large gravity anomalies occur in the midst of such large areas, as shown on Fig. 5. There are, furthermore, few sharp reversals of sign of the gravity anomalies save those at different elevations in mountainous regions and these are explained by the presence of regional compensation. There are, on the contrary, many sharp reversals of the deflection residuals. It is to be concluded, therefore, that, although some degree of balancing of irregularities in the same column no doubt exists, this is not a common or controlling explanation of the anomalies and residuals. They are overshadowed by a distribution which points, on the contrary, to regional departures from isostasy by regional excesses or defects in density. In the location of stations, the deflection observations are arranged at relatively close intervals and in linear zones, owing to the necessity of triangulation. They give the most information as to the size of areas of relative excess and defect. But two areas of relative excess and defect may both be in absolute excess or absolute defect. The gravity stations are more widely scattered. The local variations are in consequence poorly denned, but the limits of absolute excess and defect of mass are determined with more accuracy. They appear to show that areas as large as 1,000 by 2,000 km., 620 by 1,240 miles, may depart in one direction from isostasy, but only to a moderate amount. It is seen from Fig. 5 that between Florida and a line drawn from Lake Superior to the Rio Grande the broad areas of less than mean anomaly are negative. From this line a great positive area extends to the northwest. The quarter of the United States bordering the Pacific Ocean is, how- ever, another great region of negative anomalies. Upon these broad regions of mean anomaly or less are superposed smaller and better-defined areas of more than mean anomaly, negative and posi- tive areas occurring in the same broad region. These smaller areas are inclosed by the 0.020 anomaly contour. They commonly range from 300 to 400 km. across, 200 to 250 miles, but the maxima 236 JOSEPH BARRELL which reach above o . 040 are much smaller. The limits of regional isostasy appear then to vary with the amount of the load. Well- defined areas 200 to 250 miles in breadth may stand vertically 800 to i ,600 feet on the average from the level, giving isostatic equilib- rium, and their central portions reach still higher values. They represent the limits of regional isostasy discussed in an earlier part. But these are superposed on broader areas which may extend for a thousand miles or more and lie as much as 400 to 800 feet either above or below the level for equilibrium. Stresses given by loads of this order are then not restricted in area to the limits set for higher values. The size of the areas of intenser stress reveal the capacity to which the earth can carry mountain ranges uncompensated by isostasy. The size of the areas of weaker stress shows the capacity of a considerable portion of a continent to lie quiescent while the surface agencies carry forward their leveling work. This is the present state of this particular continent after a geologic period of world-wide notable vertical movement and adjustment. It is not likely, therefore, that these loads measure the maximum stress- carrying capacity of the earth. They may be more in the nature of residual stresses which the earth can hold through periods of discharge of stress. East of the Cordillera there has been but little local differential movement and these areas have lain in crustal quiet for long geologic ages, being subject only to broad and uni- form crustal warping of moderate amount. It is to be presumed, therefore, that the strains which exist in such regions by virtue of the regional departures from isostasy are of ancient date and well within the limits of crustal strength. It would seem probable for such conditions, from the stand- point of mechanics, that the zone of compensation is not sharply limited, with its implication of marked lowering of rigidity at its base; nor the distribution of compensation uniform to the base. It seems more probable that the abnormalities of density and the resultant strains should fade out through a considerable depth more after the manner suggested by Chamberlin. [To be continued] VOLUME XXII NUMBER 4 THE JOURNAL OF GEOLOGY MAY-JUNE 1914 THE STRENGTH OF THE EARTH'S CRUST JOSEPH BARRELL New Haven, Connecticut PART IV. HETEROGENEITY AND RIGIDITY OF THE CRUST AS MEASURED BY DEPARTURES FROM ISOSTASY INTRODUCTION AND SUMMARY 289 VARIABLE OR CONSTANT DEPTH OF COMPENSATION .... 291 DEPARTURES FROM ISOSTASY SUSTAINED BY RIGIDITY IN THE ZONE OF COMPENSATION . 296 INTERPRETATION OF DEFLECTION RESIDUALS IN TERMS OF MASSES . 