RETURNING MATERIALS: MSU Place in book drop to remove this ‘ checkout from your record. FINES UBRAR‘ES will be charged if book is returned —_- after the date stamped below. SEISMIC ANISOTROPY IN THE SURFACE LAYERS OF THE ROSS ICE SHELF, ANTARCTICA BY James L. Fuchs A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Geology 1989 . ()gj ,. .:‘ z I..- 5 Z? Z". 1. ‘V‘ -' z.“ t V. :1 ABSTRACT SEISMIC ANISOTROPY IN THE SURFACE LAYERS OF THE ROSS ICE SHELF, ANTARCTICA BY James L. Fuchs Seismic refraction surveys from the Ross Ice Shelf, Antarctica, are analyzed for the purpose of studying the effects of the near surface layering on the propagation of seismic waves. Velocity anisotropy is observed for three types of seismic waves. The best indication of this anisotropy are the patterns which develop in the velocity surfaces with increasing depth. The correlation between energy radiation plots and the velocity surfaces add support to the presence of anisotropy. A theoretical model, based on observable surface features of the study area, is developed and shown to be transversely isotropic. The transverse isotropy of the surface layers in the study area appears to be a form of structural anisotropy. This structural anisotropy is attributed to the interlayering of north-south oriented sastrugi and snow in the study area. ACKNOWLEDGEMENTS Special thanks are owed to Dr. Hugh Bennett for suggesting the idea behind this study, helping to see it through, and for braving Antarctic weather to obtain the data. Many thanks are due to the following people and groups for the assistance provided: To Mark Schoomaker for his invaluable computer programs and suggestions. To Dr. Wilband for his aid in using the computer system and for serving on the thesis committee. To Dr. Larson for his help with reference material and for also serving on the thesis committee. To Dr. Fujita for helping critique thesis drafts. To the National Science Foundation for providing the funds used to collect the data and support the research. To my wife and parents who always supported my efforts to pursue an education. ii TABLE OF CONTENTS LIST OF TABLES . . . . . . . . . . . LIST OF FIGURES . . . . . . . . . . Chapter 1 INTRODUCTION . . . . . . . . Chapter 2 LOCATION AND PARAMETERS OF STUDY AREA Chapter 3 FIELD METHODS . . . . . . . . Chapter 4 ANALYSIS METHODS . . . . . . . Chapter 5 DATA ANALYSIS . . . . . . . . Time Picks . . . . . . . . Curve Fitting . . . . . . . Depth of Penetration . . . . . Velocity Surfaces . L. . . . . Energy Radiation . . . . . . Chapter 6 COMPARISON TO DEEPER ANISOTROPY . . Chapter 7 ANISOTROPIC MODEL . . . . . . Chapter 8 CONCLUSION . . . . . . . . . RECOMMENDATIONS . . . . . . . . . . . APPENDIX I : Time - Distance Data . . . . . APPENDIX II : Power and Log Curve Statistics . APPENDIX III : Velocities and WHB Depths . . APPENDIX IV : Log of Energy Radiation Values . iii PAGE vii 10. 12 12 14 52 59 67 72 74 9O 92 93 99 104 Ill APPENDIX V : Basic Program for Determining Model 112 Velocities APPENDIX VI : Velocities from Anisotropic Model . 114 LIST OF REFERENCES . . . . . . . . . . . 115 GENERAL REFERENCES . . . . . . . . . . . 118 iv LIST OF TABLES TABLE PAGE 1 P wave time-distance data 93 2 SH(+) wave time-distance data 94 3 SH(-) wave time-distance data 95 4 SV(+) wave time-distance data 96 S SV(-) wave time-distance data 97 6 SH wave average time-distance data 98 7 Power curve statistics P wave 000 99 Power curve statistics P wave 045 99 9 Power curve statistics P wave 090 99 10 Power curve statistics P wave 135 99 11 Power curve statistics SH wave 000 100 12 Power curve statistics SH wave 045 100 13 Power curve statistics SH wave 090 100 14 Power curve statistics SH wave 135 100 15 Power curve.statistics SV(+) wave 000 101 16 Power curve statistics SV(+) wave 045 101 17 Power curve statistics SV(+) wave 090 101 18 Power curve statistics SV(-) wave 000 102 19 Power curve statistics SV(-) wave 045 102 20 Power curve statistics SV(-) wave 090 102 V TABLE PAGE 21 Power curve statistics SV(-) wave 135 102 22 Log curve statistics P waves 103 23 Log curve statistics SH waves 103 24 Log curve statistics SV waves 103 25 Velocities and WHB depths P wave 000 104 26 Velocities and WHB depths P wave 045 104 27 Velocities and WHB depths P wave 090 105 28 Velocities and WHB depths P wave 135 105 29 Velocities and WHB depths SH wave 000 106 30 Velocities and WHB depths SH wave 045 106 31 Velocities and WHB depths SH wave 090 107 32 Velocities and WHB depths SH wave 135 107 33 Velocities and WHB depths SV(+) wave 000 108 34 Velocities and WHB depths SV(+) wave 045 108 35 Velocities and WHB depths SV(+) wave 090 108 36 Velocities and WHB depths SV(-) wave 000 109 37 Velocities and WHB depths SV(-) wave 045 109 38 Velocities and WHB depths SV(-) wave 090 110 39 Velocities and WHB depths SV(-) wave 135 110 40 Logs of energy radiation values P waves 111 41 Logs of energy radiation values SH waves 111 42 Velocities from anisotropic model 114 vi FIGURE 1 (hm-b 10 11 12 13 14 15 16 17 18 19 Map of the study area on the Ross Ice LIST OF FIGURES Shelf, Antarctica Power Power Power Power Power Power Power Power Power Power Power Power Power Power Power curve curve curve curve curve curve curve curve curve curve curve curve curve Curve curve fit fit fit fit fit fit fit fit fit fit fit fit fit fit fit t0 to to to to to to to to t0 t0 t0 to to t0 Log curve fit to P Log curve fit to P Log curve fit to P P wave 000 P wave 045 P wave 090 P wave 135 SH wave 000 SH wave 045 SH wave 090 SH wave 135 SV(+) wave SV(+) wave SV(+) wave SV(-) wave SV(-) wave SV(-) wave SV(-) wave wave 000 wave 045 wave 090 vii 000 045 090 000 045 090 135 PAGE 16 17 18 19 20 21 22 23 24 26 27 28 29 3O 33 34 35 FIGURE PAGE 20 Log curve fit to P wave 135 36 21 Log curve fit to SH wave 000 37 22 Log curve fit to SH wave 045 38 23 Log curve fit to SH wave 090 39 24 Log curve fit to SH wave 135 40 25 Log curve fit to SV(+) wave 000 41 26 Log curve fit to SV(+) wave 045 42 27 Log curve fit to SV(+) wave 090 43 28 Log curve fit to SV(-) wave 000 44 29 Log curve fit to SV(-) wave 045 45 30 Log curve fit to SV(-) wave 090 46. 