551.22 St29 V.10 cop. 2 ytypq MISCELLANEOUS PAPER S-73-1 STATE-OF-THE-ART FOR ASSESSING EARTHQUAKE HAZARDS IN THE UNITED STATES Report: 10 ATTENUATION OF HIGH-FREQUENCY SEISMIC WAVES IN THE CENTRAL MISSISSIPPI VALLEY by Otto W. Nuttii, John J. Dwyer Department of Earth and Atmospheric Sciences St. Louis University St. Louis, Missouri 63156 -, July 1978 Report 10 of a Series Approved For Public Release; Distribution Unlimited Vm \.W»t* ,fl ♦! SEP 2 8 WT8 1,1111111 j Prepared for Office, Chief of Engineers, U. S. Army Washington, D. C 20314 Under Purchase Order No. CW-77-M-2480 Monitored by Geotechnical Laboratory U. S. Army Engineer Waterways Experiment Station P. O. Box 631, Vicksburg, Miss. 39180 Whe The person charging this material is re- sponsible for its return to the library from which it was withdrawn on or before the Latest Date stamped below. Theft, mutilation, and underlining of books are reasons for disciplinary action and may result in dismissal from the University. To renew call Telephone Center, 333-8400 UNIVERSITY OF ILLINOIS LIBRARY AT URBANACHAMPAIGN DEC 2 NOV 18 i^ my 2 L161— O1096 Unclassified V. /o SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) REPORT DOCUMENTATION PAGE READ INSTRUCTIONS BEFORE COMPLETING FORM 1. REPORT NUMBER Miscellaneous Paper S-73-1 2. GOVT ACCESSION NO, 3. RECIPIENT'S CATALOG NUMBER 4. TITLE (and Subtitle) STATE- OF- THE- AET FOR ASSESSING EARTHQUAKE HAZARDS IN THE UNITED STATES; REPORT 10, ATTENUATION OF HIGH-FREQUENCY SEISMIC WAVES IN THE CENTRAL MISSISSIPPI VALLEY 5. TYPE OF REPORT & PERIOD COVERED Report 10 of a series 6. PERFORMING ORG. REPORT NUMBER 7. AUTHORfsJ Otto W.'Nuttli John J. Dwyer V - 8. CONTRACT OR GRANT NUMBERfs; Purchase Order No. CW-T7-M-2U80 9. PERFORMING ORGANIZATION NAME AND ADDRESS Department of Earth and Atmospheric Sciences St. Louis University St. Louis, Missouri 63156 10. PROGRAM ELEMENT. PROJECT, TASK AREA a WORK UNIT NUMBERS 11. CONTROLLING OFFICE NAME AND ADDRESS Office, Chief of Engineers, U. S. Army- Washington, D, C. 2031U 12. REPORT DATE July 1978 13. NUMBER OF PAGES 75 t4. MONITORING AGENCY NAME ft AODRESSC// d//feren( from Controlling Ofllce) U. S. Army Engineer Waterways Experiment Station Geotechnical Laboratory P. 0. Box 631 Vicksburg, Mississippi 39l80 15. SECURITY CLASS, (ot thia report) Unclassified 15a. DECLASSIFI CATION/ DOWN GRADING SCHEDULE 16. DISTRIBUTION ST ATEMENT fo/ Ui/« RoporO Approved for public release; distribution unlimited. 17. DISTRIBUTION STATEMENT (of the abstract entered In Block 20. U different from Report) 18. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on reverse slda If necesaaiy and Identify by block number) Earthquake engineering Mississippi Valley Earthquake hazards Seismic waves Earthquakes State-of-the-art studies Ground motion Wave attenuation 2Qv ABSTRACT (Caatbtue aa rararwa afdto ff rra^ceaaary aad Identify by block number) This study was concerned with the attenuation of high-frequency earthquake waves in the central Mississippi valley. The data were obtained from seismo- graphs which measured the vertical component of ground motion. Recording was on analog magnetic tape and on l6-mm photographic film. Most attention was devoted to a study of Lg waves, which are higher mode surface waves that produce the largest ground motion. At frequencies of 1 to 10 Hz the specific dissipation ( Continued) DO FORM \ JAN 73 1473 EOrnON OF t NOV 65 IS OBSOLETE Unclassified SECURITY CLASSIFICATION OF THIS PAGE (Whert Data Entered) Unclassified SECURITY CLASSIFICATION OF THIS PAGE(Wiaii Data Entered) 20. ABSTRACT (Continued). factor Q of the Lg waves was found to be 1500. The corresponding coefficient of anelastic attenuation is O.OOO6 km" for 1-Hz waves and O.OO6 kin"^ for 10-Hz waves. Other investigators have found Q for tectonic areas such as California to be about 200 to 250, which implies that the value of the coefficient of anelastic attenuation in those regions is almost ten times greater than in the central Mississippi valley. The results of the present study indicate that in the central United States high-frequency waves will produce significant ground motions at relatively large distances, which is not the case in California or other tectonic areas. In the frequency domain the Fourier displacement spectra of the Lg motion showed the typical flat level at the lower frequencies and the rapid fall-off of amplitude with increasing frequency at the high frequencies. In the time domain, on the other hand, the level of ground displacement in the source region was essentially constant between frequencies of 1 to 10 Hz. This fact, together with the relatively low attenuation of the Lg waves, indicates that waves of frequencies as high as 10 Hz may have relatively large amplitudes and accelerations at epicentral distances as large as hundreds of kilometers for central United States earthquakes. Unclassified SECURITY CLASSIFICATION OF THIS PAGEflWien Dale Entered) THE CONTENTS OF THIS REPORT ARE NOT TO BE USED FOR ADVERTISING, PUBLICATION, OR PROMOTIONAL PURPOSES. CITATION OF TRADE NAMES DOES NOT CONSTITUTE AN OFFICIAL EN- DORSEMENT OR APPROVAL OF THE USE OF SUCH COMMERCIAL PRODUCTS. PREFACE This report was prepared by Dr. 0. W. Nuttli and Mr. J. J. Dwyer, Department of Earth and Atmospheric Sciences, St. Louis University under Purchase Order No. CW-7T-M-2U80. It is part of ongoing work at the U. S. Army Engineer Waterways Experiment Station (WES) in Civil Works Investigation Study, "Methodologies for Selecting Design Earthquakes," sponsored by the Office, Chief of Engineers, U. S. Army. Preparation of this report was under the direction of Dr. E. L. Krinitzsky, Chief, Engineering Geology Research Facility. General direction was by Dr. D. C. Banks, Chief of the Engineering Geology and Rock Mechanics Division, and Mr. J. P. Sale, Chief, Geotechnical Laboratory. COL J. L. Cannon, CE, and Mr. F. R. Brown were Director and Technical Director, respectively, of WES during the period of this study. CONTENTS Page PREFACE 2 PART I: INTRODUCTION ....... 5 PART II: DATA ' 8 PART III: INTERPRETATION OF DATA 45 PART IV: SUMMARY AND CONCLUSIONS - 72 REFERENCES 74 Digitized by the Internet Archive in 2013 http://archive.org/details/stateoftheartfor10chan ATTENUATION OF HIGH-FREQUENCY SEISMIC WAVES IN THE CENTRAL MISSISSIPPI VALLEY PART I: INTRODUCTION 1. Most of the damage done by earthquakes results from ground shaking with frequencies of about 1 to 10 Hz. In order to design structures to withstand the effects of such ground motion the engineer needs information on the size of the motion in the source region and on the attenuation of the motion with distance from the source. In the western United States, where moderate to major earthquakes occur rather frequently, an empirical data base of strong-motion seismograms has been built up. This data base is invaluable for developing formulas which can be used to predict ground motion at a selected distance from the earthquake, assuming certain source characteristics of the earth- quake. 