297 MAXIMUM LOADS INDICATED BY ANOMALIES . . 302 FURTHER GEODETIC WORK NEEDED FOR GEOLOGIC PROBLEMS ... 313 INTRODUCTION AND SUMMARY In Part I were examined certain geologic tests of the strength of the crust; in Part II the geodetic evidence in regard to the effective areal limits of rigidity; in Part III the influence of variable vertical distribution of density. All three lines of investigation converge toward showing the rigidity of the outer crust the zone of isostatic compensation to be such that very considerable stresses can be carried over areas whose radii range between 100 and 300 km. There arise to be considered next the following problems: first, the variability in depth of compensation and its influence; second, Vol. XXII, No. 4 289 290 JOSEPH BARRELL whether the stresses represented by the incompleteness of isostasy are carried by the rigidity of the outer crust, or are transferred in some measure to the deeper body of the earth; third, the magni- tudes of the stresses, measured in terms of loads, which are indi- cated by the gravity anomalies and deflection residuals. It is found in answer that under the hypothesis which forms the basis of Hayford's work, that of uniform compensation, com- plete at a given depth, there are indications, given by comparing different areas, of a great range in the depth of the bottom. Under an assumption which is probably nearer to nature that is, the hypothesis of a variable and gradually disappearing compensa- tion there is room for even a greater heterogeneity of the crust and a greater variability in the depth reached by the zone of compensation. But, on the other hand, it is concluded that the zone of compensation, as an outer rigid crust separated from the rigid inner earth by an intervening zone of lowered rigidity, is a reality in earth structure. The stresses due to the heterogeneities of density and relief within and upon this crust appear to be borne by the crust, not by the inner earth. Under the third subject it appears, upon review of the evidence given by the deflection residuals, that these may be interpreted so as to show departures from equilibrium comparable to the results given by the gravity anomalies, instead of the 250 feet which Hayfofd thought to exist. The two independent lines of geodetic investigation are thus seen to agree and it may be concluded with some confidence that the individual isostatic regions of the United States are on the average between 600 and 900 feet out of equilibrium. Evidence from other parts of the world appears to show, furthermore, that a number of regions exhibit greater departures from isostasy than those observed within the United States. The strain imposed on the crust by the Niger Delta, though large, is apparently not as large as some made known by geodetic measurements. Thus from various directions of attack the crust is shown to be an earth shell of high rigidity and consequently high elasticity. Geodetic evidence justifies the view, brought forward by geologic evidence, that the delta of the Niger is to be looked upon as sup- ported by the strength of the crust. THE STRENGTH OF THE EARTH'S CRUST 291 VARIABLE OR CONSTANT DEPTH OF COMPENSATION The Cordilleran region awoke to an era of great orogenic and igneous activity near the beginning of the Tertiary, and, especially in the Neocene, has become broadly elevated into one of the great plateau regions of the world. Large areas like the Colorado plateaus, which since the beginning of the Paleozoic had rested near sea-level, at times beneath and again slightly above, have been lifted many thousands of feet. Block-faulted structures indicate the dominance of vertical forces rather than surficial compression as the cause of these movements. The uplift has not been of the nature of a broad even upwarp, and adjacent regions show great contrasts in elevation. These different surface results of the interior forces suggest differences in elevatory forces at compara- tively shallow depths. The region is known to be in a fair degree of isostatic equilibrium notwithstanding the high relief. Davis has shown why these movements cannot be regarded as differential sinkings toward the center of the earth. 