31 Log curve fit to SV(-) wave 135 47 32 Time versus distance plots P waves 48 33 Time versus distance plots SH waves 49 34 Time versus distance plots SV(+) waves 50 35 Time versus distance plots SV(-) waves 51 36 Velocity versus depth plot for P waves 55 37 Velocity versus depth plot for SH waves 56 38 Velocity versus depth plot for SV(+) waves 57 39 Velocity versus depth plot for SV(-) waves 58 40 Velocity surfaces for P waves 62 41 Velocity surfaces for SH waves 63 42 Velocity surfaces for SV(+) waves 64 43 Velocity surfaces for SV(-) waves 65 viii FIGURE PAGE 44 Log of energy versus distance for P waves 70 45 Log of energy versus distance for SH waves 71 46 Elemental volume of theoretical model 75 material. 47 Velocity Surfaces for P Waves 87 48 Velocity Surfaces for SH Waves 88 49 Velocity Surfaces for SV Waves 89 ix Chapter 1 INTRODUCTION The purpose of this study is to determine if seismic anisotropy is present in the near surface layers of the Ross Ice Shelf, and to compare this anisotropy to the velocity anisotropy observed in deeper zones of the Ross Ice Shelf (Wanslow, 1981; Bennett et al., 1978; Bennett et al., 1979). A theory is developed to explain the anisotropy of the near surface layers. In seismic exploration surveys it is usually assumed that the material through which seismic waves propagate is isotropic. However, it has been demonstrated by several authors that many surface rocks are anisotropic to some extent (Hagedoorn, 1954; Cholet & Richard, 1954; Uhrig & Van Melle, 1955; Krey & Helbig, 1956; Buchwald, 1959; Anderson, 1961; Backus, 1962; Sato & Lapwood, 1968; Nur & Simmons, 1969; Crampin, 1970; Nur, 1971; Tillman & Bennett, 1973; Daley & Hron,-1977; Crampin, 1977; Crampin & Bamford, 1977; Keith & Crampin, 1977; Crampin, 1978; Levin, 1978; Berryman, 1979). The behavior of seismic waves in anisotropic material varies with the direction of propagation. 2 Variation of velocity is one of the anomalies associated with anisotropic material. Furthermore, the variation of velocity with direction must exhibit centrosymmetry if the material is anisotropic, since it is directly related to the effective elastic constants in a crystalline symmetry (Crampin, et al., 1977). Anisotropy in its purest form is exhibited in single crystals (Anderson, 1961). In a seismic survey fairly uniform material would be best suited for the purpose of a detailed study of velocity anisotropy (Bennett, 1968). The Ross Ice Shelf provides a simple, monomineralic material in which to conduct this study. Anisotropy of ice has been verified in several studies (Bennett, 1968; Dewart, 1968; Bentley, 1972; Bennett et al., 1978,1979). It is suspected that the near surface layers in the study area may exhibit some form of anisotropy due to observation of abundant sastrugi on the surface. Sastrugi are surface features that are observed on many ice shelfs throughout the world. They are wavelike ridges of extremely hard snow which are formed on a level surface by the action of the wind, and with axes parallel to the wind direction. The seismic refraction method is used in this study since the reflection method can only be used to determine an average velocity for the entire thickness of the ice shelf. The refraction method yields a more detailed velocity analysis. In other studies anisotropy has been more apparent for shear waves than for compressional waves (Jolly, 1956; Levin, 1979). Therefore, it was expected that shear waves would yield the best results for analysis of anisotropy in this study also. Chapter 2 LOCATION AND PARAMETERS OF STUDY AREA The study area is located 18 kilometers due east of Minna Bluff, Antarctica, on the Ross Ice Shelf (78.40 N latitude, 167.10 E longitude) (Figure l). The area was chosen to test the effects of the shear zone, created by the movement of the ice shelf against Minna Bluff, on seismic wave propagation. The study area was located far enough east of Minna Bluff in an attempt'to avoid zones of fractures near Minna Bluff. It has been shown that fractures can cause anisotropy (Nur, 1971) The Ross Ice Shelf was discovered by Sir James Ross in 1841. It is the largest single sheet of floating ice in the world, comprising approximately 525,000 square kilo- meters. The ice shelf flows northward at an estimated rate of .2 - 1.5 kilometers per year. The ice shelf moves in response to the annual net accumulation of snow on the ice shelf itself, and to the flow of ice from the interior of the continent (Crary et al., 1962). Sastrugi are observed at many places on the Ross Ice Shelf. The elongations of the sastrugi are predominantly north-south or northeast-southwest, and they are much more 5 pronounced near Minna Bluff than other areas of the shelf (Crary et al., 1962). The