THESIS Llii.;AHiES EAST LANSING, MICH. 48824 This is to certify that the thesis entitled A STUDY OF VELOCITY ANISOTROPY WITH RESPECT TO HORIZONTAL RECEIVERS presented by Tedd F. Sperling has been accepted towards fulfillment of the requirements for MS degree in Geophysics Magma / ‘/ Major professor Date FJ’ ngLlagL/ 0-7639 MS U is an Affirmative Action/Equal Opportunity Institution MSU LIBRARIES “ RETURNING MATERIALS: Place in book drop—to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. A STUDY OF VELOCITY ANISOTROPY WITH RESPECT TO HORIZONTAL RECEIVERS By Tedd F. Sperling A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Geology 1984 ABSTRACT A STUDY OF VELOCITY ANISOTROPY WITH RESPECT TO HORIZONTAL RECEIVERS By Tedd F. Sperling Analysis of seismic data indicates significant velocity anisotrOpy occurring in a stressed segment of the Ross Ice Shelf, Antarctica. The seismic data, recorded in 1976-77 by Bennett, et al, consisted of data generated by both dynamite and mortar and recorded by in-line transverse and longitudinal (horizontal) receivers. The ice sheet, in the study area, is approximately 300 meters thick overlaying an approximately 724 meters of ocean. The ice layer is in a stressed environment with the C crystallographic axis oriented horizontal. Investigation, of the reflections from both the ice/water interface and the ocean bottom, indicated a P to S conversion at the ice/water interface. The P-Wave generated Shear arrivals were the main subject of the investigation, and paradoxically appeared on both longitudinal and transverse receivers. Analysis of the longitudinal data did not confirm or dispute velocity anisotrOpy. However, the transverse data supported a velocity anistrOpic model. ACKNOWLEDGMENTS My sincere thanks: to Dr. Hugh Bennett for his help, support, guidance, and friendship; to Professors Jim Fisher, Jim Trow, and Kazuya Fujita for their particapation on my thesis committee; to Carol, my beautiful wife, for her support and patience throughout my study; and finally, to my Apple computer which provided great assistance in data analysis and word processing. 11 TABLE OF CONTENTS Page LIST OF TABLES......................................... iv LIST OF FIGURES........................................ v LIST OF APPENDICES.....................................vii INTRODUCTION........................................... 1 Background............................................. 1 Theory................................................. Experimental Design.................................... Data AnalYSiSOOOOOOOOOO0.0.0....OOOOOOOOOOOOOOOOOOOOOOO QU'I-bm Longitudinal Data Analysis............................. Transverse Data Analysis............................... 21 CONCLUSIONS............................................ 59 LIST OF REFERENCES..................................... 62 APPENDIX A ............................................ A1 APPENDIX B ............................................ B1 APPENDIX C ............................................ C1 O...OOOOOCOOOOOOOCOOOCOOOOOO000...... ....... D1 APPENDIX D APPENDIX E ............................................ El APPENDIX F ............................................ F1 APPENDIX G ............. ..... ............ ..... ......... G1 APPENDIX H ............................................ H1 APPENDIXI OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO I1 iii LIST OF TABLES Page Arrival Times for various events.................. 13 Event a, observed and calculated Arrivals......... 15 Event b, observed and calculated Arrivals......... 17 Relationship of ray paths with C-axis............. 58 iv LIST OF FIGURES Figure Page 1. (Stress Field).I...O...O..0.0000000000000000000000 3 (Shot POint map).00......OOOOOOOOOOOOOOOOOOOOOOOOO 6 (EventaandbArrivalS)O0.0...OOOOOOOOOOOOOOOOOOO 9 (Ray PatnS)..0.00......0.0.0.0...OOOOOOOOOOOOOOOOO 1O (AllArrivalS).0.00.00.00.00...OOOOOOOOOOOOOOOOOOO12 (Event C, A and B-DirectionS).OOOOOOOOOOOOOOOOOOOO 22 > (Event C, Right and Left)..OOOOOOOOOOOOOOOOCOCOOOO 24 (DO Sum).......................................... 27 Chao‘o‘m-pwm (DO Reverse sum).000......OOOOOOOOOOOOOOOOOOOOOOOO 28 (R45 Sum)......................................... 29 KC) 10. (R45 Reverse Sum)................................. 30 11-14. (A-Direction Arrivals).......................... 32 15-18. (B-Direction Arrivals).......................... 33 19. (Frequency Plots, A—Direction).................... 35 20. (Frequency Plots, B-Direction).................... 36 21. (Phase Plots, A-Direction)........................ 37 22. (Phase Plots, B-Direction)........................ 38 23. (A—Direction Arrivals with static shift).......... 40 24. (B-Direction Arrivals with static shift).......... 41 25. (Event c on A and B-Directions)................... 42 Figure Page 26. (P and S Reflection/Refraction)................... 44 27. (Amplitude Ratios)................................ 46 28. (Amplitude Ratios)................................ 46 29. (Event 0 Separation).............................. 50 30. (Transverse Motion)............................... 51 31. (Event a Wavelet with Time Shift)................. 53 32. (Ricker Wavelet with Time Shift).................. 54 33A and 33B. (Wave Surfaces in a Single Ice Crystal)... 56 vi LIST OF APPENDICES Appendix A momwcow Recording Equipment............................ A and B Velocity Profiles.... ..... ............. Longitudinal Records........................... P-P—P-P Ray Path Parameters.................... P-P—P—S Ray Path Parameters.................... Computer Equipment............................. Events a and b Frequency Analysis.............. P—P and P-S Ray Path Parameters................ Transverse Records.0......OOOOOOOOOOOOOOOOOOOO. vii Pages A1 B1—B4 C1—C4 D1-D2 E1—E2 F1 G1-G2 H1—H4 I1-I8 INTRODUCTION The intent of this thesis is to show examples, using actual seismic data, which appear to demonstrate velocity anisotropism, and to compare these observations with theory. The seismic data obtained and used, for this thesis, were solely limited to ice seismic investigation on the Ross Ice Shelf in Antarctica. Several events were observed and identified by implementing a computer ray tracing program and determining normal move out calculations. These events were digitized, summed, normalized, and analyzed by the Fast Fourier Transform method. To render explanations for event characteristics a modified Zoeppritz's equation was used. Background: The study area is located on the Ross Ice Shelf approximately 130 Km south of Ross Island, in Antarctica. The actual location of the study site is approximately 18 Km west of Minna Bluff. The ice sheet in the study area is known to be in a state of stress. The choice of the site was made by air and ground reconnaissance to avoid areas 1 where any surface fracturing was visible. The floating ice shelf in the study area is known to be in a stressed state due to: One, the known movement of the ice shelf, which is to the north at a rate of approximately 1 meter per day (H.F. Bennett Personal Communication); and two, the closeness of the ice shelf, in the study area, to Minna Bluff, where the ice is grounded. These conditions place the ice shelf in a state of internal stress. The results of this stress can be seen in ice fracturing from Minna Bluff to within 3-4 Km from the study area. Ice studies have shown (Rigsby 1955) that the ice crystals, in a shear stressed environment, tend to orient the basal planes parallel to the plane of shear (A—axis is in the plane of shear). Ice has a hexagonal crystalline structure and the A-axis is oriented orthogonal to the C-axis, thus rendering the C-axis normal to the shear stress plane. The study area is believed to have the C-axis oriented horizontal with an azimuth direction toward Minna Bluff (See Figure 1). Theory: A velocity anisotrOpic medium is one in which sound is transmitted with different velocities in different directions. This is due to the internal crystalline C-AXIS 4 l l I l MINNA BLUFF I l l l I I Stress Field in Study Area Figure 1 (Stress Field) 4 structure of the medium having elastic properties that are dissimilar with direction. With consideration that ice is a