1 These features suggest, then, subcrustal decreases in density during the Tertiary as a cause of the broad movements of elevation. The rising of great bodies of magma to high levels in the zone of isostatic compensation, their irregular distribution, the great quantities of heat and gases which would invade the roofs are suggested by the observed evidences of regional igneous activity at the surface as the probable causes of the changes in density and regional vertical movements. A consequence of such a cause would be a lessened strength of the crust to resist strain, a lessened depth to the zone of isostatic compensation, and a decreased size of the unit areas departing from equilibrium. The history of the Cenozoic in the Cordillera has repeated the history of other regions at other times, either in the Archean igneous activity or later. The slow conduction of this excess heat from the outer crust, the solidification of the reservoirs of magma, would, in the course of ages, bring about a new rigidity. Upon disturbances of the equilibrium by erosion or compressive forces there would be found a new and greater depth to the zone of compensation. l " Bearing of Physiography upon Suess's Theories Abstract," Intern. Geog. Cong., 8th Report, 1905, p. 164; Amer. Jour. Science (4), XIX (1905), 265-73. 292 JOSEPH BARRELL Where ages of uplift and erosion have followed periods of igneous activity there are revealed great bodies of intrusive rock varying in density from granites at 2.65 to gabbros at 3 . o. These great batholiths are of irregular distribution in the crust, both vertically and horizontally. Their abundance increases downward so far as erosion has revealed the evidence. The outer crust of the earth has become vertically and areally heterogeneous by such means and should cause variations and irregularities to an appre- ciable degree in the distribution of isostatic compensation, as noted under the topic of the influence of variable rate of compensation upon gravity anomalies. Here we note in addition the decreased depth of compensation and decreased rigidity at the time of intrusion. Hayford notes that the stations classified into geographic groups show as a rule as great contradictions in depths of compensation between adjacent groups as in those which are far apart. This variation between adjacent groups is taken by him as weakening the evidence that there is any real variation in the depth of compensation over the whole area investigated. 1 For the reasons outlined previously, the present writer, influenced by the geologic inferences, does not view such irregularity of distribution as proof that the evidence is weak and conflicting. The strength of the evidence must be judged rather by the nature of the residuals. Hayford points out that the depth of compensation in the West seems on the whole to be somewhat less than in other parts of the United States, though he does not regard it as safe to assert that it does exist. On dividing the whole area into four sections, the minimum sum of the squares of the residuals indicates depths as follows as best satisfying the hypothesis of uniform distribution of compensation: From all residuals of the central group, 174 km. From all residuals of the northeastern group, 187 km. From all residuals of the southeastern group, indeterminate. From all residuals of the western group, 107 km. 2 In the 1909 paper Hayford gives a tabulation of the residuals for fourteen geographic groups. The results for the United States as a 1 1909, pp. 58, 59. 2 1906, pp. 142-46. THE STRENGTH OF THE EARTH'S CRUST 293 whole and for the groups showing the shallowest, deepest, and the most irregular compensation are quoted below. 1 That solution is regarded as nearest the truth which gives the smallest mean value of the squares of the residuals. TABLE XIX PROBABLE DEPTHS OF COMPENSATION MEAN VALUES OF THE SQUARES OF THE RESIDUALS IN VARIOUS GROUPS No. OF MOST GROUP RESIDU- ALS Solution Solution Solution Solution Solution PROB- ABLE 8 B E H G A DEPTH Infinite 162.2 120. Q "3-7 o.o Depth Km. Km. Km. Km. Km. United States (all observa- tions) 772 146. 50 14 cx 17.71 17 7tr 2< 77 122.2 Group 12 (parts of Minn., / oo Ai T ' V O * O 1 O o / o Oil N.Dak., S.Dak., Neb., Kan.) 36 196.57 7.OO 7-47 7.59 II .46 305 Group 5 (Mich., Minn., Wis.) 52 34-97 23.6O 23.64 23.67 27-53 152 Group 8 (parts of Utah, Nev., CaL). . . 42 128.97 22. 27 18.79 18.25 35.78 66 United States (residuals multiplied by 1.327 to compare with Group 8) 194.40 18.65 18.23 18.25 34-21 It is seen that the mean value of the squares of the residuals in group 12 with most probable depth of 305 km. is considerably less than for the United States as a whole, in part no doubt owing to the moderate relief, yet the differences between the residuals in group 1 2 for the different solutions is much more pronounced than for the United States as a whole. The number of stations, 36, is large enough so that this can hardly be regarded as accidental. On the contrary, it would appear that for the whole United States the group differences are sufficient to mask in part the accuracy of the mean result of 122 km. and that the depth of compensation within certain groups is more reliable than for the United States as a whole. In group 8 with most probable depth of 66 km. the mean value of the squares of the residuals is nearly 50 per cent higher than for 1 1909, pp. 55-58. 