study area contained abundant north-south oriented ridges of sastrugi on the surface, with snow or hoarefrost between the hardened ridges (Communication with Dr. H.F. Bennett). The annual snow accumulation is estimated at 20-23 centimeters. The density of the upper ten meters of the ice shelf ranges from 0.40 to 0.55 grams per cubic centi- meter. The thickness of the ice shelf ranges from 250 to 700 meters. In the study area the shelf is approximately 320 meters thick as determined from reflection arrivals from the ice-water interface (Crary et al., 1962). ROSS ICE SHELF ANTARCTICA 5? K30 |§O |+ [O FIGURE I O 20 40h w FIGURE 1: Map of the study area on the Ross Ice Shelf, Antarctica. Chapter 3 FIELD METHODS The seismic surveys were conducted by Bennett and others in the 1976-1977 austral summer. Compressional seismic waves (P waves) and two types of shear seismic waves (SH & SV waves) were generated and recorded. The format of the data consists of 24 traces that are digitally recorded on magnetic tape at a sampling interval of 2.083 milliseconds. This odd sampling interval is used because the maximum sampling rate of the equipment was 480 samples per second. The Nyquist frequency for the maximum sample rate is 240 Hertz. Recorded gains and filtering were controlled by analog amplifiers. The data can be divided into two distinct sets of seismic lines. The first set are the long spread lines, which have source to geophone offsets ranging from 50 to 3300 feet. The second set are the short spread lines, which have offsets from 5 to 100 feet. ' The long spread lines were used primarily for analy- sis of the deeper zones of the ice shelf. Since these were analyzed by others (Bennett, 1978,1979; Wanslow, 1981) further discussion will only consider the results of these analyses. 8 The short spread lines were used to analyze the near surface layers of the study area. The lines consist of 24 geophones that are divided into two sets of 12 geophones each. The two sets of geophones were oriented at an angle of 45 degrees to each other. The spacings of each group of 12 geophones were as follows: 5, 10, 15, 20, 30, 40, 50, 60, 70, 80, 90, and 100 feet, from source to receiver. Initially the spread was arranged with one set of 12 geo- phones oriented east-west (000), and the other set of 12 geophones oriented northeast-southwest (045). Separate events were then recorded for each type of seismic wave. The two sets of geophones were then rotated 45 degrees counterclockwise to obtain lines oriented north-south (090) and northeast-southwest (045). This procedure was repeated once more such that the final position of the spread was one set oriented north-south (090), and one set oriented northwest-southeast (135). The source for the short spread data was a hammer and board. As a P wave source the hammer was manipulated so that it struck the board vertically, or perpendicular to the surface of the ground. As a shear wave source the hammer was manipulated so that it struck the board horizon- tally, or parallel to the ground. The orientation of the board was important for the SH and SV waves. The board was oriented such that first motions were parallel to the di- rection of the seismic line for SV waves, and perpendicular 9 to the direction of the seismic line for SH waves. Shear waves of opposite polarity were produced by changing the direction of the hammer blow by 180 degrees. The orientation of the geophones for P waves is relatively unimportant as long as they are approximately vertical to the ground. However, the orientation of geo- phones for shear waves is extremely important in order to Orecord the proper arrival with a significant amplitude. The geophones must always be oriented such that the plane which defines the movement of the coil within the geophone is parallel to the particle motion of the seismic wave. For SH waves the geophones were oriented in a way that they would detect the horizontal component of motion perpendic- ular to the azimuth of the seismic line. For the SV waves the geophones were oriented to detect the horizontal com- ponent of motion parallel to the azimuth of the seismic line. Chapter 4 ANALYSIS METHODS A series of computer programs developed by Mark Schoomaker are used to facilitate analysis of the data. The raw seismic data is stored on two nine track magnetic tapes (VRN-6746, VRN-6770) in the Michigan State University Computer Tape Library. Separate events were removed from the main data tapes using the program Datasetup. The initial step was to make plots of the event using the program Pitasource. These plots are essentially the uninterpreted seismic records. Arrival times for each geophone can then be picked visually from the plots, and these arrival times are in turn plotted on time versus distance graphs. Velocities were determined for the time picks by use of various curve fitting methods. The inverse of the slope of a particular portion of the curve is used to indicate the cross spread velocity. The methods of fitting various curves to the data will be discussed further in the data analysis section. Depths of penetration were determined from the velo- cities and distances by use of the Wiechert, Herglotz, Bateman integral (Slichter, 1932; Officer, 1958). 