nearly pure monomineral medium, it lends itself well for this type of seismic wave prOpagation study. For a detailed eXplanation of velocity anisotrOpy, the reader is referred to Kraut (1963), Helbig (1956) or Musgrave (1970). Experimental Design: The seismic data collection was done during December 1976 through February 1977 at the site previously mentioned. The recording parameters are noted in Appendix A. The recording equipment configuration is shown in Figure 1. The lines, or profiles, were arranged in a star pattern consisting of four (4) separate lines (Line O, 45, 90, 135) intersecting in the center and oriented 45 degrees from one another. The Zero (0) degree direction was defined as the direction toward Minna Bluff. The line entitled forty-five (45) degrees was oriented 45 degrees counter-clockwise from the Zero direction. The line entitled ninety (90) degrees was located 90 degrees counter-clockwise from Zero and so on... All data collection was limited to in-line recording and shooting. Seismic data were collected in several different categories. Each seismic line contained twenty-four (24) vertical, or horizontal, or longitudinal geophones. Each line was subject to two types of sources (Compressional 5 "P—wave" and Shear "SH—Wave and SV—Wave"). The source was located at three set distances (Station 1, 2, and 3 see Figure 2) and on Opposite ends of the line. Records obtained with source stations located at O, 45, 90, and 135 degrees were labeled "Direct". Records obtained with source locations located at 180, 225, 270, and 315 were labeled "Reverse". Records obtained with the shear wave generator (hereinafter referred to as mortar) were designated with the direction of shot, relative to the receivers. This criterion was used for field clarity and data collection continuity. The records obtained from the mortar pointing toward the array were entitled "Toward" and conversely those pointed away from the receivers were entitled "Away". Records obtained when the mortar was pointing at right angles to the line of receivers (normal to the profile) the terms "Right" and "Left" were used, with respect to facing the array. For example, when the mortar was pointing to the right, as one viewed the mortar and the receivers, the term "Right" was given to the records. Data Analysis: The ice sheet in this study is approximately 300 meters thick, overlying approximately 724 meters of ocean. The length and width of the ice sheet is considered to be, for o0 270 O O 0 3'5 0 225 O O O O O O O O O O 180 O 0 0 Station 1 O O 0 Station 2 O O ‘5 135 0 Station 3 90' Source Locations = o Receiver Locations = Receivers: 24 Geophones In-Line Source Locations 625, 1675, 2725 Ft Geophone Spacing: 50 Ft from center of receiver locations Figure 2 (Shot Point Map) 7 sake of the study, infinite. The ice is known to be in a state of stress thereby inducing preferred orientation of crystals resulting in velocity anisotrOpy. The thickness of the ice shelf and depth of the ocean is confirmed by computed velocities and observed arrivals. The vertical velocity structure was determined from arrival times analyzed and provided by H.F. Bennett (Personal Communication). These vertical velocity profiles are shown in Appendix B. Note that there are two sets of velocity data. Set A was derived from analysis of records obtained from O, and 90 profiles, and Set B was derived from 45, and 135 degree profiles. These two directions shall be defined as "A-Direction" (O, 90, 180, 270 degrees), and "B-Direction" (45, 135, 225, 315 degrees). In comparing one way transit times, through the ice only, for both sets of velocity data, one finds that a difference of 0.24% exists between the P-Wave velocities (Set A vs Set B) and a difference of 1.35% exists between the SH-Wave velocities (Set A vs Set B). Longitudinal Data Analysis: The first set of data analyzed was generated by a dynamite source and received by longitudinal geophones. An event appeared on all records at approximately 1.15 to 1.19 seconds at a distance of 1700 Ft (518.16 M). This event was 8 generally consistent throughout all records for distances ranging from approximately 1100 Ft (335.28 M) to 3000 Ft (914.4 M) (See Appendix C). Following this event, some 90 to 100 ms later, a second event appeared. These events, for sake of clarity, shall be addressed as Event a and Event b respectively. (See Figure 3) The first order of analysis was to identify Event a and b, and then to study their relationship. Considering that the data were recorded with a dynamite source (P-Wave generator), and longitudinal receivers (recording motion horizontal and in the vertical plane), the ray paths possible (see Figure 4), in this analysis, are as follows: (1) Direct P-Wave, or refracted P-Wave, or multiple refracted P-Wave (ie. PP,PPP, etc.); (2) Reflected P—Wave from ice/water interface; (ie. P-P) (3) Reflected P—Wave to Shear—Wave conversion at the ice/water interface; (ie. P-SV) (4) Reflections from ocean bottom interface; (ie. P-P—P—P and P-P-P—SV); (5) All combinations of reflections and multiples with respect to the three interfaces (surface, ice/water, VV‘NVV‘A/P‘MW-r I W W EMWM 18L 3, .m‘ Hzm>m.v Amam>wuu< n was m u=o>mv m ouswwm ”it: :1..:_: 0mm mmoomm Her-.m.r.rm.a..l L .a \ .r~ m s . .- .:..\ ' omQ amoomm l 1 . 1 l uln. u uh v v | I M “I; 1 l I “In... 'll'" 1 1 u . . . l r l 1 l v I l l Wr" am—m n-v—-—-—n . H II lO \ ICE OCEAN OCEAN BOTTOM P—Wave to S-Wave Conversion dashed Figure 4 (Ray Paths) 11 and ocean bottom) and with respect to P-Wave to Shear-Wave conversions at these interfaces; (6) Same as item 5, considering possible sub ocean bottom interfaces and conversions; (7) Rayleigh Wave (Surface wave). These arrivals must be viewed in their prOper time perspectives. Using the vertical velocity profiles provided, a time vs depth study was performed and is shown in Appendix B. Using this study one can account for the ray path travel times. In addition, a Normal Move Out (NMO) calculation was performed for various events and times (See Figure 5). The results of the NMO calculation for a distance of 518.16 M are shown in Table 1. The observed times for arrival of Event a correlate well with the calculated P-P-P-P arrival and the observed times for Event b correlate well with the P-P—P—S arrival. The vertical reflection from the ocean bottom, namely P-P—P—P, renders a total travel time of 1.1368 sec. (Set A velocities) and 1.1392 sec. (Set B velocities). To compare the actual arrival times, from receivers offset from the source, with calculated travel times a ray tracing computer program was implemented. This program, written by the Figure 5 (All Arrivals) 13 TABLE 1 - Arrival times for various events RECEIVER DISTANCE OF 518.16 Meters Event Time (Vel A) Time (Vel B) P—P (Reflected Ice/water) 230 ms 226 ms P-S (Reflected Ice/water) 315 332 1st Order Mult (P-P * 2) 574 388 8-8 (Reflected Ice/water) 420 470 2nd Order Mult (P-P * 3) 540 549 1st Order Mult (P-S—S—S) 673 567 1st Order Mult (s-s * 2) 774 692 3rd Order Mult (P-P * 4) 712 720 4th Order Mult (P-P * 5) 885 895 2nd Order Mult (P-S—(S-S) * 2) 1020 950 2nd Order Mult (S—S * 3) 1107 999 5th Order Mult (P—P * 6) 1056 1060 P—P-P-P (Ocean Bottom) 1695 1715 6th Order Mult (P—P * 7) 1225 1259 P-P-P-S (Ocean Bottom) 1267 1248 14 author, used the P-Wave velocity functions provided (Appendix B) to calculate, via Snell's Law, P-P-P-P ray paths. The output of this program rendered ray path travel distances, transit times, and incident angles for various boundaries and receiver distances. The results of this program are included in Appendix D. A sample comparison, between the calculated arrival times and the actual arrival times (taken from records R90 and R45*) are noted in Table 2. The results, from record R90, were used because this record is considered typical Of all records in the A-Direction. Similarly, the results of record R45 were shown because this record was typical Of all records in the B-Direction. The arrival of Event a (on all records), at a distance Of 518.16 M, ranged from 1.165 to 1.18 seconds and at a distance of 670.5 M, ranged from 1.19 to 1.20 seconds. The arrival times for Event a were greater in the southeast and lesser in the northwest. This Observation may be due to ice thinning to the northwest. Considering the previous findings, it is apparent that Event a is a result Of a P-P-P-P ray. Event b cannot be a multiple of Event a due to the short separation (95 ms) 15 TABLE 2 - Event a, observed and calculated arrivals Using velocity function from Set A: Record R90 - Dist: 518.16 M Event a Arrival: 1.1650 sec. Calculated " 518.10 M " " " 1.1695 sec. Difference.OOOOOOOOOOOOOOOO0.0.00.00000-00004’5 sec. Record R90 - Dist: 670.50 M Event a Arrival: 1.1900 sec. Calculated " 677.35 M " " " 1.1898 sec. DifferenceOOOOOOOO0.0000000000000000000 0.0002 sec. Using velocity function from Set B: Record R45 - Dist: 518.16 M Event a Arrival: 1.1800 sec. Calculated " 511.33 M " " " 1.1715 sec. Difference............................. 