294 JOSEPH BARRELL the United States as a whole, a value which may be ascribed to the mountainous relief and the support of individual mountains and ranges by the rigidity of the crust. Nevertheless the residuals for the several solutions fall into a somewhat regular system, and solu- tions E, H, and G are more sharply differentiated from the most probable one than for the whole United States. They may be compared better with the latter if the residuals for the whole country are multiplied by i . 327 as a factor in order to give the same numerical value under solution G. This is done at the bottom of the table. It would appear from these figures as though the argu- ments previously given from geologic analysis receive considerable support from the geodetic results and point to a much shallower depth for isostatic compensation in the Great Basin than over cer- tain other portions of the United States. Furthermore, in the examination of the question of local versus regional compensation, it was only the forty mountain stations classified into two groups according to elevation which gave any suggestion that regional compensation to a radial distance of 166.7 km. was not about as probable as more local compensation. In these two lines of geodetic evidence as to limited depth and breadth of compensation there are suggestions therefore which support the geologic inference that the crust of the Cordilleran region may be weaker than over the United States as a whole. On the other hand, the warping or faulting- down of ancient continental areas into marginal sea-bottoms implies an increasing density of the subcrust and therefore possibly an increasing rigidity and strength under such areas. Such a contrast between the Atlantic Ocean bottom and the Great Basin would correspond to the great strength of crust necessary to sustain the delta of the Niger as compared with the moderate rigidity found by Gilbert for the crust beneath extinct Lake Bonneville, located within the limits of group 8. The regions of shallower compensation in the United States are on the whole marked probably by a higher temperature gradient, the regions of deep compensation by a lower. This is illustrated by the very high gradient of the Comstock mine in Nevada and the very low gradient which is found in the Lake Superior copper mines. The temperature gradient may measure the depth to a zone of low THE STRENGTH OF THE EARTH'S CRUST 295 rigidity, determined by a certain relation of temperature and pressure. Within an overlying zone of high rigidity, even where it is of uniform depth, the geodetic measurements of the depth of com- pensation may not, however, show uniformity. If the density is unequally distributed, the compensation of a region may be nearly completed at some depth above the base of the rigid zone, the lower part consisting of rock of mean density and therefore not possessing influence. A region of deep and marked rigidity, if characterized by notable irregularities in the distribution of either density or relief, would show large residuals. A region characterized by more uniform distribution of density and gentle relief would show lower residuals even with the same rigidity. A region with deep com- pensation would show within the limits of the group lower residuals for the same degree of uniform compensation, than where compen- sation was at lesser depths, since the attracting masses are spread over a greater distance. As applications and tests of these principles, it is to be noted that group 5, embracing the Lake Superior region with its low- temperature gradients, has the highest residuals of any group in the United States. Further, the mean values of the least squares for the different solutions show less differentiation than in any other group. These facts suggest irregular distribution of density, high rigidity, and the zone of rigidity may extend below the most probable depth, 152 km., indicated for the limits of compensation. The topographic deflections are only 58 per cent compensated. The contiguous group to the southwest, No. 12, shows the lowest residuals of any group, the separate solutions are sharply differen- tiated and the depth is the greatest in the United States. On the side of this area, the gravity anomaly at St. Paul, 0.059 dyne per gram, is, next to Seattle, the largest found thus far in the United States. It may be concluded, then, that in this part of the con- tinent, undisturbed by igneous activity or mountain-building since the pre-Cambrian, the depth of the zone of rigidity appears to be very great. The irregularities in residuals in group 5 may date from the Keweenawan period, when enormous masses of