2. The existing data base of strong-motion seismograms in the central and eastern United States is small because the frequency of occurrence of moderate to major earthquakes in those regions is less than in the western region, and because strong-motion seismographs have only been operating in the central and eastern regions for less than ten years, as opposed to fifty years in the West. Thus the central and eastern United States data base of strong-motion seismograms is inadequate for developing empirical formulas to be used for the pre- diction of ground motion. Also, it is too limited to determine to what extent the western United States data are applicable to the cen- tral and eastern regions. 3. The felt and damage areas of United States earthquakes east of the Rocky Mountain front are appreciably larger than those of the same magnitude to the west of the front (Gutenberg and Richter , Brazee , Nuttli , Nuttli and Zollweg , Necioglu and Nuttli ), Nuttli concluded that this is the result of differences in attenuation of high frequency waves in the two areas. From an analysis of the seis^ grams of moderate-sized earthquakes (body-wave magnitude, m^, between mo 3 and 5.5) he determined that the coefficient of anelastic attenuation of 1-Hz surface waves v/as 0.0006 km in the central United States, ten times smaller than in the western region. Later studies by Street and by Jones et al indicate that the coefficient of anelastic attenu- ation for 1-Hz waves in the northeastern and southeastern reeions is similar, but not identical to, that in the central reeion. 4. Data On the attenuation of 1-Hz waves are readilv obtainable from the seismoerams of the World-Wide Standardized Seismograph Network (WWSSN) . However, this network does not have the capability of pro- viding data for higher freauencv waves, up to 10 Hz, which are respond sible for much of the damage done to structures. The WWSSN is in^~ adequate for this purpose because 1) the magnification of the seismo- graphs peaks at less than 2 Hz, and falls off rapidly at higher fre- quencies, 2) the recording rate is too slow to permit resolution of the higher frequency waves, 3) the seismograph stations are too far apart to record the high frequency waves which attenuate relatively rapidly with distance. 5. Networks of seismographs designed to detect and locate micro- earthquakes are ideally suited for studies of the attenuation of high frequency waves. The seismographs have peak magnifications at fre- quencies of 10 to 20 Hz, and have high magnification over the frequency range of interest. Furthermore, the seismographs are closely spaced so that there are an adequate number of data points to determine the fall-off of amplitude with distance. Thus the 14-station network of microearthquake seismographs operated by Saint Louis University since 1974 in the central Mississippi Valley provides the kind of data re- quired to determine the attenuation of high frequency waves at small epicentral distances. Because microearthquakes of the desired magni- tude occur on the average about twice a month in that region, there is a sufficient amount of data to do a meaningful study. 6. All the instruments of the Saint Louis University micro- earthquake network measure the vertical component of ground motion only. This presents no problems for attenuation studies, because the horizon- tal and vertical components of ground motion attenuate in the same way. However, the lack of horizontal component data makes it im- possible to say anything about the ratio of the amplitudes of the horizontal to the vertical component of motion, which is another quan- tity of engineering interest. Furthermore, the horizontal component of high frequency ground motion of earthquakes usually is larger than the vertical. Thus the motion obtained in this study will not repre- sent the largest motions that were generated by the earthquakes. PART II: DATA 7. Figure 1 shows the location of the seismographs which pro- vided the data used in this study, as well as the microearthquakes that occurred between July^ 1974 and December 1977. Table 1 lists the name of the stations, their code abbreviations, theiT latitude and longitude and their peak magnification, both for Develocorder recording and magnetic tape recording. The seismographic data are recorded in two ways; on photographic film (Develocorder) and on analog magnetic tape. Figure 2 shows a normalized frequencyr-response curve for the film recording and Figure 3 a similar curve for the magnetic tape re- cording. To obtain actual magnifications the ordinates in Figures 2 and 3 must be multiplied by the peak magnifications given in Table 1, 8. Eighty-nine microearthquakes, occurring during the interval 16 August 1974 through 13 February 1977, provided the basic data used in the studies. The earthquakes had body-wave magnitudes of 0.8 to 2.4, Smaller earthquakes did not produce waves of sufficient amplitude to be useful for attenuation studies, and larger earthquakes saturated the recording system. Earthquake focal depths are in the range of 1 to 20 km. Most of the earthquakes are associated with the New Madrid faulted zone, which is about 175 km long and 25 to 50 km wide. Epi- central distances varied from 3 to 250 km, although for any given earthquake the range of distances usually was less. Table 2 lists the earthquakes studied. 9. Three procedures were employed to obtain the data used in the study. The first two made use of time-domain measurements, and the 8 92 88 39- 38 . ROL 37- 36- mn #ou 35- 92 REGIONAL MfiP CUriULflTIVE EVENTS 01 JUL 1974 TO 31 DEC 1977 LEGEND . A STATION o EPICENTER Figure 1. Location of seismograph stations and microearthquakes in central Mississippi valley Table 1 List of Seismograph Stations Code Location Crutchfield, KY Latitude Longitude W Peak Magnif Develocorder 340,000 ication Analog Tape CRU 36.595 89.020 80.000 DON Dongola, MO 37.176 89.933 1,200,000 320,000* DWM Dogwood , MO 36.805 89.490 85,000 20,000 ECD Elkchute Ditch, MO 36.060 89.940 180,000 40,000 ELC Elco, IL 37,285 89.227 1,300,000 320,000* CRT Gratio, RN 36.264 89.425 300,000 80,000 LST Lone Star, MO 36.523 89.731 170,000 40,000 NKT Nankipoo, TN 35.850 89.544 350,000 40,000 OKG Oak Grove, TN 35.626 39.835 390,000 80,000 PGA Paragould, AK 36.060 90.620 200,000 40,000 POW Powhattan, AK 36,150 91.180 1,400,000 320,000* RMB Rombauer , MO 36.886 90.278 680,000 320,000* TYS Tyson Valley, MO 38.515 90.568 680,000 160,000* WCK Wilson Creek, KY 36.934 88,874 680,000 160,000* *At some times the magnification was one-half the value given in the table. 