10 11 Subsequent plots of the velocity surfaces at various depths are used to determine if velocity patterns are developing with increasing depth of penetration. The programs Processor and Finale were used to determine energy radiation patterns. Processor is used interactively at a Tektronix terminal to extract various waveforms from individual traces of a specific event. Finale performs a fast Fourier transform on the extracted waveform, normalizes all waveforms of one event to a speci- fied gain, plots the amplitude and phase spectrum for each waveform, and integrates the amplitude spectrum of the waveform within a given frequency range. The integrated values of each trace for one event are then normalized with respect to other events such that energy versus direction at a given distance can be compared. Chapter 5 DATA ANALYSIS TIME PICKS Time picks for P, SH, and SV waves from the short spread lines are listed in Appendix I, Tables 1-5. The tables for the SH and SV waves indicate picks were made for sources of opposite polarities. Therefore, there are two tables at each direction for each type of shear wave. The first refraction arrival is picked for all modes of seismic waves. Time picks for the P waves (Table 1) were made from seismic records using vertically oriented geophones. The "first break" of the seismic trace is picked, and the first motion is always in the upward direction. Time picks for the SH waves were made from seismic records using horizontally oriented geophones that were perpendicular to the seismic line. The "first break" of the seismic trace is again picked, as in the P wave records. However, one set of lines has the "first breaks" of the seismic traces in the upward direction, and the other set of lines has the "first breaks" in the downward direction. This is due to the reversal of source polarity. Seismic lines with "first breaks" in the upward direction 12 13 are denoted as having a positive (+) source (Table 2). Seismic lines with "first breaks" in the downward direction are denoted as having a negative (-) source (Table 3). Time picks for the SV waves were made from seismic records using horizontally oriented geophones that were parallel to the azimuth of the seismic line. The SV wave events can be divided into two sets of seismic lines that had sources of opposite polarities. As in the case of the SH waves events with "first breaks" in the upward direction are denoted as having a positive (+) source (Table 4), and events with "first breaks" in the downward direction are denoted as having a negative source (-) (Table 5). There is no data listed for the SV(+) 135 degree direction seis- mic line because that event could not be located on the main data tapes. CURVE FITTING Several methods of curve fitting were used to obtain velocities from the time distance data of the previous section. The two methods that gave the best results were a log curve and a power curve, with the former giving the superior fit. The power curve used is a moving power curve. A moving power curve takes a specified number of points, fits a power curve to them, then the last data point is elimi- nated and a new data point is added. The formula for a . power curve is: b T=ax arrival time H! II distance from source to receiver N II a & b = regression coefficients Once the regression coefficients are determined the velo- city may be obtained by transforming the equation into the form below: ‘ b-l -1 QX = (abX ) dT The number of data points used to fit the power curve must be great enough so the velocity will always increase for points farther from the source. This becomes a neces- sary condition upon examination of the Wiechert, Herglotz, 14 15 Bateman integral, which is used to determine depths of penetration. This will be explained further in the Depth of Penetration section. The moving power curve for the P waves required a seven point moving curve for the best fit. The statistics for the power curve fits of the P wave data are listed in Appendix II, Tables 7-10. The curves defined by the statistics are plotted with the original time versus distance data in Figures 2-5. The moving power curves for the SH waves required a seven point moving curve for the best fit. The data that is used is the average of the SH wave picks of opposite polarity (Appendix I, Tables 6). The average times are used becauses the values are close to each other. Statis- tics for the power curves of the SH data are listed in Appendix II, Tables 11-14. The curves defined by the sta- tistics are plotted with the original data in Figures 6-9. The moving power curve for the SV wave data required a seven point moving curve for the best fit. Unlike the SH wave data the SV data of opposite polarity was not averaged because the values varied by a considerable amount, making the SV data suspect. Therefore, the SV data of opposite polarity are analyzed separately. The statistics for the power curve fit of the SV data are listed in Appendix II, Tables.15-21. The curves defined by the statistics are plotted with the original data in Figures 10-16. 0 1 00'02 1 00'0? 33NUISIG 1 00'09 (1333] 00'09 L OO'POI FIGURE 2: 16 TIME [MILLISECI 5.00 10.00 15.00 20.00 1 l l 1 Power curve fit to P wave 000°. 