0.0085 sec. Record R45 - Dist: 670.50 M Event a Arrival 1.2100 sec. Calculated " 667.02 M " " " 1.1913 sec. DifferenceCOOOOOOOO00......0.00.0000... 0.0187 sec. 16 between arrival times. Therefore Event b must be some other phenomenon. The calculated difference between the vertical one-way travel time for a P-Wave and a Shear-Wave is approximately 91 ms (A Set Velocities) and 73 ms (B Set Velocities). The actual separation seen on the data appears to be approximately 95 ms. However, this separation occurs at distances of 518.16 M and 670.56 M from the source. Due to the Offset distance, the arrival times Of Event a and b should be greater. TO calculate the arrival times, the previous ray tracing program was again implemented and instructed to calculate a P-P-P-SV ray path from both P-Wave and Shear—Wave velocities given in Appendix B. The program calculates ray paths, transit times, and incident angles for the input model at various receiver distances. These calculations are shown in Appendix E. A sample comparison of the results of the calculations for arrival of Event b, for distances Of 518 M and 670 M, are noted in Table 3. The comparisons show that the A velocity set has a higher degree Of correlation, with the data, than the B velocity set. The following, shows the comparison of the Observed difference of arrival times for Event a and b and the calculated arrival times: 17 TABLE 3 — Event b, Observed and calculated arrivals Using velocity function from Set A: Record R90 — Dist: 518.16 M Event b Arrival: 1.2600 sec. Calculated " 522.83 M " " " 1.2665 sec. DifferenceOOOOOOOOOO0.00.0.000000000000-000065 sec. Record R90 - Dist: 670.50 M Event b Arrival: 1.2840 sec. Calculated " 679.16 M " " " 1.2865 sec. DifferenceOOOOOO00.0000000000000.0.0.00-000025 Sec. Record R45 - Dist: 518.16 M Event b Arrival: 1.2750 sec. Calculated " 511.08 M " " " 1.2480 sec. Difference..............................0.0270 sec. Record R45 - Dist: 670.50 M Event b Arrival: 1.2900 sec. Calculated " 665.34 M " " " 1.2702 sec. DifferenceOOOOOO...0.0.0.000...0.0.0.000000198 sec. 18 Distance 518.16 M Event a Arrival: Event b Arrival: Separation: Record R90 1.1650 sec. 1.2600 sec. 95.00 ms Vel. A Set 1.1695 sec. 1.2665 sec. 96.93 ms Record R45 1.1800 sec. 1.2750 sec. 95.00 ms Vel. B Set 1.1715 sec. 1.2480 sec. 76.52 ms Distance 670.50 M Event a Arrival: Event b Arrival: Separation: Record R90 1.2100 sec. 1.2840 sec. 94.00 ms Vel. A Set 1.1898 sec. 1.2895 sec. 99.69 ms Record R45 1.2100 sec. 1.2900 sec. 80.00 ms Vel. B Set 1.1913 sec. 1.2702 sec. 78.86 ms (Note that these events, although appearing on the same trace, are from two different ray paths with different ray parameters.) The Observed Event a and b separation, as previously mentioned, is approximately 95 ms. The calculated separation, as shown, ranges from 96.93 to 99.69 ms (A Set velocities) and 76.52 ms to 78.86 ms (B Set velocities). The difference between the average times for the observed and calculated arrivals is believed to be due to any combination Of the following: l9 (1) Possible errors in the determination of the velocity profiles; (2) The application of an isotrOpic velocity profile to an anisotropic material; (3) Inhomogeneity in the ice shelf. (fractures, basal ice irregularities); (4) Irregular thickness of ice; (5) Errors in selecting arrival times. In any event, considering the amount of difference between Observed and calculated arrival times for Event b, it is probable that Event b is the result of a P-P—P—SV ray using the Set A velocity profile. TO study the relationship of Event a to Event b, the data had to be digitized to facilitate computer application. All data analyzed, in this thesis, was derived from analog plots of the original digitized data. The data was first digitized from these plots via equipment noted in Appendix F and software written by the author. The digitizing software utilized an algorithm which allowed 20 the user to digitize random points and then interpolate between points and provide 2 ms sampled data. A cubic algorithm was selected based upon best comparison of the sampled data to the original data. The digitized data were visually compared to the original data, prior to use in the study. The greatest amplitude and consistency, of Event a and b, from one record to another appeared on traces from 1700 Ft (518.16 M) to 2200 Ft (670.56 M). Therefore, on each record, eleven (11) traces were digitized with a 200 ms window. This window began at a point 30 ms before the maximum amplitude of Event a. This allowed the window to contain both Event a and Event b. The eleven windowed traces per record were first summed and then normalized. Normal Move Out (NMO) was, in effect, considered in the summing process, due to the fact that the traces were digitized with respect to the actual arrival Of Event a. The times Of event separation were noted and an average range of 87 ms to 94 ms were found to exist between Event a and b for various directions. The greatest separation, between Event a and b, occurred in the southeast quarter of the study area, again this suggests ice thinning to the northwest. Each window was analyzed via a Fast Fourier Transform (FFT) 21 to determine frequency and phase comparisons (Appendix G.) This was done to try to determine if the Event b had been subjected to birefringence due to anisotrOpy. The results proved negative. Frequency analysis Of all windows indicated no significant pattern with recording direction. Transverse Data Analysis: The second set of data analyzed was generated by mortar and received by horizontal transverse geOphones. The mortar was set normal to the shot point-receiver line, generating horizontal shear motion (SH-Wave). A consistent and strong event appeared on several records for distances of 2150 Ft (655.32 M) and 3300 Ft (1005.84 M) and times generally Of 380 ms to 440 ms reSpectively. For clarity in this report this event shall be referred to as Event c. These records were from B-Direction with "Right" and "Left" mortar orientations and from the A-Direction With "Right" and Left" mortar orientations. Event c was Eibsent on records obtained from the A-Direction (See Figure 6). Ir“Spection of Event c suggests two important aspects Of its OI‘igin: (1‘) Event 0 appears before the shear refraction arrival. 22 h/ w MKV" \— W W, .’\/\ [\1‘ f‘ Amaowuomufiaim paw < .o / , A, : a , K. N fix... 1 /r~rrw-axcme W F. w 0mm amoumm \ a fl % W W W W W m \ ucm>mv as, . : _ rrrrae>eeu< dud MW , WW: . AAA-rJ-w o muswfim Aw I‘ll“ :W \ men amoomm a- I. i. I. i U u I. ia- a i I. a I a i a a t w i i T i a u i I. u .0 of Kl (2) 23 Figure 5 shows that the only events appearing before the shear refraction is the P-P event and the P—S event. (Both events from the ice/water interface); Event c arrives with the same apparent polarity regardless of the "Right" and "Left" orientation of the mortar (See Figure 6A). If Event c was shear generated then the polarity of Event 0 would change with orientation of the mortar (Right and Left). However the polarity did not change and therefore Event 0 is P generated. This is not unusual considering that the mortar, although used to produce shear horizontal motion, also produces a component of compressive vertical motion. Analysis of the data, later in this report, will support this conclusion. However, this vertical motion (P or SV) should not, in an isotrOpic medium, be seen on transverse motion receivers. To identify the ray path of Event 0, again the ray path program was implemented. This program was used to the calculate the ice thickness of 300 M. The ocean bottom was not considered because of two factors: One, water will not transmit a shear wave; And two, the time restraint of 440 ms, and less, would prohibit such ray path consideration. Using only the ice thickness, and the two velocity sets (Set A and B) the ray path program calculated ray paths for 24 " V ”‘3 \/*((.