10 1 1— I — I I I I 1 1 T 1 1 — I I I I LiJ O H Q UJ N -J < Qc: o 0.1 0.01 I I M ll 10 f (Hz) J I I I I 1 1 100 Figure 2, Normalized magnification curye for Develocorder recording 11 10 L I I I I I I < < 10 10 T 1 1 I i I II I Mini J I ' I I 1 1 1 1 T — n 10" 10' FREQUENCY (HZ) Figure 3. Normalized (to 1000) magnification curve for analog magnetic tape recording 12 Table 2 List of Earthquakes Studied No. Date 16 Aug 74 Origin Time Latitude U. T. °N Longitude \ 1 07-30-57.9 36.15 89.70 1.1 2 04 Jan 75 09-22-04.6 36.28 89.46 1.9 3 01 Feb 75 16-04-24.5 36.05 89.87 1.9 4 20 Feb 75 02-52-21.4 36.08 89.84 1.3 5 01 Jun 75 03-40-11.9 36.56 89.60 2.0 6 28 Jun 75 13-11-01.3 36.57 89.66 1.5 7 05 Jul 75 18-38-16.7 36.13 89.78 1.4 8 09 Aug 75 06-40-24.9 36.59 89.59 1.8 9 09 J*-Ug 75 19-08-39.4 36.88 89.43 1.9 10 01 Sep 75 15-33-11.2 36.55 89.86 1.0 11 05 Sep 75 21-46-14.5 36.13 89.43 1.7 12 10 Sep 75 12-41-45.9 36.30 91.80 0.6 13 13 Sep 75 06-53-52.9 36.73 89.21 1.4 14 17 Sep 75 00-00-34.2 36.59 89.63 1.8 15 18 Sep 75 08-20-23.3 36.63 89.51 1.7 16 21 Sep 75 08-08-32.6 36.31 89.51 1.1 17 21 Sep 75 22-09-21.5 36.57 89.76 0.8 18 24 Sep 75 10-37-54.4 36.72 89.69 2.2 19 04 Oct 75 06-53-15.3 35.81 90.17 1.4 20 12 Oct 75 14-47-40.1 36.08 (Continued) 89.78 1.9 (Sheet 1 of 5) 13 Table 2 (Continued) No. Date 03 Dec 75 Origin Time U.T. Latitude °N Longitude \ 21 10-54-42.2 36.56 89.80 1.3 22 07 Dec 75 12-18-28.7 35.71 90.06 1.8 23 05 Jan 76 03-46-30.0 35.94 89.52 1.5 24 10 Jan 76 10-28-35.9 36.13 89.74 1.2 25 15 Jan 76 07-40-52.6 37.37 90.00 1.5 26 20 Jan 76 12-44-08.5 36.57 89.60 1.5 27 23 Jan 76 00-56-39.6 36.55 89.60 2.0 28 03 Feb 76 07-04-01.3 36.48 89.56 1.2 29 16 Feb 76 04-31-50.3 36.04 89.84 1,1 30 28 Feb 76 00-14-35.2 36.51 89.54 1.9 31 06 Mar 76 23-07-32.1 36.48 89.56 1.4 32 15 Mar 76 16-15-26.7 36.57 89.46 1,2 33 26 Mar 76 08-50-37.4 36.61 89.59 1,6 34 04 Apr 76 02-16-17.8 37.82 90,99 2.0 35 06 Apr 76 18-42-54.4 36.51 89.62 1,4 36 08 Apr 76 16-28-17.8 37.12 88.88 2,1 37 10 Apr 76 02-47-55.9 36.55 89.66 1,4 38 10 Apr 76 03-20-23.4 36.05 89.82 1,4 39 10 Apr 76 12-50-34.6 36.44 89.51 1.2 40 10 Apr 76 14-16-18.3 36.10 89.73 1,2 41 14 Apr 76 23-47-54.0 (Cont: 35.65 inued) 90.47 i.g (Sheet 2 of 5) 14 Table 2 (Continued) No. Date 15 Apr 76 Origin Time U. T. Latitude °N Longitude \ 42 10-25-33.9 36.72 89.52 1.0 43 09 May 76 10-11-29.5 37.10 90.97 1.5 44 17 May 76 05-17-57.9 36.38 89.53 1.2 45 20 May 76 03-12-46.4 35.82 90.18 1.5 46 21 May 76 10-41-28.2 36.22 89.38 1.2 47 23 May 76 08-37-09.5 36.13 89.74 1.7 48 24 May 76 07-30-17.5 36.07 89.45 1.6 49 27 May 76 08-47-47.2 35.67 90.42 1.7 50 28 May 76 07-10-50.7 36.60 89.59 1.2 51 28 May 76 07-41-36.0 35.85 90.01 1.2 52 03 Jun 76 13-54-14.4 35.94 90.13 1.8 53 18 Jun 76 20-13-31.8 36.40 89.54 1.1 54 27 Jun 76 02-41-35.1 36.30 89.51 1.0 55 04 Jul 76 03-02-50.5 36.77 89.15 1.7 56 04 Jul 76 07-21-53.9 36.77 89.15 1.5 57 23 Jul 76 11-38-36.3 36.91 88.96 1.3 58 27 Jul 76 01-38-27.8 36.46 89.53 1.0 59 03 Aug 76 04-52-39.0 36.69 89.79 1.4 60 11 Aug 76 02-15-29.3 36.67 89.56 1.6 61 21 Aug 76 07-31-01.0 35.03 90.41 2.1 62 27 Aug 76 04-03-52.5 (Cont: 36.17 Lnued) 89.41 1.0 (Sheet 3 of 5) 15 Table 2 (Continued) No. Date 11 Sep 76 Origin Time U. T Latitude °N Longitude \ 63 05-59-13.2 35.97 89.81 1.2 64 15 Sep 76 11-08-40.9 36.57 89.63 1.2 65 01 Oct 76 14-44-56.1 36.55 89.67 1.5 66 03 Oct 76 03-46-03.5 36.56 89.72 1.3 67 04 Oct 76 12-06-00.2 35.84 90.14 1.6 68 19 Oct 76 07-15-58.3 37.08 88.77 1.2 69 22 Oct 76 13-12-22.1 36.43 89.51 1.3 70 22 Oct 76 09-59-02.3 36.43 89.49 1.2 71 29 Oct 76 06-29-54.8 36.43 89.39 1.0 72 06 Nov 76 11-37-59.4 37.28 89.47 1.7 73 14 Nov 76 11-39-46.0 35.66 90.46 2.4 74 15 Nov 76 01-31-46.4 35.61 89.90 1.4 75 23 Nov 76 01-24-15.5 36.55 89.62 1.2 76 23 Nov 76 05-36-10.2 36.26 89.45 1.3 77 06 Dec 76 23-14-53.2 35.82 90.15 1.1 78 15 Dec 76 11-57-07.1 36.07 89.80 1.9 79 01 Jan 77 11-40-06.2 36.92 90.42 1.3 80 02 Jan 77 20-33-23.3 36.47 89.55 1.4 81 04 Jan 77 03-59-18.2 36.54 89.66 1.3 82 04 Jan 77 12-21-27.6 36.12 89.73 1.1 83 23 Jan 77 21-03-15.3 37.55 (Continued) 89.78 2.2 (Sheet 4 of 5) 16 Table 2 (Concluded) No. Date 29 Jan 77 Origin Time U. T. Latitude °N Longitude \ 84 22-08-37.8 36.53 89.58 2.2 85 01 Feb 77 09-30-04.3 36.28 89.47 1.2 86 08 Feb 77 10-20-42.5 36.50 89.57 1.6 87 09 Feb 77 06-25-47.5 35.86 90.09 1.2 88 13 Feb 77 09-15-29.2 36.23 89.49 1.2 89 17 Feb 77 08-34 00.8 36.15 89.51 2.1 (Sheet 5 of 5) 17 third of frequency-domain measurements. The simplest time-domain meas- urement technique utilized the Develocorder film records. Wave ampli- tudes were read directly by means of a millimeter scale from an enlarged image of the film. This gave amplitude data at a single fre- quency, 10 Hz, which is near the frequency of peak magnification of the Develocorder system. The other time-domain method utilized narrow bandpass filtering of the analog magnetic tape. Playbacks gave filtered seismograms with center frequencies of 0.5, 1, 2, 3.12, 5 and 8 Hz. Wave amplitudes were measured from the playbacks by means of a millimeter scale. For the frequency-domain method a broadband play- back of the magnetic tape record was obtained, and this playback was digitized and Fourier analyzed to obtain the spectrum of the ground motion. The digitizing interval was 0.025 sec and the sample length varied from 7 to 20 sec, depending on the distance from the earthquake. For all three types of analysis the records were corrected for system magnification, so that the end product was a time history or a spectrum of the ground motion, 10. The Develocorder film records were used for an analysis of the P-wave motion. Sometimes the P wave is impulsive, consisting of a single cycle of wave motion, and other times it consists of a train of waves, depending upon the individual earthquake and upon soil condi- tions at the recording site. In any case the amplitude which was read was that of the peak of the P-wave motion (zero-to-peak amplitude or one-half peak-to-peak amplitudes). The P-wave amplitudes, corrected for instrument magnification, were plotted on log-log paper as a 18 function of epicentral distance. A, and fitted by a straight-line curve. The slope of the curve is minus N, where A ^ A"^ (1) 11. Figures 4 and 5 give examples of plots of P-wave data, for earthquakes number 52 and 73. The dashed lines are separated from the straight-line curve by one standard deviation of the logarithm of the amplitude. It is customary to fit close-in P-wave data by an empirical equation such as (1), even though that equation does not take account explicitly of the source radiation pattern, anelasticity , and construc- tive and destructive interference of reflected and refracted waves. The fluctuations in the P-wave amplitude data, which can be as large as an order of magnitude, can be attributed to these and other phenomena such as scattering and soil amplification. 