25:00 HAHN-d 0 [I] 17 TIME (MILLISECJ SHOO 10.00 15:00 1 20:00 25:00 00'02 1 00'0? HUNUISIG 00:09 [1333) 00'08 I 00'001 L; FIGURE 3: Power curve fit to P wave 045°. HAHN-cl S? [D 0 18 TIME [MILLISECJ 5.00 10.00 15.00 20.00 I 1 l J 25:00 00'02 00'0? HJNUISIO l (1333) L 00'09 00°08 OO'OOI L FIGURE 4: Power curve fit to P wave 090. BAUM-d 05 [I] 19 TIME [MILLISEC] 5.00 10.00 15:00 20:00 1 1 25.00 #1 0 l 00'02 1 00'09 BJNUISIU 00'09 L (1333) 00'08 OO'POI FIGURE 5: Power curve fit to P wave 135. [D HAUMrd SST 0 8300 16:00 24.00 32.00 1 l 20 TIME [MILLISECJ 40.00 I 1 00'02 1 00'07 33NUISIG 1 00'09 (1333] 00'08 I OO'OOI L_ FIGURE 6: Power curve fit to SH wave 000. HAHN-HS 0 [I] 0 21 TIME (MILLISECJ 8.00 16.00 24.00 32.00 1 l l 1 40.00 J 1 00'02 1 00'0? (1333) BJNUISIG 00109 00'08 OO'POI FIGURE 7: Power curve fit to SH wave 045. BAUM-HS 917 [II 0 22 TIME [MILLISECJ 8300 16:00 24:00 32.00 1 40.00 I 1 00'02 1 00‘07 BJNUISIO 1 00'09 [1333] 00'08 00'001 LA; FIGURE 8: Power curve fit to SH wave 090. HAHN-HS 05 [D 23 TIME [MILLISEC] 8.00 16.00 24:00 32.00 t 1 1 40 .00 J 0 1 00'02 1 00'0? 33NUISIU l [1333) 00'09 00'08 l 00°90! FIGURE 9: Power curve fit to SH wave 135. HAHN-HS SEI [I] 0 8.00 16.00 24.00 32.00 L l J 0 24 TIME [MILLISEC] l 40.00 J 1 00'02 1 00'0? BJNUISIO 00'09 L (1333) 00'09 L 00'00I L FIGURE 10: Power curve fit to SV(+) wave 000. 1ASOEU 00°0V 00°02 0 BUNUISIU (1333) 00°09 00°08 00°00! 0 8.00 16-00 24-00 32.00 L 1 1 1 25 TIME (MILLISEC) 40:00 l J L 1 FIGURE 11: Power curve fit to SV(+) wave 045. 1A8 ‘31? III 0 8. 0 26 TIME [MILLISECJ 00 16.00 24.00 32.00 I l L 1 40.00 ] 1 00°02 00°07 J BJNUISIU 1 00°09 (1333) 00°08 00°OOI L FIGURE 12: Power curve fit to SV(+) wave 090. 1A9 06 [I] 0 27 TIME [MILLISEC] 0 8.00 16.00 24.00 32.00 L l 4 L 40.00 J (1333) 33NUISIU 00-09 oo-ov oo~oz 00°08 l L l 1 00°90! FIGURE 13: Power curve fit to SV(-) wave 000. UASOED 28 TIME (MILLISECI 24 0 8 .l00 16.00 .00 32.00 1 1 1 40.00 J 1 00°02 00°07 L 33NUISIU 00'09 1 (1333) 00'09 1 00'00! L, FIGURE 14: Power curve fit to SV(-) wave 045. HAS 317 [I] 00°C? 00°02 0 HJNUISIU 00°09 (1333) 00°08 00°00! 29 TIME [MILLISECI 0 8.00 16.00 24.00 32.00 40.00 J l L l I [3 I [3 (.0 C) O) < D FIGURE 15: Power curve fit to SV(-) wave 090. 0 8. 0 30 TIME [MILLISEC] l00 15:00 24:00 32.00 I 40.00 I 00°02 J l 00°0V BJNUISIU 00109 [1333) 00°08 00'00! L_1 FIGURE 16: Power curve fit to SV(-) wave 135. E] HAS 98! 31 The best fit to the time versus distance data was ob- tained by using a log curve. The formula for the log curve used is as follows: T: a + b (1n (x + c)) arrival time *3 ll distance from source to receiver X I! a & b = regression coeffients c= constant The constant, c, is used in the equation because when X=0, T must also equal zero. However, for the usual log curve equation, T=a+b(lnX), T= -inf when X=0, hence the introduc- tion of the constant c. Once a, b, and c are determined, velocities may be obtained by transforming the equation to the following form: §=X_:_Q dT b The statistics of the log curve fit for the P wave data in Appendix I, Table l, is listed in Appendix II, Table 22. The log curves defined by the statistics with the original data superimposed are plotted in Figures 17-20. The statistics for the log curve fits for the average SH wave data is listed in Appendix II, Table 23. The curves defined by the statistics with the original data superimposed are plotted in Figures 21-24. The statistics of the log curve fits for the SV wave data in Appendix I, Tables 4-5, are listed in Appendix II, Table 24. The curves defined by the statistics with the 32 original data superimposed are plotted in Figures 25-31. Examination of the plots of all types of seismic waves, and of the correlation coefficients, reveals that the log curves provide the best fit to the seismic data. Furthermore, the log curves are preferred since only one set of regression coefficients are required, creating one smooth curve. The time versus distance data for all directions are plotted for each type of seismic wave in FIgures 32-35. The P wave data in Figure 32 shows that for the last data points at 80, 90 and 100 feet the 090 direction has the smallest arrival time followed by the 000, 045, and 135 directions respectively. This indicates that the 090 dir- ection should have the highest velocity for P waves. The SH and SV plots in Figures 33-35 are more diff- icult to analyze in this manner because the arrival times group together more closely than the P wave arrival times. One observation that can be made from these graphs is that if the difference in the time of P wave arrivals is caused by anisotropy, then apparently the P waves exhibit a greater percent anisotropy than the shear waves. This is contrary to the results found by others (Levin, 1979). 33 TIME [MILLISEC] 0 5.00 10.00 15.00 20.00 25.00 LL _1 L l J 0 1 00°02 00' or 1 BUNHISIU 1 00°09 (1331) 00°08 00°90! HAHN-cl 0 E] FIGURE 17: Log curve fit to P wave 000°. 0 1 00°02 00°07 LL1 BJNUISIU 00'09 1 [1333] 00°08 00°90! FIGURE 18: 34 TIME (MILLISECJ 5.00 10.00 15.00 20.00 1 l _L 4 Log curve fit to P wave 045°. 25:00 BAUM-d 9’? [II 0 00°02 1 00°07 L BJNUISIG 1 00°09 (1333) 00°08 00°90! FIGURE 19: 35 TIME [MILLISECI 5.00 10.00 15.00 20.00 L J 1 J1 Log curve fit to P wave 090°. 25.00 J HAHN-cl 06 [I] 36 TIME (MILLISECI 0 5.00 10.00 15.00 20.00 25.00 J I I l I 0 1 00°02 l 00°C? 33NUISIU 00:09 (1333) E] 00°08 00°00! L HAHN-d 38! [0 FIGURE 20: Log curve fit to P wave 135°. C 37 TIME [MILLISECJ 8300 16:00 24:00 32.00 1 40:00 00'02 1 00°01? 33NUISIC 00:09 (1333) 00°08 l CC'CC! L FIGURE 21: Log curve fit to SH wave 000°. HAHN-HS 0 [II C 38 TIME (MILLISEC) 8.00 16-00 24.00 32.00 1 1 J 1 40.00 A] I 00°02 L 00°C? [1331) HJNHISIC 00109 00°08 00°90! FIGURE 22: Log curve fit to SH wave 045°. HAHN-HS S? [D 0 39 TIME [MILLISEC] 8.00 18.00 24.00 32.00 I L I L 40:00 I 00°02 I 00°C? 33NUISIC 00°09 L [1333] 00°08 00°90! FIGURE 23: Log curve fit to SH wave 090°. HAHN-HS 06 E] 40 TIME (MILLISEC) 0 8.00 16.00 24.00 32.00 40.00 L I I I I C 1 00°02 I 00°C? 33NUISIC [1333] 00109 00°08 00°90! HAHN-HS 98! [I] FIGURE 24: Log curve fit to SH wave 135°. C 41 TIME [MILLISEC] 8300 15:00 24.00 32.00 I I 40.00 I I 00°02 00'0? 