‘v \11‘ \\ 2M) 11,( '1 W WW ‘1’ v 1&89‘3411111111 Right and Left) Figure 6A (Event c, 25 distances of 655.32 M to 1005.84 M. The ray paths that were considered were reflected P—Wave (P—P) and reflected P—Wave to SV-Wave conversions (P-SV). The results of this program are shown in Appendix H. The calculated P-SV arrivals, using the Set B Velocities, were within 5 ms of the actual Event 0 arrival on the 45 and 135 degree profiles (Appendix I). There was not an apparent Event 0 arrival on the O and 90 degree profiles (Appendix I). This phenomena will be addressed later. The calculated P-P arrivals, using both Set A and Set B Velocities, were nearly identical. However, no P—P arrival was Observed on any record for any direction or orientation. One should eXpect the P-Wave arrival, to be recorded, as having only small amplitudes on the transverse geOphones. Furthermore, the P-Wave amplitude for this arrival is theoretically small, as is shown later. Further analysis required the digitization of 200 ms windows that would contain Event c. The start Of all windows was determined by the calculated arrival Of the P-P event at each trace distance. At the time Of digitization it was believed that the actual ice thickness was 322 M. This rendered an arrival of the P-P event some 15 ms later than what is presently believed. However, this did not affect the analysis, for Event c was still contained within the window. 26 To emphasis analytically that Event c was a P-Wave generated arrival, the following was preformed. If Event 0 was P-Wave generated then the polarity Of the event would be the same for both "Right" and "Left" records. However, if Event c was shear generated then the polarity of the event would be dependent upon the polarity of the source, namely "Right" and "Left". To do the analysis, records R45 "Right", R45 "Left", DO "Right", and DO "Left" were used. These records were chosen because of their apparent good data quality and direction. Again, 200 ms windows were utilized in digitizing the traces. Each record had twenty-four traces digitized. The twenty-four traces of each record were then summed and normalized. Again, Normal Move Out (NMO) was, in effect, considered due to starting the windows at the calculated arrival time for the P-P event. After summing and normalization of the data sets, both the "Right" and "Left" data sets were then summed together. Then the "Left" data set, for both R45 and D0, were reversed, in polarity, and then summed to their respective "Right" counterparts. The results are shown in Figures 7-10. Inspection of these figures, shows clearly that summing of both "Right" and "Left" records for the R45 direction renders a pronounced event (See Figure 9). Whereas, -1 llllLllllllllllllllllllllllllllllllllll .1 l9! 1 r .. . _ :- . x .... .n. at I . a . .1! . a... . 4 u‘ ‘I - | ' _ m . _ . u _ r v ill-Illa! I‘IF'JI . 0| .1 llulll‘Hv. 1' 1.!- \ ‘41.".I till] I I i. In I .. Ilnl. I , .me 1W .- - 28 1 O -1 ~ 1 RECORD D0 "LEFT" (REVERSED) 1 V'VV .11. 1‘ . 0 1 -1 SUM OF ABOVE RECORDS 0 -1 .1.m.1.lr1.|.|.|.l.|.|.|.|.l.|.|.|.l. 0 100 ZOOms Figure 8 (D0 Reverse Sum) 29 RECORD R45 "RIGHT" .|.|.1.I.l.1.|.1.lJ.LI.|.I.l.|.|.|.I. 0 100 200ms Figure 9 (R45 Sum) 30 RECORD R45 "LEFT" (REVERSED) .11. SUM OF ABOVE RECORDS '1 lllllllllllllllllllllllljlllllllllllll O 100 200ms Figure 10 (R45 Reverse Sum) 31 reversing the "Left" record and then summing the two records destroys the event (See Figure 10). It is apparent that Event 0 is P—Wave generated and is very pronounced on the R45 direction and subdued on the D0 direction. The next step in the investigation was to determine the presence, or absence, of Event c, with reSpect tO all directions. TO do this additional traces were digitized. Each "Right" record twenty-four traces digitized in the same manner as the previous traces. The decision to use only "Right" record determination was purely arbitrary. Once the Event c had been determined to be P-Wave generated, it makes no difference which orientation "Right" or "Left" would render preferred data. In addition, to digitize both "Right" and "Left" records would only increase the fold of the analysis. The data were considered to be Of good enough quality to yield the same results with 24 fold as with 48 fold. Each set Of traces, from each direction, were then summed and normalized. These results can be seen in figures 11 through 18. Figures 11 through 14 were from the 0 (Direct and Reverse) and 90 (Direct and Reverse) degree directions. Figures 15 through 18 were from the 45 (Direct and Reverse) and 135 degree directions. 32 Amam>wuu< coauoowfiolHHu< cowuomuwnlmv wauma mouswfim macaw o0fi 1 o -—-—-—u_q—u—qfiu—4_u—u—q—d_u—-—u—u—-—-— r _ _ WW _ ._ _____.__WW WWWWWWW: Am“ runwaav «mama—Moo: ASH runaway mes amoumm macaw OCH 0 .—-—-—-d#._—-—-—-—-———u—-qd—u Asa meswfimv mmfia amoomm Ann euewamv men Queens 34 Inspection of these figures indicates that an event (Event 0) is pronounced and consistent on the 45 and 135 degree directions. Whereas, on the 0 and 90 degree directions render again an inconclusive determination. To try to achieve a more conclusive answer, additional work was done on each summed Data Set. Each Data Set was then analyzed via the FFT program. The frequency distribution and phase relationships are shown in Figures 19 through 22. Inspection of the frequency and phase relationships show clearly that there is a uniform frequency distribution of approximately 20 Hz to 70 Hz, with a corresponding uniform phase spectrum, for records Obtained in the B-Direction. Whereas, no such consistency exists on the A-Direction records. As previously mentioned, Event c was apparently absent on records in the A-Direction. TO test this in a quantitative fashion the data were stacked after visual static determinations. First, all Data Set sums were viewed with reSpect to determining the time of the maximum amplitude "Peak" of Event c. The RO Data Set was considered to be the reference for the A-Direction and the R45 Data Set sum was considered as the reference for the B-Direction. From the reference 35 Amam>wuw< coauomufia|< .muOHm aocoaumumv ma muswwm Nmmma con on o ummNH ooH an o _ _ _. _ ._ a fiJV_ ._ — _. ‘11— .1_. _ _ I __ _ <4 I _u _ ._ q _._ I_ I _. — . I I I o I, III I, _ I VI... I I I. I _I II I . I. _ . . . A I. I II. I." ... I.. I.I ... I I .III In I“. .I. . I I .I .. .I I. .I, .I.. . A .I I I .I .I I I ...A .. .I I ~ I ‘ I I. I . I I _ I. A II. . _I. _I.. W. I . I“ . II. _. VI“: I AA II I. I. I I. . IW. . . I I _w. .u. I-. .. . _ I. I I .I W .I .VI I. I I. I III.I : .V W I II _ .W I AWII _ I. . _ . I I I I I ‘ . I I I I I — a ,W WV I I I I . o I . I I . n n . W I I _ I ,I I I . ; _ . I I . I I I A III V I . , I .II _I II I . I WI. _II II I IV . I I A _II .VI_ . . I I I.. I I I I _ ,II I.I I, .. I I ILA . I. I . A III A IV I I I W I A. IIIA III. . II I I II I. II W.IW.I II III I I. III. ._.V. A._ II. III .I I I ”W I . I”. _ . IIWW II.W .IIV “ .II. A. _ IIIAI A II I . I I .I . I I I .I I V I . IIAI . _II I .I .... .I I I. II. ..I... II. .I I I... I .IIII VI "I. VW.W I. II I_ a I._ I I I I. If“ . III . .I II I II . _.I . . W I III ..I... IV I.:W _ I. III I. I. .V II I. A I. I VI. . I. . _.A . . . . I .._. I A.. VV I . .I I WI WI. I...A . IIII VV I . AA .I “I. . I . I . I ..I — _. I.I .I . I .."I I. .I I: I I . II. II. I I V I VI .. IIV .I. A I .II V I I I. A, U .I. AA . II I V. . I .. _ I V I. . . I I I . I cam excomm con QMOUMM om Qmoomm on amoomm 36 emmNH Ame>Huu< :owuouuwoim .muOHm hocmsauumv om ousmam OOH on o —-—- u—-—-—-—-—-—-_-—-— _ I W _ I _ — A I . _— II I». I. . IW I .V I I II. .. I . W. I.V . I V ... A II T. .. I I. I I I . I. H; II ..I . I > . . v. _ I. I _ I V. .VI V I I— I mqm amoomm - n _ _ — II I I . . II I . .. . V . I . I . . I V A _II I. W V V V I . I . . . .I I. .