basic and therefore heavy magmas were intruded and extruded in the Lake 296 JOSEPH BARRELL Superior region. If such be the case it shows the long endurance of strains borne by this part of the earth. In the almost universal epeirogenic movements which marked the close of the Tertiary and opening of the Pleistocene, the Lake Superior basin showed notable down warping, its bottom being now beneath the level of the sea. It formed a trough which directed the flow of glacial ice. The latter must have scoured it clean but can hardly be ascribed as the cause of the existence of the basin. The crust movements have doubtless been in the direction of relief of stress, but the relief has been but partial; geodetic investigation reveals that the age-long load is yet borne. DEPARTURES FROM ISOSTASY SUSTAINED BY RIGIDITY IN THE ZONE OF COMPENSATION It was concluded under the last topic that the rigidity over certain parts of the earth probably carries the zone of possible com- pensation as deep as 300 km. even under the assumption of uniform rate, an assumption which tends to minimize the depth; whereas in other regions under that hypothesis it is less than 100 km. in depth. This raises the question whether the regional departures from isostasy are carried as strains within the zone of compensation or are transferred in part to the deeper body of the earth. There are reasons for believing that the former is the case, pointing by inference to a zone of markedly diminished rigidity between the rigid lithosphere and still more rigid centrosphere. The geodetic evidence consists in the large values of the squares of the residuals for solution B, the solution which postulates extreme rigidity and compensation at infinite depth. For the whole United States, as shown in the Table XIX, p. 293, the mean value of the squares of the residuals for solution B is 10.7 times the value for solution H. But for group 12, that for which the most probable depth of compensation is 305 km., the distinction is still greater; solution B showing a mean-square residual 28 times greater than for solution E. Dividing in this way the value for solution B by the value for the most probable solution, and taking the mean for all those groups which indicate a depth of compensation greater than the average for the United States, it is found that the ratio is twice THE STRENGTH OF THE EARTH'S CRUST 297 as great for the groups with deep compensation as for the United States as a whole. That is, the groups with deep compensation, instead of showing a leaning toward solution B show on the con- trary more definitely that it is not true. The hypothesis of uniform compensation complete at a certain depth appears to be more nearly true for regions with deep compensation than for shallow com- pensation. This does not mean, however, a lesser rigidity of the crust for the regions with deep compensation, their high capacity to carry strain being shown by the large gravity anomalies which are found in places within them. There seems to be no evidence, however, that the zone of diminished rigidity is sharply bounded or is marked by real liquidity. It is doubtless due to the gradual rise of temperature with depth, overcoming within a certain zone the influence of the increasing pressure. Seismologic and tidal evidences show, furthermore, that under stresses of relatively brief duration the earth acts as a unit and as an elastic rigid body. The physical condition of the zone of low rigidity may approach that of a highly viscous fluid, the time element thus entering within these limits as a fundamental factor. This zone is incapable of bearing pronounced strains for long periods in the manner of the zone above. In geologic operations it thus serves to separate the mode of expression of forces gen- erated below from those originating above this level. The former give rise to the great compressive movements in the outer zone, the latter to the vertical movements not determined by tangential compression. INTERPRETATION OF DEFLECTION RESIDUALS IN TERMS OF MASSES On p. 59, paper of 1909, Hayford shows that the actual deflec- tions of the vertical average only one-tenth of what they would be if the continent and the portions of the ocean basins which were included in the calculations were both underlain by matter of the same density and the relief sustained wholly by the rigidity of the crust. The effect of the topography calculated on this assumption -that the density is uniform and the larger as well as the smaller features are sustained by rigidity gives what is known as the topographic deflections. These, as stated above, average ten times 298 JOSEPH BARRELL the value of the actually observed deflections. The surface may be regarded, therefore, as nine-tenths compensated by variations of density. The details for the five more significant groups are given below: 1 TABLE XX i 2 3 4 S 6 7 8 d "o cji M$ 1 s^S Sgg ffi No. Area of Group 1 C/2 ij & *Si O 4> Jg-3*S op g S can of Topograp Deflections wi out Regard to S can Residual of lution H withe Regard to Sign sill rcentage of Co pleteness of ] static Compen tion for Solution * dn % S > 12. . . . Parts of Minn., N.Dak., S.Dak., Neb., Kan 36 305 8.23 2.17 o. 26 74 8 Parts of Utah, Nev., Cal 42 66 32-23 3-57 . II 89 IO . . . Cal., southern part C7 126 65 44 3 9 1 06 O4. 