12. Table 3 contains the slopes (N) and the standard deviations of the logarithm of the amplitude for the P-wave motion. Figure 6 is a histogram of the N values. From it or from Table 3 it can be seen that the median value of N is 1.8. 13. Both the Develocorder film records and the analog magnetic tape records were used for time-domain studies of the Lg wave. The Lg wave consists of a train of high frequency surface waves, whose duration is controlled both by dispersion and by scattering. To be 3 consistent with Nuttli's study of 1-Hz Lg-wave attenuation the sus- tained maximum amplitude was read. The sustained maximum motion is 19 lOO a. E A (km) Figure 4. P-wave attenuation data for earthquake #52 20 100 < ^ \ ^ ^ \ ^ ^ \ ^ ^ x\ \ ^ \x ^ N \ \ \ \ ^ ^ \ ^ ^ \ N X \ \ \ ^ \ ^ \ \ \ \ V ^ \ V \ »> \ ^ X\ \ \ ^ \ ^ \ \ X \ ^ \ ^ > \ \ X \ ^ ^ \ \ " \\ ^ X 4 \ \ ^V X X \ ^ \ \ X A-2.4 10 100 A (km) Figure 5. P-wave attenuation data for earthquake //73 21 CO CO > 12 N M-l O C o •H ■P CO C OJ •u ■u o CN CO <|- in >.D 00 (Ti o CN Csl CM CM (N CN Cs! CN CO ti •H O CLJ > OJ Q <; O r^ CT\ ■<1- r-{ in V£> CO r^ 00 o CT> vO ^ 00 CO CTv O 00 O r-{ o O CO o CN CvJ CN rH CO CT^ O 00 o CTi CO r-l vO CN in CO ^ 00 22 CN vO cu <; Q • O CO 4-t 0) O 23 CD c M-l O O -H 4-J • CO O 4-1 ^ CO 0) CO • 3 O cr ^ CN in CO c^ r>. CT\ O CTi C7N ^ vO so SO O • CO o 4-) s C/D Q) ^ CO 3 • r-\ CM CO v£) ^ r^ t~-> r^ r-> ^ a •U t-i CO W 24 15 n~T — TT — I — I — I — I — I — I — I — I — n — n — i — i — i — r Z o > GO o u. o oc UJ 5 CD J l_L 1.0 f UL m «'■«■''■« ■''''''' 1.5 2.0 2.5 N Figure 6. Histogram of P-wave slope values 25 that equaled or exceeded by the largest three cycles of motion. The reason for using maximxim sustained motion rather than peak motion is that the former is a better measure of the size of the earthquake and of the damage potential of the Lg waves than the latter, because the single peak is of short duration and may result from fortuitous constructive interference. 14. In contrast to the P waves, for which an empirical attenu- ation equation was used, the Lg wave in the time domain can be fitted Q by the theoretical relation (Ewing et^ ^1 ) A 'v A"-^^-^ (sin A)"-*-^^ expC-yA) (2) where A is the epicentral distance and y is the coefficient of -1/3 anelastic attenuation. The term A takes account of the decrease -1/2 of amplitude due to wave dispersion, the term (sin A) the decrease of amplitude due to geometric spreading of the wave front, and the term exp (-yA) the decrease in amplitude due to frequency-dependent absorp- tion. Figure 7 gives an example of the attenuation of Lg amplitudes for earthquake number 65. These data are for 10-Hz waves and were taken from a Develocorder record. The dashed lines in the figure in- dicate one standard deviation of the logarithm of the amplitude. The theoretical curve was simply fitted to the data by eye. Later the consequences of this method of curve fitting will be examined. 15. Table 4 contains the absorption coefficient value (y) and the standard deviation of the logarithm of the amplitude for the Lg waves recorded on the Develocorder film. Figure 8 contains a histogram of 26 100 E 10 I I I I ' I T 1 1 — I I I I I ir= 0.008 km: I ■ > " I J I I I I I M 10 100 A (km) Figure 7. 10-Hz Lg attenuation data for earthquake //65 27 to 0) > CO Ha I o o •H I 4-> 4-> • > Q) O - CO d M-l O O -H o -u iz en >- m d <+-< o o •H W • CC o ■U a en 3 • cr o rC ;z CO W O v£) a\ in O 00 o o o o O o o o o o o o 14-1 o 4J 0) 0) en o C7N 0^ c^ in 00 CM CO CM CN CN CM CM Csl CO CO H ^ CM CM H o iH csl iH • bO . . • . . . • • • • c o O o o o O O o o d o O O O cd -H ■u en ^ 00 00 OO o o o o o o o o vO 00 00 o o o o o o 00 o o 00 00 00 o o o o o o OJ Q <; . 00 C o CO ^ •P C/3 - o O o 00 00 vD O O O O O O 00 CO 00 00 00 00 00 00 00 00 o o o o o o o o o o o o o o o o o o o o CO •u 00 00 00 a^ C7\ X) vO vX) vT) vO vO v£) vO 'a (U 1 4-1 c O o , > QJ O <: . bO c O CO ^ ■P en ON CM O in 00 m o 00 n 00 CT. vO O VO r^ H iH CO 00 -J- vO -■ m l4-t O O -H 4J • ctJ o -u :z en 00 00 00 00 00 o 00 00 00 00 00 o o o o o rH o o o o o o o o o o o o o o o o CO 00 00 o o o o o o 00 a\ 00 - 00 00 00 o o o o o o 00 00 00 00 CO 00 o o o o o o o o o o o o •u 0) CO O -P to :3 • cr o ?-i CO W 00 00 o 0^ 00 00 vD O 00 00 CM CO in vO r-» 00 00 00 00 CO 00 00 en Csl rH CTi CO 00 en 00 o CO CO CM - 00 00 00 CO 00 CO 00 o o o o o o o o o o o o o o 00 CO 00 o o o o o o M-l O O -H • CO o u 2 en 00 vO 00 00 00 O CvJ 1^ in M3 r^ 00 30 1 1 1 1 1 1 60 - - - - OBSERVATIONS o - - u. o - - CC 20 liJ m 3 Z - - - — _ 1 » 1 1 1 1 0.002 0.004 0.006 0.008 OOIO 0.012 t (km-') Figure 8. Histogram of 10-Hz Lg y values 31 the Y values obtained from the Lg-amplltude data. The median value corresponds to y = 0.008 km for 10 Hz waves. 16. Narrow bandpass filtering provides an alternate time- domain method of determining the absorption coefficient. As opposed to measurements made directly from Develocorder film, narrow band- pass filtering has the advantage of enabling one to determine the absorption coefficient at a number of frequencies. For this study the center frequencies were 0.5, 1, 2, 3.12, 5 and 8 Hz. At the lower frequencies the signal levels were not much greater than the noise. As a result no good attenuation data were obtained at those frequencies. However, this is not a serious problem, because WWSSN seismograph records provide excellent data for the determination of the absorption coefficient at 0.5 and 1 Hz. Figures 9 through 12 present sample Lg attenuation curves for frequencies of 2, 3.12, 5 and 8 Hz. In these figures the crosses refer to data points, and the bars indicate the noise level on the filtered playback records. 17. Tables 5 through 8 contain the absorption coefficient value (Y) and the standard deviation of the logarithm of the amplitude for the narrow bandpass filtered Lg waves recorded on magnetic tape for frequencies of 2, 3.12, 5 and 8 Hz. Figure 13 contains histograms of the Y values obtained from the data. The median values of Y ^^^ 0.003 km"""" for 2 Hz, 0.003 km"-*" for 3.12 Hz, 0.004 km""*" for 5 Hz and 0.005 km""*" for 8 Hz. 18. For frequency-domain studies the Lg-wave train was digitized and Fourier analyzed, using a window length of approximately 7 to 20 32 10 z o o UJIO o < -2 10 i 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 - — ^" ^nS^^Idon "* \viwcK - - \V . ^ ELCf '-^^^ 1 1 M.I 1 1 1 1 1 1 1 1 1 1 • 10' . 10^ A (KfA) Figure 12. 