- . .II, ..II III II WII I I. . I V .I I . .I A.” I .IW I II I .I . . .I . I I . .. .I A IIIVII . . I.I_ A. A I I. I A I. II I I ._ , I V. I I . M I. . V .I. I . I . In“: V.W I _I I I I . I I . I I I .4 I W W _ W. . .I V .A .. . I. I .. ... I. I I I . I .. I W I I. I I I..I V . I I .I... W I . W V. I... A. I... I . W . . V I I IW I III I I. V I.... I . I I I I II... ..I ._ I . . I I I I I I IA VI a v. I I . I I nmmmfi ooH cm 0 _ ._ .__—I _ __ _WV. _4_ __ I. q _I V o _ ., I I mman amoomm I . . men amoomm 37 AmHm>Huu< coauoouwnl< .muOHm wmmsmv Hm wnsmfim ummNH ooH on o NumNH ooH on —___ _____A\_—_——_____.~duhl HI ——_— _—~______—-__—____- cam 950mm 08 550mm 0 o _ _ _ a H - _IIIfiIIIIIIIIIIIIIIII II..- II.I_____IIIII_II_IIIIIIIII om amoumm co mmoomm o o . H u . 38 AmHm>Huu¢ coauumuwnlm .muoam mwmnmv NN wuswfim ummmH ooH on o anm amoomm ———- __-—_—-—__—_-_-—_—- uni an —-—__u—-_—__ _ __ _ _ __ . _ __ _ mqm omoomm uni nmmNH ooH an o H: 1A\1_ . _ _ _ __ _ ._ I __ _ __ I __ _ .V mmfio amoomm Ru __ __ _ __ _ ._ __ ._ _ __ __ __ _— mqo Qmoomm 39 sum, each Data Set sum static was determined by aligning all "Peaks" (See Figures 25 and 24). For example, it was determined that Data Set sum D45 required a static shift of +6 ms to align with the reference R45. Figures 25 and 24 show the determined "Peaks" and statics. Second, Data Sets in the A—Direction (namely R0, DO, R90 and D90) were shifted, per their static correction and then summed. Data Sets in the B-Direction (namely R45, D45, R155 and D155) were shifted, per their static correction, and then summed. Both A and B—Direction sums were then normalized to the greatest value within both sets of data. This provided a true comparison of the A and B-Direction sums (See Figure 25). Inspection of Figure 25 shows that Event 0 remains on the B-Direction data and is the greatest in amplitude. The A-Direction sum shows what may be an Event 0, but the amplitude of the "Peak" is approximately 62% of "Peak" appearing in the B-Direction. In addition, the background noise (average absolute value) is approximately the same, 16.45% for the A-Direction and 15.75% for B-Direction. This suggests that if the A-Direction does indeed have an Event 0, that the arrival is much weaker, in amplitude, than the arrival in the B—Direction. Event c (P—S reflection) is very pronounced and therefore 40 AuMHsm afiumum spas mam>fiuu¢ cowuumuwnlwuu< coauomuwnumv «N muswam maoom 00H 0 Gem Hut d—uflddd—-—-—-— III u—qu—q—q—udd—u_u—-—-dd—- I .. mmfim nMoomm > I: III-IIII mam nmoomm I III III _IIIII_.-_III_I 60H 6 I 1.. mEONrIIIIJ III r III. 25+ dfiu—u_d—- —-—d—dd1—-—- mmdn nmoomm b D II. _IIIIIIEZII mcn nmoomm fiat 42 .IHHH...IHi .m' .1 I I ! ”HIV U‘HHHILV o B-Direction JJllilllJlllllllilLll[illilllllllllllll ‘1 0 100 200ms Figure 25 (Event c on A and B-Directions) ..‘II ‘, .o. 43 one would eXpect that the P—P arrival to be present. However, the P—P reflection is absent and this must be explained. The calculated arrival times, via the ray path program (Appendix H), show that the P—P event should appear at approximately 250 ms, for 655.32 M, and 445 ms, for 1005.84 M. However, as previously mentioned, there is no observed arrival. The amount of energy that is returned to the surface, from a reflection, is dependent upon the ratio of acoustic impedances, across the boundary, and the angle of incidence of the incoming ray. If an incoming ray strikes a boundary obliquely, then the compressional energy will be transformed into four types of waves, namely reflected compressional, reflected shear, refracted compressional, and refracted shear (See Figure 26). These relationships are eXpressed by the Knott's and Zoeppritz's equations and shall not be proved in this thesis. In addition, these equations deal with solid—solid boundary. The example set forth in this thesis deals with a solid-liquid boundary (ice/water interface). This differs from the solid-solid boundary in that liquid does not transmit a shear wave and thus the equations must be altered to accommodate this. H. F. Bennett provided this author with a modified 44 P 1 P1 UNIT 1 UNIT 2 V1D1§V2 D2 V81 V82 52 P2 P = Incident P-Wave P1 = Reflected P-Wave P2 = Refracted P-Wave $1 = Reflected S-Wave $2 = Refracted S-Wave Vl = P and P1 Velocities V2 = P2 Velocity VSl = 81 Velocity V82 = $2 Velocity D1 = Density of UNIT 1 D2 = Density of UNIT 2 Figure 26 (P and S Reflection/Refraction) 45 Zoeppritz's equation that conforms to a solid-liquid boundary. This equation was entered into a computer Boundary program, written by the author, that yielded relative amplitudes (for reflected P and S and refracted P) for any input angle of incidence. Appendix H also shows the angles of incidence for the various P—P and P-SV ray paths. The angles include: the angle of incidence at the source (departing ray); the angle of incidence at the reflector (incoming ray); the angle of incidence of the reflected ray (out going ray); and the angle of incidence of the ray at the receiver (arriving ray). Using the Boundary program, Figures 27 and 28 were produced. Figures 27 and 28 were produced by incrementing the angle of incidence from 0 to 90 degrees and using the following basal ice/water interface parameters: Parameters for Figure 27 Parameters for Figure 28 Ice P Vel:.... 3.8147 Km/s Ice P Vel:.... 3.7333 Km/s Ice S Vel:.... 1.8223 Km/s Ice 8 Vel:.... 2.0754 km/s Water P Vel:.. 1.500 km/s Water P Vel:.. 1.500 km/s Ice Den:...... 0.917 g/cc Ice Den:...... 0.917 g/cc Water Den:.... 1.03 g/cc Water Den:.... 1.03 g/cc Amplitude Ratio Amplitude Ratio 46 1 0 Figure 26 1 h. lllllllLlllLlllll O 10 20 30 40 50 60 70 8O 90 Degrees IIIIIIII!:II,.._,..... _- nu..." "..." P2 gun: I S]. ........................ "...“... 0).,- on"... o ... r... I 0 P1 Figure 27 1 lllJLJlllllLlllil 0 10 20 3O 40 50 60 7O 80 90 Degrees Angle of Incidence P1 = Reflected P-Wave P2 = Refracted P-Wave S1 = Reflected S-Wave Figures 27 and 28 (Amplitude Ratios) 47 Note that the P-Wave and S—Wave velocities were taken from the A and B Velocity functions, Figures 27 and 28 respectively. InSpection of Appendix H (A Velocity Function) shows that for rays (P—P) that surface, at distances of 655 M through 948 M, have angles of incidence of 49.78 degrees to 60.24 degrees, reSpectively. Correlating this fact with Figure 26 renders a very low, and negative, reflection coefficient for the reflected P-Wave. Conversely, inspection of Appendix H (A Velocity function) shows that for rays (P-SV) that surface at distances of 659 M to 987 M, have angles of incidence of 62.89 to 72.94 degrees. Correlating this with Figure 26 indicates a very high, and positive, reflection coefficient for the reflected SV-Wave. Inspection of Appendix H (B Velocity Function) and comparison of the results thereof with Figure 27 suggests similar conclusions. The reflected compressional (P-P) event is very weak, if at all present, and the reflected shear (P-SV) event is near maximum amplitude. Note that the arriving birefringent Shear-Wave rays, for both velocity functions, are nearly vertical. If one was to consider the study area as being velocity isotrOpic, Event c would present a two fold paradoxical phenomena with respect to: 48 (1) Event c appears on records that were generated with a compressive source (both P-Wave and SV-Wave) in the vertical plane and then recorded with transverse receivers that record motion in a plane orthogonal to the vertical plane; (2) Event 0 appears strong on the B-Direction records and weak, at best, on the A-Direction records. A velocity anisotrOpic model would provide an eXplanation of this paradox. Take for example the previously mentioned velocity sets (Set A and Set B). The P-Wave velocities for both A and B sets are approximately the same (varying in transit time approximately 0.24%) whereas the Shear-Wave velocities vary in time apprOXimately 1.35%. This means that for directions 0 and 90 degree (A-Direction) the Shear velocity would be, in effect, isotropic. Whereas, for other directions, namely the B-Direction, the Shear velocities would be dependent upon particle motion with respect to the C and A crystallographic axis. Considering a P—S conversion, in the B-Direction, the Shear-Wave would Split into two wave types, leaving the point of conversion at different shear velocities (Set A and B), with different ray paths (velocity dependent), and vibrating in different planes (C-axis/ray and A-axis/ray). 