9 Cal., northern part 60 176 60.50 2-93 05 95 14 Northern Cal., western Ore., and Wash 37 84. 53 68 337 06 QA Whole United States 733 122 3O 37 2 01 O IO no Group 12 gives the greatest depth for uniform compensation. By using the residual for Solution E, 2.09, the percentage of completeness of compensation would have been 75, a trifle more than for Solution H, but still next to the least perfect in the United States. Group 8, the Great Basin region, has the lowest depth of com- pensation but shows about the average approximation to isostatic equilibrium. Groups 10, 9, 14 comprise the Pacific Coast Ranges. They give the highest topographic deflections of the United States, doubtless on account of the great relief of the ocean basin and continental border, but the actually observed deflections do not differ greatly from group 8 or the mean for the whole United States. The result is that in this mountain region bordering the continent the degree 1 Taken from pp. 56, 58, 69, and illustration No. 2, Hay ford, 1909. THE STRENGTH OF THE EARTH'S CRUST 299 of completeness of compensation is the highest in the United States. On the basis of the figures for the whole United States Hayford writes: "The average elevation above mean sea-level being about 2,500 feet, this average departure of less than one-tenth from com- plete compensation corresponds to excesses or deficiencies of mass represented by a stratum only 250 feet (76 meters) thick on an average." 1 It is this last statement, interpreting the deflection in terms of mass, which has meaning to the geologist. It has been widely quoted as perhaps the chief geologic result of the work and yet the writer believes that it is without basis. By an oversight of the author he misinterprets his results. If the present writer is correct in making this statement it should not be taken, however, as a criticism of the mathematical portion of the work. The sea-level is from the standpoint of the problem of isostatic compensation but little more than a datum surface. Imagine the ocean water to be converted into rock of density 2 . 7 of the same mass as the water and resting on the present ocean bottom. Every thousand feet of water would be replaced by 380 ft. of rock. Then the sea-level surface after this transmutation is seen to lose all real significance. 2 To show the fallacy of taking this level as a basis for interpreting the departures from compensation in terms of thick- nesses, let attention be given to groups i, 2, 3, 4, 6, n, 3 which cover the United States east of the Mississippi River. The average departure of these from compensation is o . 1 1 , which on the basis of Hayford's statement means that the surface on the average departs but 275 ft. from the level which would give complete isostatic equilibrium on the hypothesis of uniform distribution of compensa- tion to a depth of 122 km. If, however, this eastern third of the United States be regarded by itself, its average elevation may be assumed as 1,000 ft. (it is probably less). By the same reasoning as Hayford applied to the whole United States, n per cent of this is no ft. Therefore although the average deflections are slightly 1 1909, p. 59. 2 More accurately, the equivalent rock should be imagined as suspended at the mean depth of the water, but the effect of the difference in level is negligible upon the topographic deflection. 3 1909, p. 59. 300 JOSEPH BARRELL greater than for the United States as a whole, it would be concluded that for the region east of the Mississippi the departure from the levels giving complete compensation averages not more than no ft. instead of the 275 ft. previously stated. Or, again, imagine a rise of ocean-level so that the average eleva- tion of this part of the continent is reduced to 100 ft. without changing the detail of the topography. The deflections would suffer 'only small alterations due to the added mass of water. Although the crust remained without change, the same reasoning would then lead to the conclusion that the topography departed on the average but n ft. from the levels which would give complete compensation. In computing the influence of the topographic irregularities and their compensation