8-Hz Lg-wave attenuation for earthquake #27 36 Table 5 Absorption Coefficient Values of 2-Hz Lg Waves from Narrow Bandpass Data Standard Deviation Number of log amplitude units Observations 0.257 6 0.146 7 0.270 9 0.339 8 0.243 8 0.334 10 0.226 9 0.186 8 Earthquake Number km 5 0.004 27 0.004 33 0.002 47 0.006 48 0.004 55 0.001 78 0.002 89 0.002 37 Table 6 Absorption Coefficient Values of 3.12-H2 Lg Waves Standard Deviation Number of log amplitude units Observations 0.042 5 0.239 6 0.195 7 0.292 6 0.169 7 0.212 7 0.164 5 0.284 7 0.334 8 0.275 7 0.256 6 0.220 6 0.254 9 0.300 7 0.324 9 0.318 7 0.306 9 0.279 8 0.324 10 0.243 9 0.215 8 0.239 8 38 Earthquake Number L-1 km 2 0.002 5 0.004 6 0.004 7 0.002 8 0.002 9 0.004 11 0.004 14 0.004 21 0.002 22 0.002 23 0.002 24 0.002 27 0.004 30 0.004 33 0.002 37 0.003 47 0.001 48 0.004 56 0.002 78 0.004 84 0.002 89 0.003 Table 7 Absorption Coefficient Values of 5-Hz Lg Waves from Narrow Bandpass Data Standard Deviation Number of log amplitude units Observations 0.153 6 0.206 6 0.148 7 0.219 6 0.164 7 0.307 7 0.168 6 0.155 8 0.192 8 0.171 7 0.173 7 0.199 7 0.254 9 0.239 7 0.267 9 0.309 7 0.228 11 0.227 8 0.301 10 0.240 10 0.236 8 0.304 9 39 Earthquake Number L-1 km 2 0.002 5 0.006 6 0.006 7 0.002 8 0.004 9 0.004 11 0.006 14 0.004 21 0.006 22 0.004 23 0.004 24 0.003 27 0.004 30 0.004 33 0.004 37 0.003 47 0.002 48 0.006 56 0.004 78 0.004 84 0.004 89 0.002 Table 8 Absorpt ion Coefficient Valu( es of 8-Hz Ls Waves from Nar row Bandp; ass Data Earthquake Number km 0.002 Standard Deviation log amplitude units 0.226 Number of Observations 2 6 5 0.004 0.260 6 6 0.006 0.172 7 7 0.004 0.183 6 9 0.006 0.260 7 11 0.006 0.194 6 14 0.002 0.187 8 21 0.006 0.246 8 22 0.004 0.127 7 23 0.006 0.201 7 24 0.004 0.228 7 27 0.004 0.285 9 30 0.004 0.245 7 33 0.004 0.183 9 37 0.002 0.265 7 47 0.004 0.237 11 48 0.006 0.205 8 56 0.006 0.339 10 78 0.006 0.193 10 84 0.006 0.272 8 89 0.004 0.201 9 40 T 1 1 1 r 2 HZ T 1 1 r 3.(2 HZ 10- (/) < > LU if) o Li- o LU CD ± I ± ± ± ± J. ± .000 .002 .004 .006 .008 .000 .002 .004 .006 .008 5 HZ 8 HZ 10- TJTO" isi> 1 z .004 .006 .008 iAf 1 1 1 :5ro .004 .006 .008 y (Km"') Figure 13. Histograms of y values of Lg from narrow bandpass recording 41 sec and a digitizing interval of approximately 0.025 sec. Figure 14 contains a typical amplitude spectrum for the ground motion at Gratio, Tn. for the earthquake of 17 February 1977. The spectrum can be idealized by the two straight lines drawn in the figure, one of which is. horizontal (long periods) and the other has a slope of approximately two (short periods) . Because of low seismograph magnification and low signal-to-noise ratio the spectrum is unreliable at periods greater 9 than 1 sec or less than 0.08 sec. Street ^t al found the spectrum of the Lg ground motion of central United States earthquakes had this simple shape for all earthquakes of m], less than or equal to 3.5, with the corner frequency (frequency at which the two straight-line segments of the spectrum intersect) decreasing as the magnitude or seismic moment increases. 19. The spectra of the ground motion at the stations Dongola, Mo. and Powhattan, Ark. departed from the ideal shape shown in Figure 14. They showed enhanced amplitudes at frequencies near 8 Hz. Such a behavior apparently results from beats in the time history of the ground motion, which is believed due to local site conditions, 20. In the frequency domain the Lg amplitudes for a given fre- Q quency satisfy the relation (Ewing ejt al^ ) A ^ (sin A)"-^''^ exp (-yA) . (3) The data, which consist of spectralamplitudes at a given frequency for a number of stations at various distances, can be fitted by a curve of the type (3) to yield the best value of y fo^ an assigned 42 GRT SPZ FEB 17. 1977 LU CO o Q_ CL PERIOD (SEC) Figure 14. Fourier displacement spectrum of Lg motion at GRT for earthquake #89 43 frequency. 21. Spectral data for 19 earthquakes were analyzed. In general there were fewer usable spectra for a given earthquake than there were available time-domain amplitude data. As a consequence no reliable es- timates of absorption-coefficient values could be made from the fre- quency-domain data. Although unfortunate, this finding does not present a serious problem because the absorption-coefficient values as a function of frequency are well determined by the time-domain measurements. The Lg spectra are useful, however, for determining the 9 seismic moment of earthquakes, as was done by Street et al . 44 PART III: INTERPRETATION OF DATA 22. Table 9 presents the average deviation of the P-amplltude data from the dtralght-llne curves for each station. A value of 125% indicates that on the average the observed amplitude at that station exceeded the value expected from the straight-line curve by 25%. From the table it can be seen that stations DWM, ECD, ELC and PGA had lower than expected amplitudes, by as much as a factor of two, and that stations OKG, POW and RMB had higher than expected amplitudes, by as much as a factor of one and a half. Stations DON, ELC and RMB may be classified as hard-rock sites, CRU, CRT, OKG and WCK as in- termediate-rock sites and DWM and LST as soft-rock sites. From the above it can be seen that there is no correlation between anomalously large or small amplitudes and the rigidity of the surficial rock layer at the station. 23. Table 10 presents the average deviation of the P-wave amplitude data from the straight-line curves for 25-km distance inter- vals. At small distances the amplitude deviations are negative, indicating lower than expected amplitudes. There is a progression to more positive values as the distance increases. From this it follows that the slope of the attenuation curve, corresponding to N = 1.^ is too large. Figure 15 shows the deviations, plotted as crosses, from the straight-line curve of slope -1.8. The dashed-line curve drawn through the crosses has a slope of 1.4, indicating that a value of N = 1.4 in equation (1) will provide the best fit to the P-wave amplitude data. 45 Table 9 Average P-Wave Deviations by Station Average Deviation Station log amplitude units percentage CRU +0 . 018 104 . 