49 Using arrival times and distances from Appendix H (P-S Ray Tracing) the following figure (Figure 29) was produced. From this figure, a time separation of approximately 16 ms is observed for the two Shear-Wave fronts. This means that for any Specific receiver location, the two separated Shear-Waves would arrive approximately 16 ms apart. This phenomena is similar to the E and the 0 ray in Optics. A receiver would first experience the arrival of the Shear-Wave vibrating in the C-axis/ray plane, and then, some 16 ms later, would experience the arrival of the Shear-Wave vibrating in the A-axis/ray plane. The resultant horizontal vector, from the passing of both of these Shear—Waves in time, would transcribe a quasi-circular motion. The motion seen on the transverse receivers would be the projection of these Shear-Waves on to the vertical plane. (See Figure 30) To demonstrate this phenomenon, one can: Determine the input pulse (Wavelet); Time separate two Wavelets by 16 ms; Reverse the polarity of one of the Wavelets; And, then sum both of the Wavelets. The results of this would show the response that a transverse receiver would record for the two Shear arrivals 16 ms apart. Determining the Wavelet, in this study, is difficult. There 50 m! con 00¢ Aaoaumumamm o ucm>mv mm muswfim QCUhul och _ _ _ . 000 m! Own I. a! 00' 51 .’ I To . ‘ I ” 'me I I l I Time 2 Time 3 Time 4 l I i l . llAN!’VEI§‘ .éEI—tssza = 710114 Resunant Transverse Motion Figure 30 (Transverse Motion) 52 is no apparent example of a P-S wavelet in this data. Considering this observation, an attempt at approximating the wavelet was made by digitizing and summing Event a to produce the wavelet shown in Figure 31B. This wavelet was used in the previous demonstration. The results of which are shown in Figure 31C. The comparison of Figure 310 with Event c (Figure 31A) appear similar. It should be noted that the frequency plots (See Figures 31D and 31F) of both Figure 31C and Figure 31A show an approximate 58—62 Hz notch which suggest a wavelet separation of 16 to 17ms. To further elaborate this point, an additional wavelet was used. This wavelet was a standard Ricker wavelet (See Figure 32B) with a frequency enve10pe slightly larger than the frequency enve10pe for Event c. Again, the results yield similar conclusions. However, the comparison of the 16ms separated sum (Figure 32C) with Event c (Figure 32A) shows an apparent higher degree of similarity. Note the 62 Hz notch, in Figure 32F, showing the result of a known 16 ms separation in Figure 32C. If the study area is velocity anisotrOpic, as the characteristics of Event c suggest, then another apparent paradox emerges. Analysis of the previously mentioned P-P—P-S arrival, namely Event b, did not show any 53 l 1 31A 31D H 1 ...HlllH.l”l .11. .l I ’ l 'l. llllmih “'12:: : ' v ' 151:? :s' I 1 41.1 II.. o J1l11L111111l1l111 0 - .1.1.1.1.[.1.1.1.1.l.1.1.1.1.l.1.1.1.1. 1 31C 0 0 -1 1.1.1.1.l.1.1.1.1.l.1.1.1.1.l.1.1.1.1. .1.1.1.1.l.1.1.1.1.l.1.1 0 100013 0112 50 100 12511: Figure 31 (Event a Wavelet with Time Shift) 54 1 1 H 32A 3211 0 .HhthW .w -1' I h ”hl'1MHHn ' 'I ‘‘‘‘‘ I -: 111l1l1l1l1l1l1l1l1l1l111111111111111l1 1 l1 11 l 1 1 l1liLli1 [1.1 LJ.1 l 1 3211 H 0. V 1' o -i», lllllllllllllllljlllllllllllllll 1 32C 0 o -1, .1.1.1.1.l.1.1.1.1.l.1.1.1.1. .1.1.1.1.l.1 .1 . 1 . 1.1.1.1 0 1001111 on; so 100 12511; Figure 32 (Ricker Wavelet with Time Shift) 55 indication of birefringence. This must be eXplained. To eXplain this refer to Figure 33A, taken from Bennett (1968). This figure shows the velocity relationship of a single ice crystal with reSpect to the crystallographic axis. V1, V2, and V3 correspond to the P—Wave, Shear 1, and Shear 2 velocities respectively. Note that the P velocity is approximately 2% faster, along the C-axis, than along the A-axis. Also, note that the P velocity is approximately 2% less than the mean of the A and C axis, at forty-five degrees. The greatest amount of velocity change is observed in the relationship of the two shear velocity surfaces (V2 axis, the two velocity surfaces are at their maximum separation (V2 greater than V3). There appears a cross-over point (point of equal velocity) at approximately 73 degrees. At angles of 73 degrees and greater, V2 is less than V3. Note that for shear wave prOpagation at the cross—over point, no birefringence would be observed. Inspection of Appendix E and Appendix H (P-P—P—S and P-S ray paths) yields the angle of incidence of the refracted ray. Using the following formula, one can calculate the angle made by the ray with the C-axis for ray paths corresponding to the BéDirection (See Figure 33B). 56 333.3 moH mawfium m a.“ mmommunm 965 mm muswfim :IIIII! F AwomC uumaamm Baum ~3me 0wm\m¢ubm3 80¢ 80* van” «~18 Coma 0'0“ camp («Ow «pm 9 .h p n b h b - -: u a :92 52...: u u lawn r. Qua, I 00.54 r. ova“ r 33 / 1. «Non / l 1000 Illroaoc fil 000* 4 smIn] \ff 3 = arccos Table 4 shows the relationships of the PeP-P-S and P-S ray paths with respect to similar distances and the C-axis. Inspection of Table 4 yields an important aspect. The average ray angles, with the C-axis, for the P-S rays are less than 73 degrees, whereas, the average ray angles for the P-P-P-S are greater than 73 degrees. Comparing the results of this table with Figure 34, one could conclude that both the P-S (Event 0) and the P-P-P-S (Event b) ray paths should eXperience birefringence. However, keep in mind that Figure 34 demonstrates the results that were derived from a single ice crystal, whereas, the data analyzed in this study are from an ice shelf. The presentation of Figures 33A and 33B is only to show the velocity relationship in an ice crystal and to infer that a similar relationship can be expected in a larger study. 58 Table 4 - Relationship of ray paths with C-axis Using Velocity Set A RAY DISTANCE - REFRACTED ANGLE - ANGLE WITH C-AXIS P-P-P-S 607 M 15.73 Deg 78.94 Deg P-P-P—S 891 21.31 75.11 AVERAGE......77.02 P—S 617 M 24.66 Deg 72.84 Deg P-S 898 26.83 71.39 AVERAGE......72.12 Using Velocity Set B RAY DISTANCE - REFRACTED ANGLE - ANGLE WITH C—AXIS P-P-P—S 611 M 17.99 Deg 77.38 Deg P-P—P—S 892 24.45 72.98 AVERAGE ...... 75.18 P-S 611 M 28.57 70.24 Deg P-S 899 31.54 68.29 AVERAGE......69.26 59 CONCLUSIONS In this study there were basically two sets of ray path configurations analyzed. The first sets of ray paths were the P—P-P-P and the P-P-P-S sets, which traveled through the ice layer and reflected off the ocean bottom back to the surface. At the ice/water interface there was an upward transmitted P—Wave, observed at the surface as Event a, and an upward transmitted P—S conversion, observed at the surface as Event b. All particle motion was presumably in the vertical plane and was recorded on longitudinal receivers. Event b was analyzed, with reSpect to birefringence, and the results were negative. The second sets of ray paths were the P-P and the P-S, which traveled through the ice layer and reflected off the ice/water interface. It was observed that the P—P reflection was not present on the data and that the P-S was strong and consistent on the B-Direction (45 and 135 degree records). It was further shown that the P-S event, Event 0, had been produced by a P-Wave to Shear—Wave conversion in the vertical plane and then received on transverse receivers. Event c was analyzed, with respect to birefringence, and the results were positive. 