1 BJNUISIC 00'09 L (1333) 00°08 00°90! FIGURE 25: Log curve fit to SV(+) wave 000°. 1ASCEJ C I oo-oz‘ I 00°C? HUNUISIC I (1333] 00°09 00°08 I 00°00! L FIGURE 26: 42 TIME [MILLISEC] 8100 16:00 24.00 32.00 I J Log curve fit to SV(+) wave 045°. 40.00 I 1A8 91? [I] C I 00°02 00°C? BUNUISIC I 00°09 (1333) 00’08 1 00'00! L, FIGURE 27: 43 TIME [MILLISEC] 8.00 16.00 24.00 32.00 L I I I Log curve fit to SV(+) wave 090°. 40.00 I 1A8 05 [I] C 44 TIME [MILLISEC] 8.00 16.00 24.00 32.00 1 1 1 1 40000 I I 00°02 00°C? HUNUISIC 00'09 L, [1333] 00°08 00°90! FIGURE 28: Log curve fit to SV(-) wave 000°. UASCGJ 45 TIME [MILLISEC] 8.00 15.00 24.00 32.00 I LI L J 40.00 I I 00°02 00'0? 1 (1333) BUNHISIC 00109 00°09 J 00'00! 1 FIGURE 29: Log curve fit to SV(-) wave 045°. HAS S? [I] 0 46 TIME (MILLISECJ 8.00 16.00 24.00 32.00 JJ I I I 40:00 I 00°02 I 00°C? 33NHISIC 00'09 L (1333] 00'08 1 00'OOI L1 FIGURE 30: Log curve fit to SV(-) wave 090°. HAS 05 [U 47 TIME (MILLISECJ 0 8100 16:00 24.00 32.00 I I C I 00°02 00°C? 33NHISIC I 00°09 (1333] 00°08 00'00! g FIGURE 31: Log curve fit to SV(-) wave 135°. 40000 I E] HAS SS! 48 TIME [MILLISECJ 0 5.00 10.00 15.00 20.00 25.00 0 I L L I .I B- 198 N E O (:3534 HEB h_,c: CI) I: -+ —‘-b ID 22‘ 5‘3 + no '7" IG+ ~23 ma“ E3 ‘1" m0 r'n 83+ -__’ ~48 ,3- D [a O D [30+ 8 E“ D 89+ O O + D G [3 H' to A o 0) C3 CH CH 1" T’ 7’ 1° 2: 2: I: 2: I) I) 33 :3 <: <: <= <3 F" rn rn rn FIGURE 32: Time versus distance plots P waves. 32.00 40.00 24.00 49 [MILLISEC] 16.00 TIME 8.00 1 m B O mIIZD (.0 O a) < —‘ S. FIGURE 34: Time versus distance plots SV(+) wave 51 TIME (MILLISECJ C 8.00 16.00 24.00 32.00 40.00 D I I I l I GED GE .3 (E- De," (ID P_,o 0’ GED .4 IDS Zia“ 81> 00 F” 65 mg 115‘ ‘46} mo m a _| HS 33‘ E c: [-19 31 ‘? E» c: c: + DOE) HID->0 OJ CD 01 (003030) <<<< IDDIJID FIGURE 35: Time versus distance plots SV(-) waves. DEPTH OF PENETRATION The depth of penetration for each type of seismic wave in the various directions is needed to determine velocity surfaces. The velocity surface is a diagrammatic representation of velocity versus azimuth for a given depth. The depths of penetration can be determined if the velocities and source to receiver offsets are known by applying the Wiechert, Herglotz, Bateman (WHB) integral. The WHB integral as derived from Officer (1958) is as follows: y V l -1 L 2: 77 0 cosh V dX i depth at which velocity V is reached = depth of penetra- N II tion of ray from origin to distance X distance from source to receiver where V is determined m n V L velocity determined at X distance from the source V velocity determined at x distance between the source i i and X A necessary condition that is imposed by this equation is that the velocity always increases at distances farther from the source. This may be determined by examination of in. -1 31. the WHB integral. If V} < 1 , then cosh V; is unde- fined. The assumption of there being no velocity reversal 52 53 present seems valid for an ice shelf since the material is monominerallic and the increase of overburden with depth causes compaction which will continuously increase velocity until a maximum velocity is obtained. The depths of pene- tration were determined for the velocities obtained from the log curves since they provided the best fit and do not have to be forced to show no velocity reversals. The velocities defined by the log curve fits were obtained by applying the statistics in Appendix II, Tables 22-24 to the transformed log curve equation: QX = X + c dT b The log curve velocities are listed with the appropriate depths of penetration in Appendix II, Tables 25-39. The velocities obtained from the SV(-) data exceed the values obtained in other analysis that are much deeper in the study area. Bennett et al., (1979), determined a maximum shear wave velocity of 2073 i 34 meters per second at a depth of 70 meters in the ice shelf. The SV(-) vel- ocity obtains a maximum of 2100 meters per second at a depth of 11 meters in this analysis. Therefore, the SV(-) data that was picked from the seismic records is apparently another type of arrival. A PS seismic wave conversion is a possibility that might explain the high velocity observed. The SV(-) data must be rejected as being true SV wave arri- vals, and the SV(+) data must be considered as the only 54 true SV wave arrivals in this study. Velocity versus depth, in all four directions is plotted for each type of seismic wave in Figures 36-39. Examination of the P wave velocity versus depth plot (Figure 36) reveal that for the last three stations the 090 direction has the highest velocity for a given depth. This observation is consistent with the time versus dis- tance plot for P waves in Figure 32. Examination of the SH wave velocity versus depth plot (Figure 37) shows that the data groups too closely to determine any maximum velocity direction. THe SV(+) waves velocity versus depth plot (Figure 38) reveal the 045 direction as having the maximum velocity for a given depth. 55 VELOCITY [F T/SECJ 1800.0 34.4.0.0 5080.0 0720.0 8360.0 10000.0 +9 +9 +83. a .93 m .1. :32 -T°°- :8 GE + ._.. 