2 DON -0.008 98.2 DWM -0.257 55.4 ECD -0.254 55.7 ELC -0.281 52.3 GRT -0.010 97.7 LST -0.036 92.1 NKT -0.148 71.2 OKG +0.192 155.7 PGA -0.219 60.5 POW +0.107 127.9 RMB +0.198 157.8 WCK -0.057 87.6 46 Table 10 Average P-Wave Deviations by Distance Interyal Distance Interval km log Average Deviation amplitude units p( -0.252 ^rcentage 0-25 56.0 25.1-50 -0.235 58.2 50.1-75 -0.209 61.8 75.1-100 +0.050 112.1 100.1-125 +0.128 134.2 125.1-150 +0.099 125.7 150.1-175 +0.188 154.1 175.1-200 +0.174 149.3 >200 +0.140 138.1 47 ' I ' ' ' »l T 1 — r 100 "E o 10 N=l.4 N«L8 J L J < I I t I I J L-JJ 10 100 A (km) Figure 15. P-wave deviations from slope N = 1, 48 24. Romney et^ a]L studied the attenuation of P-wave amplitudes from the underground nuclear explosion GNOME in southeast New Mexico. For paths to the west they found that the P-wave amplitudes satisfied equation (1) with N = 4.0. Romney et_ al did not specify the fre- quency of the ground motion, but presumably it was 1 Hz and higher. Evernden studied the attenuation of Pg waves from explosions in the Nevada Test Site. His data, which were for wave frequencies near 1 Hz, indicated that N = 3.0 for western paths. One expects, in general, for N to increase as the frequency increases. Thus the value N = 1.4 found in the present study represents a very low value of attenuation of high frequency P waves in the central Mississippi valley, compared to the western United States. 25. Table 11 presents the average deviation of the 10-Hz Lg-wave amplitudes by station, as determined from Develocorder records, from the theoretical curve. From the table it can be seen that DWl, ECD, ELC and LST have significantly lower than expected Lg amplitudes, and that CRU, CRT, OKG, POW and RMB significantly higher than expected amplitudes. There is no obvious correlation between site conditions and amplitude anomalies. However, DWM, ECD and ELC had low amplitudes for both P and Lg waves, and OKG, POW and RMB had high amplitudes for both wave types. 26. Table 12 presents the average deviation of the 10-Hz Lg-wave amplitudes by distance intervals from the theoretical curves. From Table 12 it can be seen that amplitudes at the smaller epicentral 49 Table 11 Average 10-Hz Lg-Wave Deviation by Station Station Average Deviation log amplitude units percentage CRU +0.082 120.8 DON +0.045 111.0 DWM -0.082 82.9 ECD -0.240 57.5 ELC -0.239 57.6 GRT +0.111 129.2 LST -0.104 78.7 NKT -0.022 95.0 OKG +0.241 174.1 PGA +0.024 105.7 POW +0.090 123.0 RMB +0.056 113.7 WCK -0.023 94.8 50 Table 12 Average 10 Hz Lg-Waye Deviations by Distance Interval Distance Interval Average Deviation fan log amplitude units percentage 0-25 -0.084 82.5 25.1-50 -0.074 74.5 50.1-75 -0.103 78.9 75.1-100 -0.009 98.0 100.1-125 +0.125 133.4 125.1^150 +0.127 134.0 150.1-175 +0.186 153.6 175.1-200 +0.138 137.5 >200 +0.182 152.1 51 distances are less than expected and at the larger distances greater than expected, with respect to a theoretical curve with y = 0.008 km" . Figure 16 shows the deviations, from which it follows that the dashed- line curve with y = 0.006 km provides a better fit to the data. 27. For ground-motion predictions it is important to know which of the wave types carries the largest amplitude at a given distance. In the present study it was apparent, from a visual inspection of the seismograms, that at distances beyond 30 km the amplitude of the 10-Hz Lg waves exceeds that of the 10-Hz P waves. Table 13 presents the amplitude ratio A(P)/A(Lg) for all observations at epicentral dis- tances less than or equal to 30 km. From the table it can be seen that of the 71 observations in this distance range only 15 correspond to the ratio exceeding unity. Of these, 8 can be explained by an anomalously small Lg amplitude. For the remaining 7, the largest value of the ratio is 1.66. Thus in general over the entire range of epicentral distance the 10-Hz Lg motion has the largest amplitude at that frequency for the vertical component of ground motion. We cannot make a similar statement about the horizontal component of motion because we do not have the necessary data to investigate the relation- ship. 28. Table 14 presents the average deviation of the narrow-band- pass filtered Lg data from the theoretical curves, by station. Stations PGA, OKG, NKT and WCK have anomalously large amplitudes for all four frequencies. These stations showed average amplitudes at 52 T 1 1 — I I I M T 1 TT 100 'E >s o k. o 3 10 : ^X=0.006 If =0.008 km-' J I ' ' ' » I M mI J I L 10 100 A (km) Figure 16. 10-Hz Lg-wave deviations from curve Y = 0.008 km 53 Table 13 A(P)/A(Lg) 0.5 5 . 1-10 10.1-15 15.1-20 20.1-25 25.1-30 km km km km km km 0.79 3.17* 1.29 2.78* 2.89* 5.96* 0.78 1.20 1.05 1.66 1.94* 1.80* 0.72 1.07 0.92 1.25* 1.29 1.33 0.60 0.96 0.75 1.00 1.16* 1.00 0.46 0.92 0.73 0.84 1.00 0.73 0.88 0.70 0.83 0.96 0.50 0.86 0.55 0.80 0.81 0.40 0.80 0.53 0.76 0.78 0.38 0.75 0.53 0.67 0.74 0.36 0.53 0.66 0.65 0.36 0.34 0.59 0.50 0.30 0.29 0.22 0.20 0.60 0.57 0.56 0.50 0.45 0.41 0.40 0.33 0.25 0.28 * The Lg amplitude was anomalously small, 54 •H 4-1 to 4J CO C o •H > o > CO :s I bO hJ in v£> 00 CO ^ 0) d en 4-1 -u •H -H d c CO B^ 0) 3 Cfl 4J 4J •H -H c c CO B^° CO Q) 3 4-> ■H c bO ED CO ^ 0) 3 CO 4J 4-1 •H -H C C bO !=) CO S o H CT> in o 00 O (Tn UO ro 00 CM I— 1 <-\ iH tH .H rH r-l rH ro O O - o in in rH O 00 CO rH O CM rH rH O CN O CO 00 o CM CN CO CO CN o CO in CO o vD O O 1 o 1 O + o 1 o 1 o + o + O + o + o 1 o 1 O + in o CO 00 ■ CO ^ I bD hJ Xl vO o cn 00 iH 00 .H .D O 00 c^ <3> o o o CT. cr. CNl in 00 O O O rH 00 'O 3 CO •U 4-1 •H -H c c CO 5r| CM O o CTi Csl o CNl O in o <3- 00 rH CJ^ iH iH CO o o o o CNl o + o + O 1 o 1 O + O 1 o + o + o + e^ r^ -cr CO vO CM o CN o o rH O in 00 o cy. CO rH 00 o CO CTn rH iH iH .H 00 r-i rH CO CO o + o 1 o 1 o 1 o + O 1 o 1 o 1 o + CO o N X CN Q> iH .H iH iH T3 in 1^ rH 1 1 1 1 O CO M S 4-t ^ O 5 10 " I • " "I T 1 — r 1 = 0.003 km-i- I 1 I I II J I L 10 Figure 18, 100 A (km) 3.12-Hz Lg-wave deviations from curve y = 0.003 km 59 I I — I — I — I I I I T 1— r 100 a> o o 10 J I L I I ■ ■ ■! X =0.004 km"' - I I L 10 100 A (km) Figure 19. 5-Hz Lg-wave deviations from curve Y = 0.004 km" 60 1 1 — I — I I I I I T 1 — r 100 V) w O o 10 Nil = 0.004 Xn \ « = 0.005 km"' ■ ' I i ' ' ' ' J I L 10 100 A (km) Figure 20. 8-Hz Lg-wave deviations from curve Y = 0.005 km ^ 61 coefficient, Y> as a function of frequency. The quantities are related by the equation Q = 7Tf/yV C4) where f is wave frequency and V is the group velocity of the seismic waves. Figure 21 shows a plot of Q versus frequency, as determined from the Y values given in Section 29. The value of V was taken as 3.5 km/sec for all frequencies between 1 and 10 Hz. At 1 Hz the y value 3 -1 was found by Nuttli to be 0.0006 km and at 10 Hz the y value was found in the present study (Section 25) to be 0.006 km 31. The y values for 1 and 10 Hz waves are considered to be more reliable than those for 2, 3.12, 5 and 8 Hz. Data were available for larger distances for 1-Hz waves, at which distances the effects of absorption become more important than those due to geometric spreading. The 10-Hz frequency corresponds to the peak in the magnification curves of the microearthquake seismographs, so data at this frequency also should be reliable. The most uncertain values of y are those obtained by narrow bandpass filtering at 2 and 3.12 Hz, where the signal-to-noise ratio is small because of the relatively low magnifi- cation of the microearthquake seismographs at those frequencies. Taking these points into consideration, a prudent Interpretation of Figure 21 is to conclude that Q for Lg waves in the central Mississippi valley has a constant value of 1500 for waves of frequency between 1 and 10 Hz. This value is significantly larger than Q values found for 12 high frequency waves by Chouet et al for tectonic provinces. They 62 2000 - 1500 O 1000 - 500- — 1 — 1 T I 1 1 1 1 1 — r— _ Y Y X i— V . ~ A ■ A A ■ - X - 1 X 1 1 1 1 1 1 1 i • 8 10 f (Hz) Figure 21. Q vs frequency 63 found Q = 65 for Stone Canyon, California, 250 for San Fernando, California, 250 for Kilaueau, Hawaii and 200 for Oishiyama, Japan. 