60 The comparison of the similar segments of P-P-P-S ray to the P-S ray and their respective events, presents some interesting relationships. (The similar segments defined by that interval from the ice/water interface to the surface.) (1) (2) (3) (4) The P-Velocities in the A-Direction are slightly greater than in the B-Direction. This suggests that the C-axis is oriented in the A—Direction (Personal Communication H. F. Bennett). Furthermore, the relationship of the similar segments of the P-P—P-S and the P—S, with respect to the cross-over point (where the two shear velocities are equal), also supports the C-axis being in the A-Direction. The P—P—P—S ray has an angle with the C-axis that is close to previously mentioned cross-over point. This suggests that birefringence would not be observed for such a ray. The P—P—P-S event, Event b, is observed in both A and B-Directions, with longitudinal receivers, without any noticeable difference in amplitude. The P—S ray has an angle with the C-axis that favors anisotropy. Thereby suggesting that birefringence would be observed for such a ray. 61 (5) The P-S event, Event 0, is observed clearly in only the B-Direction. (6) The P-S event, Event 0, although produced by a P-S conversion in the vertical plane, is seen on transverse receivers that are orthogonal to the vertical plane. Therefore, one can conclude, from the previous observations, that: (1) The crystallographic axis of the ice shelf, in the study area, is oriented with the C-axis parallel to the A-Direction; (2) The ice shelf, in the study area, behaves similar, with reSpect to sonics, to studies performed on single ice crystals; (3) The study area, demonstrates velocity anisotropic behavior with regard to horizontal receivers. LI ST OF REFERENCES 62 LIST OF REFERENCES Bennett, H. F., An investigation into velocity anistrOpy through measurements of ultrasonic wave velocities in snow and ice cores from Greenland and Antarctica, Ph.D. thesis, Univ. of Wis., Madison, 1968. HELBIG, K., Die Ausbreitung Elastischer Wellen In Anisotropen Medien, GeOphysical PrOSpecting, Vol IV, No. 1, 1956. Kraut, Edgar A., Advances in the Theory of AnisotrOpic Elastic Wave PrOpagation, Reviews of GeOphysics, Vol 1, N00 3, Po 401-448, 19630 Musgrave, M. J. P., Introduction to the study of Elastic Waves and Vibrations in Crystals: Holden-Day, San Francisco, Cambridge, London, Amsterdam, p. 5-107, 1970. Rigsby, G. P., Crystal orientation in glacier and in experimentally deformed ice: J. Glaciol., Vol 3, No. 27, p- 589-606, 1951. APPENDICES APPENDIX A Recording Equipment A1 RECORDING EQUIPMENT Recording Instrument: Digital Computer with A/D Device Number of Traces: 24 Tape TranSport Type: 9 Track Recording Tape: 800 BPI Recording Filters: Low Cut Out — 250 Hz High Cut Sampling Rate: 480 samples per second Record Length: 6 Seconds GeOphone Type: 4.5 Hz Hall Sears GeOphone Pattern: 50 Ft Spacing Cable Type: Geospace Source: Dynamite - Nitromon Charge Size: 5 lb. Source Pattern: Single hole — 3 to 4 Meter Depth Source: Mortar - 4.2 inch Charge Size: 1/4 lb. Source Pattern: Toward, Away, Right, and Left Station 1: Near Trace Distance 50 Ft ( 15.24 M) Far Trace Distance 1200 Ft ( 365.76 M) Station 2: Near Trace Distance 1100 Ft ( 335.28 M) 2250 Ft ( 685.80 M) Far Trace Distance 2150 Ft ( 655.32 M) Station 3: Near Trace Distance Far Trace Distance = 3300 Ft (1005.84 M) APPENDIX B A and B Velocity Profiles FILE NAME 8 P/A MOD-SONIC THICKNESS (M) ”I'D-1(0)-I TH(1>- TH(2)- TH(3)- TH(4)- TH(5)- TH(6)- TH(7)' TH(8)- TH(9)- TH<10)- TH(11)- TH(12)- TH<13>I TH(14)- TH(15)- TH<16>8 TH<17)I TH(18)- TH(19)- TH(20)- TH(21)- TH(22)' TH(23)' TH(24)- TH(25)- TH(26)- TH(27)- TH(28)- TH(29)- TH(30)- TH(31)- TH(32)- TH(33)- TH(34)- TH(35)I TH(36)- TH(37)- TH(38)- TH<39)- TH(40)- 0.010 2.990 3.000 2.960 3.719 3.230 3.229 3.039 3.059 2.939 2.860 2.889 2.690 2.849 2.439 2.810 2.250 2.769 2.040 2.740 1.649 2.730 1.519 2.709 1.430 2.680 1.250 2.669 0.810 2.689 1.069 2.640 0.879 2.640 0.539 2.669 0.310 2.699 1.849 211.0 724.0 VELOCITY (KM/S) SU(0)- SU(1)- 80(2)- 50(3)- SU(4)- 89(5)- SV(6)- 89(7)- SV(8)- 80(9)- 80(10)- SU(11)- 80(12)- SU(13)- SU(14)- SU(15)- 59(16)- SUI 80(18)- SV(I9)- SV<20)- SU<21)- 50(22)- 50(23)- SU(24)- SUC25)‘ SU<26)- SU(27)- SU<28)- SV<29)- 80(30)- SU<31>I SU(32)- 89(33)- SU(34)- 50(35)- 80(36)- SU(37)- 50(38)- SV(39)- SU(40)- 0.600 1.248 1.631 1.948 2.302 2.513 2.679 2.808 2.919 3.013 3.092 3.165 3.226 3.286 3.332 3.382 3.419 3.462 3.490 3.527 3.547 3.579 3.595 3.624 3.637 3.663 3.673 3.696 3.702 3.722 3.729 3.748 3.753 3.771 3.773 3.789 3.791 3.805 3.814 3.814 1.500 Bl A-Direction P Velocity Profile DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH (M) 0.010 3.000 6.000 8.960 12.67 15.90 19.13 22.17 25.23 28.17 31.03 33.92 36.61 39.46 41.90 44.71 46.96 49.73 51.77 54.51 56.16 58.89 60.40 63.11 64.54 67.22 68.47 71.14 71.95 74.64 75.71 78.35 79.23 81.87 82.41 85.08 85.39 88.09 89.94 300.9 1024. TIME (ONE TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME IN MS HAY) 0.016 2.412 4.251 5.771 7.386 8.672 9.877 10.95 12.00 12.98 13.90 14.82 15.65 16.52 17.25 18.08 18.74 19.54 20.12 20.90 21.36 22.13 22.55 23.30 23.69 24.42 24.76 25.48 25.70 26.43 26.71 27.42 27.65 28.35 28.49 29.20 29.28 29.99 30.47 85.80 568.4 AUG UEL VEL VEL UEL UEL UEL VEL UEL UEL UEL VEL VEL UEL UEL VEL UEL UEL UEL UEL VEL UEL UEL UEL VEL UEL UEL VEL UEL VEL VEL UEL VEL UEL UEL UEL UEL UEL UEL VEL UEL UEL (KM/S) 0.600 1.243 1.411 1.552 1.716 1.834 1.937 2.023 2.101 2.170 2.231 2.288 2.338 2.388 2.428 2.472 2.505 2.544 2.572 2.607 2.628 2.660 2.678 2.708 2.724 2.752 2076‘ 2.791 2.799 2.824 2.833 2.857 2.865 2.887 2.891 2.913 2.915 2.936 2.950 3.507 1.802 FILE NAME I P/8 MOD-SONIC THICKNESS (M) TH(0)- TH(1)- TH(2)- TH(3)- TH(4)- TH(5)- TH(6)- TH(7)- TH(8)- TH(9)II TH(10)- TH(11)- TH(12)- TH(13)- TH(14)- TH(15)- TH(16)- TH(17)- TH(18)II TH(19)- TH(20)- TH(21)' TH(22)' TH(23)- TH(24)- TH(25)- TH(26)- TH(27)- TH(28)- TH(29)- TH(30)- TH(31)- TH(32)- TH(33)- TH(34)- TH<35)- TH(36)I TH‘37)‘I TH(38)- TH(39)' TH(40)- TH(41)- TH(42)- TH(43)- TH(44)- TH(45)' TH(46)I 0.010 2.990 3.000 3.089 3.519 3.100 3.170 2.889 2.910 2.790 2.729 2.729 2.549 2.680 2.329 2.640 1.990 2.590 1.810 2.559 1.660 2.539 1.540 2.509 1.290 2.509 1.270 2.479 1.000 2.490 0.289 2.580 0.329 2.560 0.610 2.500 0.550 2.479 2.259 0.289 2.520 0.200 2.509 2.309 1.930 205.0 724.0 VELOCITY (KM/S) 80(0)- 50(1)- SU(2)P 80(3)- SU(4)- 59(5)- -SU(6)- SU(7)- SU(8)- SU(9)- 89(10)- 80(11)- 50(12)- SU(13)- 80(14)- SV(I5)- SV(16)II 80(17)- 80(18)- 80(19)- 30(20)- 90(21)- SV(22)- SV(23)II SU(24)- 30(25)- SU(26)- SU(27)- 80(28)- 80(29)- SU(30)- SU(31)- SU(32)- SU(33)- SU(34)- 90(35)- 50(36)- SU(37)- 89(38)- SV(39)= 30(40)- SV(41)- 30(42)- 80(43)- SU(44)- 30(45)- 80(46)- 0.600 1.282 1.631 1.998 2.328 2.526 2.688 2.806 2.908 2.993 3.066 3.132 3.187 3.240 3.282 3.326 3.356 3.393 3.416 3.448 3.467 3.495 3.510 3.535 3.546 3.568 3.378 3.597 33604 3.622 3.623 3.640 3.641 3.656 3.659 3.672 3.674 3.687 3.696 3.697 3.702 3.708 3.718 3.726 3.733 3.733 1.500 82 BvDirection P Velocity Profile DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH DEPTH (M) 0.010 3.000 6.000 9.089 12.60 15.70 18.87 21.76 24.67 27.46 30.19 32.92 35.47 38.15 40.48 43.12 45.11 47.70 49.51 52.07 53.73 56.27 57.81 60.32 61.61 64.11 65.38 67.86 68.86 71.35 71.64 74.22 74.55 77.11 77.72 80.22 80.77 83.25 85.51 85.80 88.32 88.52 91.03 93.34 95.27 300.2 1024. TIME (ONE TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME IN MS WAY) I 0.016 2.348 4.188 5.734 7.245 8.473 9.652 10.68 11.68 12.61 13.50 14.37 15.17 16.00 16.71 ‘7850 18.09 18.86 19.39 20.13 20.61 21.34 21.77 22.48 22.85 23.55 23.91 24.59 24.87 25.56 25.64 26.35 26.44 27.14 27.31 27.99 28.14 28.81 29.42 29.50 30.18 30.23 30.91 31.53 32.04 86.96 569.6 AUG UEL VEL UEL UEL UEL UEL VEL VEL UEL UEL UEL VEL- UEL UEL UEL UEL UEL VEL UEL VEL VEL UEL UEL UEL VEL UEL VEL VEL UEL UEL UEL UEL UEL UEL VEL UEL UEL VEL UEL UEL UEL UEL UEL UEL UEL UEL UEL UEL (KM/S) 0.600 1.277 1.432 1.585 1.740 1.853 1.955 2.037 2.112 2.177 2.235 2.290 2.337 2.384 2.422 2.463 2.492 2.528 2.553 2.586 2.606 2.636 2.654 2.682 2.695 2.722 2.734 2.758 2.768 2.791 2.793 2.816 2.819 2.840 2.845 2.866 2.870 2.889 2.906 2.908 2.926 2.927 2.944 2.960 2.972 3.452 1.798 FILE NAME I SH/A-SONIC THICKNESS (M) TH(0)I TH(1)I TH(2)I TH(3)I TH(4)I TH(5)I TH(6)I TH(7)I TH(8)I TH(9)I TH(10)I TH(11)I TH(12)I TH(13)I TH(14)I TH(15)I TH(16)I TH(17)I TH(18)I TH(19)I TH(20)I TH(21)I TH(22)I TH(23)I TH(24)I TH(25)I TH(26)I TH(27)I TH(28)I TH(29)I TH(30)I TH(31)I TH(32)I TH(33)I TH(34)I TH(35)I TH(36)I TH(37)I TH(38)I TH(39)I 0.010 1.990 