03> ‘U + F112- G 53 m8 + 3 9‘3 t» 3’. +013 0 8 + 9 a: a“ D + I) G E) _. u) 45 CD (.0 O 0'! (J1 T '0 ‘0 '0 Z Z Z Z I) I) D I) <1 <1 <1 <1 rn F" rn F0 FIGURE 36: Velocity versus depth plot for P waves. 56 VELOCITY [FEET/SEC] 900.00 1900.00 2900.00 3900.00 4900.00 5900.00 o I l L l I (BE) .. c9 8 8 U m % ‘0. —-1?°_ '3 3:8 I? “FIN (B I'T'IT'~ 8+ m8 0 .4 I, E’+(g 3. [3+ 8 0 l3 4. y e m—l 'o c: +9013 .1 (c) #> CD to C3 tn tn CDCDCDCD 212113: 22):): :DDDZD <1 <1 <1 <1 rn rn rn rn FIGURE 37: Velocity versus depth plot for SH waves. 57 VELOCITY [FEET/SEC 1 1200.00 2080.00 2960.00 3840.00 4720.00 5600.00 O I l l I 1 GB D (8% @59 m [> g“ ‘19: D [3 m @Eb ‘0— ——T‘3°- 9 IS E! G ; [>13 N mr'- (>8 m8 (3 _4 L. D [3 g; (3 2‘ E‘ G b a: b— :3 (>613 u: #> C3 C3 cn CDCDCD <<< -I—l—I FIGURE 38: Velocity verus depth plot for SV(+) waves. 58 VELOCITY [FEET/SEC) 1600.00 2620.00 3640.00 4660.00 5680.00 6700.00 0 I I J I 999%? GS” 2° 0% 8 + D (3P8 m + ‘U... @E} —1‘.’°_ + :8 @5+ H E] :3: °+ m9 C3? —4 @B H + ‘6; o- 513 D a e.“ D + (>613 t-‘LDAO 0) C3 01 CDCDCDO‘) <<<< I) 1) JD 33 FIGURE 39: Velocity versus depth plot for SV(—) waves. VELOCITY SURFACES As stated previously a velocity surface, as used here, is a diagrammatic representation of the variation of velocity versus azimuth at a particular depth. Plots of the velocity surfaces at depth intervals of 5 feet, from a depth of 5 to 40 feet, are shown for each type of seismic wave (Figures 40-43). Velocity surfaces were determined at 5 feet depth intervals to observe if a pattern of velocity anisotropy is developing with increasing depth. Examination of the P wave velocity surfaces (Figure 40) reveal a pattern that develops from the 15 feet depth to the 40 feet depth. At a depth of 15 feet the velocity surface indicates the 000 direction to be the fastest vel- ocity direction, but the velocity in the 090 direction has significantly increased from the 10 feet depth. The per- cent of velocity anisotropy is defined by the following equation: 2( vmax - vmin) % Anisotropy = Vmax + Vmin The velocity surfaces at a 15 feet depth has 8.6% velocity anisotropy. The percent velocity anisotropy at the 20 feet depth is 11.9%, at the 25 feet depth is 12.1%, at the 30 feet depth is 13.6%, at the 35 feet depth is 14.5%, and at the 40 feet depth is 15.6%. Velocity anisotropy increases 59 60 continuously from 8.6% at a 15 feet depth to 15.6% at a 40 feet depth. The 090 direction (North-south) is the maximum velocity direction, the 045 and 135 directions are the min- imum velocity directions, and the 000 direction is the intermediate velocity direction. The 15% difference in velocity and the centrosymmetry indicated by the proximity of velocities in the 045 and 135 directions are suggestive of velocity anisotropy. Examination of the SH wave velocity surfaces (Figure 41) reveal a pattern that begins to develop at a deeper depth, and is not as pronounced as the pattern developed.by the P waves. At a depth of 5 feet the maximum velocity direction for the SH waves is 000, and the percent aniso- tropy is 11%. This high value is presumed to be due to local heterogeneity of the shallow portion of the near surface layers. The percent anisotropy decreases from the 5 feet depth to the 25 feet depth. At the 30 feet depth a pattern begins to emerge in the velocity surface with 090 again being the maximum velocity direction, 045 and 135 being intermediate velocity directions, and 000 being the minimum velocity direction. This pattern is enhanced at the 35 and 40 feet depth velocity surfaces, with anisotropy increasing. The velocity anisotropy is 2.6% at the 30 feet depth, 3.5% at the 35 feet depth, and 3.9 % at the 40 feet depth. The difference in velocity is not as great for the SH waves as for the P waves. However, 61 it should be noted that the 045 and 135 directions are again very close in value indicating the probable existence of centrosymmetry in the velocity distribution. Examination of the velocity surfaces of the SV(+) waves (Figure 42) reveal a pattern that begins developing at the 20 feet depth, and continues to the 40 feet depth. The 045 direction is the maximum velocity direction, the 000 direction is the intermediate velocity direction, and the 090 direction is the direction of minimum velocity. Percent anisotropy increase from 3.8% at a 20 feet depth, to 15.6% at a 40 feet depth. The 135 direction has no information since the raw records were not obtainable for that event. The lack of data in the 135 direction is the reason why centrosymmetry is not observable in the SV(+) velocity surfaces. The SV(-) wave velocity surfaces are plotted in Fig- ure 43. It is important to remember that although this data is being referred to as SV waves, it is apparently another type of arrival. The percent anisotropy of the SV(-) velocity surfaces almost continuously decreases from 15% at the 5 feet depth, to 7.2% at the 40 feet depth. This pattern is contrary to the patterns observed for the other three types of seismic waves. Note that there is no correlation between the SV(-) and the SV(+) velocity sur- faces. This further supports the observation that the SV(-) waves are really another type of seismic arrival. 62 25' . .1200~ 0 0 III III 2 g 5500 1- 1- 1- 3 I: u. t 5400 , 4 ‘ ‘ 5000- . ° 1, 0° 45° 50° 135° ° 45° 50° 135° .4500 . 0 3 u 2 4400 3 I" .- ° 3 E 4000 .,_ 3500 ‘ l L 0° 45° 50° 135° 0° 45° 50° 135° 1 5' 35° . 5500 0’ 5500 a 15 O m 5200 \.5200 \ 1- 5 a: g 4500 us 7500 4400 1 ‘ 1 7400 ' 0° 45° 50° 135° 0° 45° 50° 135° 20' 40' , 5400 - . 