32. Figures 22 and 23 show the effect of differences in Q values on the spatial attenuation of high frequency waves. In constructing these figures Q was taken to be 1500 for the central Mississippi valley and 200 for tectonic provinces. Figure 22 is for 1-Hz waves, and Figure 23 for 10-Hz waves. From Figure 22 it can be seen that the ratio of amplitudes of 1-Hz Lg waves in the central Mississippi valley com- pared to tectonic provinces is 1.1 at 10 km, 1.4 at 50 km, 1.6 at 100 km and 3.2 at 300 km. From Figure 23 uhe values of the ratio for 10-Hz Lg waves are 1.5 at 10 km, 3.5 at 30 km, 7.1 at 50 km and 14.7 at 70 km. These results have profound implications for engineering studies. The 10-Hz waves, which chiefly are responsible for damage to ordinary low structures, will maintain large amplitudes to signifi- cantly greater distances in the central Mississippi valley compared to a tectonic region such as California or Japan. The 1-Hz waves, which are responsible for damage to tall or long structures, also will be larger in the central Mississippi valley than in tectonic re- gions, but not to the extent that the 10-Hz waves are. 33. Ground motion is determined both by the attenuation of waves and the level of their excitation in the source region. From the mag- 3 nitude formula of Nuttli , one can estimate the excitation level of 1-Hz Lg waves for an earthquake of a given m^ value. In the frequency domain one can use the known spectral shape of the Lg waves, such as seen in Figure 14, to estimate the excitation level at different 64 T 1 1 — I I I I I T 1 — r 100 O o < 10 — 10 Figure 22, 100 A (km) Theoretical attenuation curves for 1-Hz Lg waves 65 T I I I I I I T — r c O V. "j5 < Central Mississippi Valley f= 0.006 km-' Tectonic If =0.045 km 10 A (km) Figure 23. Theoretical attenuation curves for 10-Hz Lg waves 66 frequencies of the waves for earthquakes, of an assigned m, , and thus a known corner frequency. However, in the time domain the dependence of the excitation level on the wave frequency is not so obvious. Data from the narrow-bandpass filtered seismograms of this study and of a 13 previous study by Stirling suggest that the source excitation level for a given earthquake is approximately constant for frequencies be- tween 2 and 8 Hz. This is important for engineering studies, because it indicates that high frequency waves will contribute significantly to strong-motion seismograms. That is, there is no fall-off of ampli- tude of ground motion with increasing frequency in the source region. The only thing which causes the higher frequency waves to be smaller in amplitude at larger epicentral distances is the increase in value of the absorption coefficient with increasing wave frequency. 34. As a check on the observation that the time-domain ampli- tudes of approximately 1- to 10-Hz waves are constant in amplitude in the source region, and as a further check on the absorption-coefficient values determined in this study for 1- and 10 Hz waves, the seismo- grams of three relatively large earthquakes were analyzed. These earthquakes occurred on 28 February 1977 (23^48™18.8^ UT, 39..17°N, 88.40°W, m^ = 2.9), 04 November 1977 (11^21^06. 8^ UT, 34.01°N, 89.22° W, m^ = 3.4) and 26 November 1977 (04^8^16.4^ UT, 34.35°N, 92.80°W, m, = 3.1). The m values were determined from 1 Hz Lg waves recorded b b 3 at large distances, using the formula of Nuttli . That same formula was then used to calculate what the 1-Hz amplitude would be at points where 10-Hz amplitude data were available. The 10-Hz amplitudes were 67 measured on the seismograms and corrected for the differences in absorption of 1- and 10-Hz waves. The resulting data are plotted in Figure 24. If the deduction that 1- and 10-Hz waves have the same time-domain amplitude in the source region is correct, then at a given distance the 1-Hz amplitudes (indicated by circles) and the corrected-for-absorption 10-Hz amplitudes (indicated by crosses) should have the same value at a given station. From Figure 24 it can be seen that with the exception of one data point (at a distance of 202 km for the earthquake of 04 November 1977) all the points in the figure agree within a factor of two, or less. This confirms both that our determined values of the absorption coefficient at 1 and 10 Hz are correct and that the excitation level of Lg waves in the time domain is the same at 10 Hz as it is at 1 Hz. 35. The empirical conclusion arrived at in this study, namely that the source excitation level in the time domain is constant for fre- quencies of 1 to 10 Hz, has direct applicability to the calculation of design earthquakes. That is, if one knows the body-wave magnitude of an earthquake and the absorption coefficients of 1 to 10 Hz waves, one can calculate the high frequency Lg accelerations at any selected dis- tance, and thus arrive at the design acceleration for that distance. To test if this conclusion is valid, the strong-motion data presented 14 by Herrmann for three central Mississippi valley earthquakes were compared with values calculated using the results of this report. The results are presented in Table 16. The observed accelerations given 68 04 NOVEMBER 1977 .05- .04- 8 .03- X X ^.02k "^ ° 9 c 2.01 E X X ° X < 26 NOVEMBER 1977 .02 .01 X X .02 .01 X 28 FEBRUARY 1977 200 300 400 A (km) Figure 24. Plot of 10-Hz (crosses) and 1-Hz (circles)amplitudes corrected for absorption differences 69 Table 16 Comparison of Observed and Calculated Strong-Motion Acceleration Date Station New Madrid, 1^0 Distance km ^flO-Hz, Observed cm/sec ^^lO-Hz^ , Caxcuiated cm/ sec 13 June 1975 9 14 11 25 March 1976 00 4 1"^ UT Arkabutla Dam, MS Left Toe 99 4.6 4.2 Arkabutla Dam, MS Left Crest 99 2.7 4.2 Arkabutla Dam, MS Right Abutment 99 2.6 4.2 Tiptonville, TN 130 3,2 2.9 New Madrid, MO 131 4.5 2.9 Wappapello Dam, MO 150 3.8 2.3 Right Toe Wappapello Dam, MO 150 2.0 2.3 Right Crest 25 March 197 6 Arkabutla Dam, MS 99 0.74 1.3 01 OO"^ UT Left Toe 70 in the table are those of the sustained maximum, vertical component, 10-Hz Ls waves as measured from the processed accelerograms. The calcu- lated accelerations are those of vertical component, 10-Hz Lg waves as deduced from the m, value, taking account of differences in absorp- tion at 1 and 10 Hz and assuming that the excitation level of 1- and 10-Hz waves in the time domain is equal. The agreement between ob- served and calculated accelerations is excellent, which gives us con- fidence in using the methods developed in this report to predict design earthquake motion for the central Mississippi valley. 