upon the deflection of the vertical, all the topography was taken into account up to a radial distance of 4,125 km. from each station. This radius is approximately the length of 37 of latitude. It embraces the Pacific Ocean out to the Hawaiian Islands and to ten degrees south of the equator, and the Atlantic Ocean out to the Azores. The relief within this region ranges from 8,340 m. north of Porto Rico to +6,220 m. in Mount McKinley, +6,247 m Chimborazo; a total differential relief of about 14,590 m. About one-half of the topography surrounding the coast stations consists of ocean bed. Even for the stations in Minnesota, farthest removed from the sea, about one-third of the surrounding topography within the limits is deep ocean, but lying at a greater distance and carrying lesser influence. The average depth of the oceans influencing the deflection of the station at mean distance inland may be assumed for purposes of illustration to be about 5,000 meters. This depth of water is equivalent in mass to 1,900 m. of rock of density 2 . 67, leaving an effective ocean depth of 3,100 m. Add the mean continental elevation of 760 m. to this, and 3,800 to 3,900 m. represents about the effective mean relief between continent and ocean. On coast stations this differential relief has greatest influence. For inland stations the several portions of the continent have proportionately more effect. For the United States as a whole it is this relief of between 3,500 and 4,000 m. between continent and ocean, more than the relief between the major features of the continent, which is nine-tenths compen- THE STRENGTH OF THE EARTH'S CRUST 301 sated by the corresponding variations in crustal density, not the 760 m. which is the average elevation of the United States above sea-level. It is the belt of Pacific coast stations which measures more closely than other groups the degree of compensation accompany- ing the continental relief above the ocean bottoms. These stations lie in groups 10, 9, and 14, for which the mean residuals are but 0.06, 0.05, and 0.06 of the mean topographic deflections respec- tively. These residual deflections indicate that for this coastal zone the departures from complete compensation amount to but 5 or 6 per cent. If the mean effective relief which controls this be assumed as 4,000 m., then the mean departure from equilibrium is represented by a mass 200 to 240 m. thick, approximately between 650 and 800 ft. On the other hand, groups 5 and 12 are those farthest removed from the ocean basins and their deflections are controlled most largely by the internal continental relations. For them the departures from complete isostatic compensation as measured by the ratio of the mean residuals to the computed topographic deflections amount to 42 and 26 per cent. The mass to which this is equivalent may be no greater than the 5 per cent departure on the Pacific coast. These estimates fall into the same order of magnitude as that of the masses represented by the gravity anomalies. This reconnaissance of the problem is sufficient for present pur- poses. It is readily seen that even greater difficulties stand in the way of a precise statement regarding the equivalence of mass corresponding to deflections of the vertical than arose in the inter- pretation of the gravity anomalies. The residual for each observed deflection is the sum of the influences of all the excesses and defi- ciencies of mass as compared to solution H on all sides of a station. The effect of each unit varies inversely with the square of the distance and directly with the sine of the angle which the line of force makes with the horizontal passing through each station. A combination of the data from the measurements of the intensity of gravity with those of the deflections of the vertical would apparently be necessary to state for each region the equivalence in terms of mass which is implied by the residual at each station. 302 JOSEPH BARRELL MAXIMUM LOADS INDICATED BY ANOMALIES Hayford and Bowie consider that 0.0030 dyne of anomaly may be regarded as equivalent to 100 ft. of rock possessing a density of 2.67. From the previous considerations it would seem that this is probably too high for a mean figure, but may apply to certain areas, especially those with extremely broad boundaries. In other regions 0.003 may be far too high, since it is shown under the topic " Vari- able or Constant Depth of Compensation" that in certain parts of the United States the depth of the zone of compensation probably goes notably deeper than in other parts and the density may be distributed either nearly uniformly or with considerable irregularity. The greatest depth of compensation indicated for any region is 305 km. A unit thickness of mass uniformly distributed to this depth and to a radius of 166.7 km. would give but 0.0014 of anomaly instead of o . 