5400 0 0 II II 1’ 5000 - 2 5000 1- 1- III - . III I 5500t\/\ .‘l‘ 5500 5200 .200 L H 0° 45° 50° 135° 0° 45° 50° 135° FIGURE 40: Velocity surfaces for P waves. 63 25’ . .4200- o o m m 3 3 4100 - h h 3 I: 3000 ‘ ‘ ‘ 0° 45° 50° 135’ 10' 30' .2500- .4700 o 0 "‘ 3 '3 2400 - \ 4500 p- I- III III 1' 2300 - I 4500 2200 J 1 L 440:}, 1 1 1 0° 4 5° 00° 1 3 5° 0° 4 5’ 00’ 1 3 5' 15' 35° 3000 1- . 6200 - u 0 111 W 15 N 2000 \ 5100 .- \ h " u E 2000 I- 11. 5000 1- 2700 ‘ l L 4900 l 1 1 0° 45' 00‘ 135' 0° 45‘ 00‘ 135' 20’ . 3000 r- , o o m u 2 3500 - 2 P h :1: \/’_ 5 3300 ‘ ‘ #44 0° 45° 00° 135° 0“ 45° 00' 135' FIGURE 41: Velocity surfaces for SH waves. FIGURE 42: 50 .2400 0 III a 2200 \ p. 3 5 2000 1500 l 1 0° 45° 50° 10' .3000 0 III 3 2500 .- III N 5 2500 2400 ‘ ‘ 0° 45° 50° 1 5' _ 3500f 0 III a 3400 - \ .- 3 a 3200 - 3000 1 1 0° 45° 50° FEET/88C. 64 FEET/SEC. FEET/SEC. FEET/SEC. FEET/SEC. 25' 4400» 42001- 4000iy////F\\\\\\ 3500, ‘ 1* 0° 45° 50° 30' 4500 4500 4400 4200 ' 00 ‘50 .00 35' 5100 4500 4700 4500 0° 45° , 50° 40' 5450 5250 5050 4550 0° 45° 50° Velocity surfaces for SV(+) waves. 65 .5 d u U a Q \ \ .- I- .“ m m III a. E 0° 45° 50° 135° 0° 45° 50° 135° 10' .3700 . 0 8 :1 23500 \ h h u 3 $3300 15 3100 ° ‘ 0° 45° 50° 135° 0° 45° 50° 135° 15' 4300 6 a 2 a 4100 \ \ O- : 5 a 3500 5 3700- ‘ ‘ L- 5000 11.-A. 45° 50° 135° 0° 45° 50° 135° 40' . .720 o 0 II II 2 2 7000 I- .- u u 3 E 5500 ‘300 1 4.; 4 0.00 1 H 0° 45° 90° 135° 0" 45° 00° 135° FIGURE 43: Velocity surfaces for SV(-) waves. 66 In the Anisotropic Model section an attempt is made to match the observed velocity surfaces with velocity surfaces determined for a theoretical model. ENERGY RADIATION Anisotropic media will radiate a uniform stress in a non-uniform manner, and this energy radiation pattern will correspond to the wave surface for this media (Bennett, 1968). Furthermore, it has been shown that for the trans- versely isotropic single ice crystal, the wave and velocity surfaces are almost identical for P and SH waves, and vary by 6% at most for SV waves (Bennett, 1968). Therefore, if the near surface layers of the ice shelf are truely aniso- tropic the energy radiation pattern should bare a resem- blance to the observed velocity surfaces. If the near surface layers are not anisotropic, but instead exhibit velocity variations due to directional heterogeneity, then the energy radiation patterns should not resemble the vel- ocity surfaces. Analysis of the seismic events of the long spread surveys, which analyze the deeper zones of the study area, were undertaken in another study (Wanslow, 1981). These results indicate that the directions of maximum energy radiation for SH waves were 045, 135, 225 and 315. These directions correspond to the maximum velocity directions of the SH waves determined by others (Bennett et al., 1979). The short spread seismic events in this study were 67 68 analyzed to determine energy radiation patterns by using a series of programs developed by Mark Schoomaker in 1978- 1979. Waveforms are first removed from specific traces of a seismic event by using the Tektronix program Processor. The waveform removed starts at the beginning of the first arrival for each trace. The program Finale is then used on the extracted waveform to perform a fast Fourier transform. The program then plots the amplitude and phase spectrum for each waveform. The plot of the amplitude spectrum is used to determine the frequency band over which the waveform is to be integrated. This frequency band is then fed back into the Finale program and the waveforms are integrated within the specified limits. Logarithms of the integrated values of energy are listed in Appendix IV, Tables 40-41. Logs of the integrated values of energy are plotted versus distance (Figures 44-45). Energy radiation data was not determined for the SV waves. The log of the energy values is used since there is sometimes a difference of four orders of magnitude between energy arrivals at 10 feet and at 100 feet. Examination of the P wave energy radiation plots (Figure 44) reveal that 090 is the direction of maximum energy radiation from 60 to 100 feet. This corresponds to the maximum velocity direction for P waves as defined by the velocity surfaces. 69 Examination of the SH wave energy radiation plots (Figure 45) reveal that the 045, 090, and 135 directions, from 60 to 100 feet, are grouped together, having higher energy radiation values than the 000 direction. This observation is consistent with the velocity surfaces of SH waves which show a minimum velocity at the 000 direction, with the other three directions falling within 100 feet per second of each other. The correlation between the determined energy radia- tion patterns and the velocity surfaces indicate that the near surface layers of the ice shelf in the study area are demonstrating some form of seismic anisotropy as opposed to having directional heterogeneity alone. 70 L00 OF ENERGY .00 1- N... a o 5.225% e e a 728mm 0. o a 5 8 .0158 p r m..- w a + :8 51:82 .. G 5. m .05. E w a 0 O m 0 w . m e a m m w. nw- .5... m. .m 0 g a... .o. 0 m m 0 . . q 4 J G o 8.8 8.8 8.8 8.8 _8.8 n DHmHDZOm 2.4mm: 71 LOG OF ENERGY 0.60 0.70 0.80 0.90 1.00 0.50 I I I [E-EP [3 D GBI> 4 - Mo.oo 59.90 DHmaDzmm q E mo.oo mo.oo Hmmmag .om.oo -F D GBEB 5m mo wwm mzuzmSVVELNAX THEN SVVELNAX=SVVEL 860 IF SVVELéSVVELNIN THEN SVVELNIN=SVVEL 850 IF SHVEL>SHVELNAI THEN SHVELNAI=SHVEL 860 IF SHVEL