71 PART IV: SUMMARY AND CONCLUSIONS 36. From an analysis of the microearthquake selsmo^rams in the central Mississippi valley the coefficient of absorption of Lg waves in that region has been found to be 0.0006 km for 1-Hz waves, 0.0012 km"""" for 2-Hz waves, 0.0018 km""*" for 3-Hz waves, 0.0030 km" for 5-Hz waves, 0.0048 km" for 8-Hz waves and 0.0060 km"-*" for 10-Hz waves. These values correspond to a constant Q value of 1500 which is indicative of extremely small anelastic attenuation. Thus high frequency Lg waves will propagate to much greater distances in the central Mississippi valley than in tectonic regions such as California or Japan. Correspondingly, their damage potential will be greater at larger distances in the central Mississippi valley. 37. From an analysis of microearthquake seismograms, conven- tional earthquake observatory seismograms and strong-motion accelero- grams, the excitation level of 1- to lOHz Lg waves in the time domain has been found to be constant, for earthquakes as small as m = 1.0 and as large as m^ = 5.0. This unexpected finding indicates that accelerograms and thus design earthquake motions can be pre- dicted if one knows the body-wave magnitude of an earthquake. It also indicates that high frequency Lg waves will have larger accelerations in the central Mississippi valley than previously expected. 38. The spectra of lg waves as determined in this report are 9 consistent with those previously reported by Street et^ al and by 13 Stirling . That is, for m^ _< 3.5 the spectra consist of a level part at frequencies less than the corner frequency and a straight-line, 72 -2 sloping part, with a slope of f , at the higher frequencies. For larger magnitude earthquakes the spectra in general consist of three straight-line segments: a level part at the low frequencies, a portion -1 -2 of slope f at the intermediate frequencies and a slope of f at the high frequencies. 39. For the vertical component of ground motion the Lg waves in general have a larger amplitude than the F waves over the entire range of epicentral distances. Thus the Lg waves are the waves with the greatest potential for damage to structures in the central Mississippi valley. 73 REFERENCES 1. Gutenberg, B. and Richter, C.F., Seismicity of the Earth an d Associated Phenomena , Princeton University Press, Princeton, 1959. 2. Brazee, R. J., "Attenuation of Modified Mercalli Intensities with Distance for the United States East of 106 W," Earthquake Notes, Vol 43, No. 1, 1972, pp 41-52. 3. Nuttli, 0. W. , "Seismic Wave Attenuation and and Magnitude Relations for Eastern North America," Journal of Geophysical Research. Vol 78, 1973, pp 876-885. 4. Nuttli, 0. W. and Zollweg, J. E., "The Relation between Felt Area and Magnitude for the Central United States," Bulletin, Seismological Society of America , Vol 64, 1974, pp 73-85. 5. Necioelu. A. and Nuttli. 0. W. , "Some Ground Motion and Intensity Relations for the Central United States," Earthauake Eneineerine and Structural Dynamics . Vol 3,1974, pp 111-119. 6. Street, R. L. , "Scaling Northeastern United States/Southeastern Canadian Earthquakes by their Lg Waves," Bulletin, Seismological Society of America . Vol 66, 1976, pp 1525-1537. 7. Jones, F. B. , Long, L. G. , and McKee, J. H. , "Study of the Attenu- ation and Azimuthal Dependence of Seismic Wave Propagation in the Southeastern United States," Bulletin, Seismological Society o f America, Vol 67, 1977, pp 1503-1513. 8. Ewing, M. , Jardetzky, W. S., and Press, F. , Elastic Waves in Layered Media , McGraw-Hill Co., 1957, p. 358. 9. Street, R. L., Herrmann, R. B., and Nuttli, 0. W. , "Spectral Characteristics of the Lg Wave Generated by Central United States Earthquakes," Geophysical Journal, Royal Astronomical Society , Vol 41, 1975, pp 51-63. 10. Roraney C, Brooks, E.G., Mansfield, R. H. , Carder, D. S., Jordan, J. N. , and Gordon, D. W. , "Travel Times and Amplitudes of Principal Body Phases, Recorded from GNOME," Bulletin, Seismological Society of America , Vol 52, 1962, pp 1057-1074. 11 Evernden, J. F. , "Magnitude Determinations at Regional and Near- Regional Distances in the United States," Bulletin, Seismological Society of America , Vol 57, 1967, pp 591-639. 74 12. Chouet, B. , Akl, K. , and Tsujiura, M. , "Regional Variation of the Scaling Law of Earthquake Source Spectra," Bulletin , Seismological Society of America, Vol 68, 1967, pp 49-79, 13. Stirling, W. A., Local Earthquake Ground Motion Scaling for Southeast Missouri , M. S. Thesis, Saint Louis University, 1977, 96 pp. 14. Herrmann, R. B., Analysis of Strong Motion Data from th e New Madrid Seismic Zone : 1975-1976, Saint Louis University, 1977, 144 pp. 75 In accordance with letter from DAEN-RDC, DAEN-ASI dated 22 July 1977, Subject: Facsimile Catalog Cards for Laboratory Technical Publications, a facsimile catalog card in Library of Congress MARC format is reproduced below. Nuttli, Otto W State-of-the-art for assessing earthquake hazards in the United States; Report 10: Attenuation of high-frequency seismic waves in the central Mississippi Valley / by Otto W, Nuttli, John J. Dwyer, St. Louis University, Department of Earth and Atmospheric Sciences, St. Louis, Missouri. Vicksburg, Miss. : U. S. Waterways Experi- ment Station ; Springfield, Va. : available from National Tech- nical Information Service, 1978. 75 p. : ill. ; 27 cm. (Miscellaneous paper - U. S. Army Engi- neer Waterways Experiment Station ; S-73-1, Report 10) Prepared for Office, Chief of Engineers, U. S. Army, Washington, D. C, under Purchase Order No. CW-77-M-2480. References: p. 74-75. 1. Earthquake engineering. 2. Earthquake hazards. 3. Earthquakes 4. Ground motion. 5. Mississippi Valley. 6. Seismic waves. 7. State-of-the-art studies. 8. Wave attenuation. I. Dwyer, John J., joint author. II. St. Louis University. Dept. of Earth and Atmospheric Sciences. III. United States. Army. Corps of Engineers. IV. Series: United States. Waterways Experiment Station, Vicksburg, Miss. Miscellaneous paper ; S-73-1, Report 10. TA7.W34m no. S-73-1 Report 10 UNIVERSITY OP ILUNOIS-URBANA 3 0112 084235313