0024 as given by a depth of 1 14 km., or o . 0030 as taken by Hayford and Bowie. For general use 0.0024 dyne is perhaps the best value, corresponding to a uniform distribution of a unit excess or defect of mass to a depth of 114 km. and to a radial dis- tance of 1 66. 7 km. For the mean anomaly of 0.018 this would give 750 ft. of elevation as the mean departure of the surface of the United States above or below the position giving isostatic equi- librium, instead of 600, or more exactly, 630 ft. as taken by Bowie. The largest known anomaly in the United States is at Seattle, 0.093. This corresponds to a defect in mass equivalent to a stratum 4,000 ft. thick if the divisor is 0.0024, a stratum 3,200 ft. thick if the divisor is 0.0030. At Olympia, but 50 miles or 80 km. distant, the anomaly is +0.033, corresponding to excesses of mass of 1,375 or 1,100 ft., according to the divisor. The difference of regional load between Olympia and Seattle becomes 5,375 or 4,300 ft. But these relations of unit thickness of mass to the gravity anomaly are based on the assumption that the excess or deficiency of mass extends to as great a radial distance as 166.7 km. radius. This minimizes the thicknesses or densities needed to account for the anomalies above what would be required for a more local concentration of mass. But an inspection of the distribution of gravity and deflection residuals shows that in many cases the masses THE STRENGTH OF THE EARTH'S CRUST 303 producing the greater disturbances have much smaller size. This is especially striking in the case of the largest negative anomaly in the United States, that at Seattle, only 50 miles from the large positive anomaly at Olympia. The latter is surrounded on all sides by negative anomalies as follows: DISTANCES FROM OLYMPIA, WASHINGTON Astoria, Ore 76 miles S.W. . 013 dyne anomaly Heppner,0re 195 " S.E. -.027 " Skyhomish, Wash.. 84 " N.E. -.028 " Seattle, Wash 50 " N.N.E. -.093 " The excess of mass which exists in the vicinity of Olympia, above that required for compensation under solution G, must therefore be much less than 166.7 km. (102.5 miles) in radius. The same is doubtless true of that excessive deficiency which exists at Seattle, since the anomaly sinks to less than one-third the value at Sky- homish only 45 miles east, and changes to a large positive anomaly at Olympia, 50 miles south-southwest. The large positive mass in the vicinity of Olympia must dimin- ish appreciably the effect of the still larger negative mass in the vicinity of Seattle. The latter with the other surrounding negative masses must diminish still more the anomaly due to the positive mass at Olympia. Furthermore, it is highly improbable that the observations at Seattle should happen to be made at the point of really maximum anomaly. Let the very moderate assumption be made then that the abnormal Seattle mass as a unit by itself would give a maximum anomaly of o.ioo dyne. It would doubtless give more. Let limiting assumptions be made as to the dimensions and density of this mass such that the actual volume and density are quite probably embraced somewhere within these limits. Tables XXI 1 and XXII show the results of such assump- 1 Table XXI is readily derived from Table X, Part III. Take, for example, the cylinder of radius 1,280 meters, depth of 1,000 feet, and density o. 267. Multiply its dimensions by 30 and the volume of each unit portion will be increased by the cube of 30. The attraction of each unit of mass on the given point will vary inversely with the square of the distance and will therefore be diminished by the square of 30. The anomaly will consequently increase directly with the dimensions, provided that the density remains constant. This gives the basis for the calculations in column 2, Table XXI. 34 JOSEPH BARRELL tions. In Table XXI the attracting mass is supposed to have the form of a vertical cylinder. With a given anomaly the deficiency TABLE XXI VERTICAL CYLINDERS GIVING A NEGATIVE GRAVITY ANOMALY OF o.ioo DYNE AT CENTER OF TOP SURFACE OF CYLINDER I 2 3 4 5 Diameter 76 . 8 km. 51 .2 km. 102.4 km. 51 .2 km. Depth. . 9.15 km. 30.5 km. 61 .0 km. 61 .0 km. Density o 3i o i? o 07 o 12 2.80 Density 2.49 2.65 2.73 2.68 Thickness of cylinder of same area and mass, but density 2 67 !i,o8o m. 3,550 ft. 1,700 m. 5,600 ft. 1,700 m. 5,600 ft. 2,770 m. 9,080 ft. Anomaly per 100 feet of mass of density 2.67 expanded to depth of cylinder as given in second line 0.0028 dyne 0.0018 dyne 0.0018 dyne o.oon dyne TABLE XXII SPHERES GIVING A NEGATIVE GRAVITY ANOMALY OF o. 100 DYNE AT POINT VERTI- CALLY ABOVE ON THE SURFACE OF THE EARTH I 2 3 4 5 Diameter 50. km. 100. km.