3.000 2.890 4.169 3.300 3.519 2.989 3.110 2.849 2.780 2.750 2.510 2.679 2.230 2.629 1.939 2.590 1.719 2.560 1.439 2.540 1.209 2.519 0 .840 2.529 0.709 2.520 0.549 2.520 0.129 2.590 2.189 2.439 0.360 2.509 0.050 0.050 0.049 221.0 VELOCITY (KM/S) SV(0)I SV(1)I SV(2)I SV(3)I SV(4)I SV(5)I SV(6)I SV(7)I SV(8)I 8V(9)I SV(10)I SV(11)I SV(12)I SV(13)I SV(14)I SV(15)I SV(I6)I SV(17)I SV(18)I SV(19)I SV(20)I SV(21)I SV(22)I SV<23)I SV(24)I SV(25)I SV(26)I SV(27)I SV<28)I SV(29)I SV(30)I SV(31)I SV<32)I SV(33)I SV(34)I SV(35)I SV(36)I SV(37)I SV(38)I SV(39)I 0.349 0.765 0.923 1.125 1.234 1.328 1.391 1.448 1.493 1.531 1.565 1.593 1.620 1.640 1.662 1.677 1.695 1.706 1.722 1.730 1.744 1.749 1.761 1.764 1.775 1.777 1.787 1.788 1.797 1.797 1.804 1.810 1.815 1.816 1.822 1.822 1.822 1.822 1.822 B3 A—Direction 8 Velocity Profile DEPTH (M) DEPTH I 0.010 DEPTH I 2.000 DEPTH I 5.000 DEPTH I 7.890 DEPTH I 12.05 DEPTH I 15.35 DEPTH I 18.87 DEPTH I 21.86 DEPTH I 24.97 DEPTH I 27.82 DEPTH I 30.60 DEPTH I 33.35 DEPTH I 35.86 DEPTH I 38.54 DEPTH I 40.77 DEPTH I 43.40 DEPTH I 45.34 DEPTH I 47.93 DEPTH I 49.65 DEPTH I 52.21 DEPTH I 53.65 DEPTH I 56.19 DEPTH I 57.40 DEPTH I 59.91 DEPTH I 60.75 DEPTH I 63.28 DEPTH I 63.99 DEPTH I 66.51 DEPTH I 67.06 DEPTH I 69.58 DEPTH I 69.71 DEPTH I 72.30 DEPTH I 74.49 DEPTH I 76.93 DEPTH I 77.29 DEPTH I 79.80 DEPTH I 79.85 DEPTH I 79.90 DEPTH I 79.95 DEPTH I 300.9 TIME (ONE TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME IN MS HAY) 0.028 3.544 7.466 10.59 14.30 16.97 19.62 21.77 23.92 25.83 27.64 29.40 30.98 32.63 33.99 35.57 36.73 38.26 39.26 40.75 41.58 43.04 43.73 45.16 45.64 47.06 47.46 48.87 49.18 50.58 50.65 52.09 53.30 54.64 54.84 56.21 56.24 56.27 56.30 177.5 AVG VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL 'VEL VEL VEL VEL VEL VEL VEL ‘VEL VEL VEL VEL VEL VEL VEL VEL VEL (KM/S) 0.349 0.564 0.669 0.744 0.843 0.904 0.961 1.004 1.044 1.077 1.107 1.134 1.157 1.181 1.199 1.220 1.234 1.252 1.264 1.281 1.290 1.305 1.312 1.326 1.331 1.344 1.348 1.360 1.363 1.375 1.376 1.388 1.397 1.407 1.409 1.419 1.419 1.419 1.420 1.694 FILE NAME I SH/B-SONIC THICKNESS (M) TH(0)I TH(1)I TH(2)I TH(3)I TH(4)I TH(5)I TH(6)I TH(7)I TH(8)I TH(9)I TH(10)I TH(11)I TH(12)I TH(13)I TH(14)I TH(15)I TH(16)I TH(17)I TH(18)I TH(19)I TH(20)I TH(21)I TH(22)I TH(23)I TH(24)I TH(25)I TH(26)I TH(27)I TH(28)I TH(29)I TH(30)I TH(31)I TH(32)I TH(33)I TH(34)I TH(35)I TH(36)I TH(37)I TH(38)I TH(39)I TH(40)I TH(41)I TH(42)I TH(43)I TH(44)I TH(45)I 0.010 1.990 3.000 3.210 3.939 3.310 3.379 3.100 3.160 2.979 2.930 2.929 2.770 2.889 2.610 2.849 2.460 2.829 2.370 2.810 2.240 2.799 2.019 2.789 1.860 2.780 1.770 2.769 1.539 2.770 1.469 2.759 1.300 2.770 1.459 2.740 1.109 2.760 0.680 2.799 0.879 2.780 1.050 2.739 2.130 192.0 VELOCITY (KM/S) SV(0)I SV(1)I SV(2)I SV(3)I SV(4)I SV(5)I SV(6)I SV(7)I SV(8)I SV(9)I 8V(10)I SV(11)I SV(12)I SV(13)I SV(14)I 9V(15)I SV(16)I SV(17)I SV(18)I SV(19)I SV(20)I SV(21)I SV(22)I SV(23)I SV(24)I SV(25)I SV(26)I SV<27)I SV(28)I 8V(29)I SV(30)I SV(31)I SV<32)I SV(33)I SV(34)I SV(35)I SV(36)I SV(37)I SV(38)I SV(39)I SV(40)I SV(41)I SV(42)I SV(43)I SV(44)I SV(45)I 0.349 0.590 0.801 0.938 1.178 1.291 1.383 1.453 1.513 1.563 1.606 1.645 1.678 1.711 1.737 1.764 1.786 1.809 1.827 1.848 1.863 1.882 1.894 1.911 1.921 1.936 1.945 1.958 1.965 1.978 1.984 1.995 2.001 2.011 2.016 2.026 2.029 2.038 2.040 2.049 2.051 2.059 2.062 2.070 2.753 2.075 84 BvDirection S Velocity Profile DEPTH (M) DEPTH I 0.010 DEPTH I 2.000 DEPTH I 5.000 DEPTH I 8.210 DEPTH I 12.14 DEPTH I 15.45 DEPTH I 18.83 DEPTH I 21.93 DEPTH I 25.09 DEPTH I 28.07 DEPTH I 31.00 DEPTH I 33.93 DEPTH I 36.70 DEPTH I 39.59 DEPTH I 42.20 DEPTH I 45.05 DEPTH I 47.51 DEPTH I 50.34 DEPTH I 52.71 DEPTH I 55.52 DEPTH I 57.76 DEPTH I 60.56 DEPTH I 62.58 DEPTH I 65.37 DEPTH I 67.23 DEPTH I 70.01 DEPTH I 71.78 DEPTH I 74.54 DEPTH I 76.08 DEPTH I 78.85 DEPTH I 80.32 DEPTH I 83.08 DEPTH I 84.38 DEPTH I 87.15 DEPTH I 88.61 DEPTH I 91.35 DEPTH I 92.46 DEPTH I 95.22 DEPTH I 95.90 DEPTH I 98.70 DEPTH I 99.58 DEPTH I 102.3 DEPTH I 103.4 DEPTH I 106.1 DEPTH I 108.2 DEPTH I 300.2 TIME (ONE TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME TIME IN MS HAY) 0.028 3.401 7.146 10.56 13.91 16.47 18.91 21.05 23.14 25.04 26.87 28.65 30.30 31.99 33.49 35.10 36.48 38.05 39.34 40.86 42.07 43.55 44.62 46.08 47.05 48.48 50.81 51.59 52.99 53.73 55.11 55.76 57.14 57.87 59.22 59.76 61.12 61.45 62.82 63.25 64.60 65.11 66.43 67.20 159.7 AVG VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL VEL (KM/S) 0.349 0.587 0.699 0.776 0.873 0.938 0.995 1.042 1.084 1.120 1.153 1.184 1.211 1.237' .260 1.283 1.302 1.323 1.339 1.358 1.372 1.390 1.402 1.418 1.428 1.443 1.453 1.467 1.474 1.488 1.494 1.507 1.513 1.525 1.531 1.542 1.547 1.557 1.560 1.571 1.574 1.584 1.588 1.597 1.611 1.879 APPENDIX C Longitudinal Records C1 8986? _ H 111 1 111' 1 1 1 11 1 1 1 1 1 1 1 1 1 1 11 ‘1 1'1 1 111,1, 1 1’1! 1 11 11 111 1111 111 1’11 1 1 111 11 1 1 '11 H111 ' 11 11 1 1 1 ’1 ’1 11‘ I1 1 '1 1'31 1 1 1 1 1 1 1R 1' 11 . I 1 11 111111111 1 1 1 11111111 111. 1 11 I1 111. , 1 .F 11. 1 1.. 1. N 11111111111111 . 1””. $1 M M M M” 31.1.35 I. a; on Qmoomm 1 1‘1 ' 1‘11 1 1 '1 1 H 1‘11)!- 11111111111111.11H111 1 1 ‘11.. 11.111111111111111H111w1111 .II 1- 1 1 1 111.111.1H11.IH11||11111 111.11.111.11: 11111.1I 11111 “ “1I1IIIIF-1'H1 Jll11l1l1| 11 1 1 1| .1 ‘HIHIHI 1 11.11 ‘11“ 11 11. 111 1vl11|1111111 11 1111.111111H111A1111 h11_”‘111m.1l111m1|m|m'1ur111111 1.11111 ‘ 11"“ 1 11 I" 11 H 1 E1 1 1 .1 1 . '1 1‘ =11 '11 '11 1 1 ‘1 11 111 1 1.11 1111“ “’1 11 1111 1‘11 11| IE .‘!1 C2 I 1 .1H11111M11111H1111N11111 1111. 1.1.11.1 11111.1 1 11111111111111.1111 11.1WW 111 WWW .1 H11... HHH,11.1H1HH.H._1. w 1.11 __~_‘. _ :g 5 men amoomm 1 1’1. 1 11 11111 1’ '11. ll 1" 1,1,1 (ll, 1‘1! 1' 11 1 1! )1 I"? $1 1 1 1 1 1 1 1 111111 m11n1111111111.H111m11H1 1 1‘1“ 1‘1 1.111111111111me “11“ 1H1”. 1‘1 . 111111111 1111111111111 11111111 1. 1111111111.. 1‘ 111M11|111111111111111 1 11 I11 H1. I..." . 1511...“.“\ 1‘011u111'111n111111‘1‘11111flu ” ««« 1. 111 1' 11111-1111V1 ‘v'r 1 11111111. 11' 1111 111 1111.1-1MVAUHM.1111111111M111H1 1 1 I 111111 ”11’ '1'111'11111111 “W1 1 1.111.111... 1 11.111 11111.11 1.111 111.11.111LN11111111 W11 111111 11 ’11.! 111wa 1.11111'11111111111111111511'15515wmw mu 11111111 ”111“) 111w1IHVquPU11H1 ‘1 "w 11.11.11.11IH111H11 1W1 11111111111 “11m“ 1‘1.‘1'.'I.IM11..11111111I1M””1 11111 1‘ 1'11"“, “11.11Mr1111111111H1111111111111111 11 11.1 1 111 11...:11u1111111111111 1111.11.11 1 - 111 111.11,.1111111.11.1111.11111111.I1 ......... 1 u ”.15.. 11.11111, 1H1. ........ .1. 1. . .1 .111 .................... n 1.. I 11.11111 1 Lu]! .... 1 . C3 “111......1___. .:.1._1. .: _ _1 cam amoomm ........ . . . ... .. ... ' .r A. r 1. ,- .... H 1|...1P.».11....1.r.r ..11am1r1n11u1 ......” . r .. 1.. WAFWTI. ............. . -1. 1 . . . 1 . . .11. u . . .. ... . . . ....1. 1. 111! pa {LI 151 :1 1 I. IN 11 .... .l, ‘.W.VIJ1JII M s m .....W..E¢.~ M ~ " ~..4.1\m..\—. 11 ~ ~ . . 1. . u. y 2233: can amoomm C4 i a. ,_,.__. 2: ~ WM". Wm; g E3 H WI” WW“: E g E 'v 3 H. ”m: E) : ! NVMLW; 1 ~ W, “mg-- W «5*— 4" 5 *5 —_—Z_$~—. Ag; ' ‘ W W m3? MM‘H’W “ ’W W: 7 I ! 1km Irv-m ‘1-“7‘1 11;.” n- APPENDIX D P-P—P-P Ray Path Parameters D1 P-P-P-P _ , _ _ FRO-1 P/A noo-P/A HOD-sm1cs P P P P Ray Path A “31°C“? ““113 I DERART I INCOME I OUT I ARRIVE I TOTAL I TOTAL I HORIZ I vERT I RAY I I RAY I RAY I RAY I RAY I DIST I TIME I DIST I 013T I FARM I I (DEG) I (050) I (0,001 I (050) I <14) I (110) I <14) I (m I I 1.00 2.50 6.36 0.99 2054.60 1141.37 126.94 1024.94 0.02900 1.12 2.01 7.16 1.12 2055.96 1141.06 142.93 1024.94 0.03272 1.25 3.12 7.97 1.25 2057.41 1142.42 150.90 1024.94 0.03635 1.37 3.43 0.77 1.37 2059.01 1143.03 175.07 1024.94 0.03999 1.50 3.75 9.57 1.50 2060.77 1143.71 191.22 1024.94 0.04362 1.62 4.06 10.30 1.62 2062.70 1144.44 207.43 1024.94 0.04726 1.75 4.37 11.19 1.75 2064.79 1145.24 223.71 1024.94 0.05009 1.07 4.69 12.00 1.07 2067.05 1146.10 240.07 1024.94 0.05453 2.00 5.00 12.01 1.99 2069.40 1147.03 256.51 1024.94 0.05016 2.12 5.31 13.63 2.12 2072.09 1140.02 273.03 1024.94 0.06179 2.25 5.63 14.45 2.25 2074.00 1149.00 209.65 1024.94 0.06543 2.37 5.94 15.27 2.37 2077.04 1150.20 306.30 1024.94 0.06906 2.50 6.26 16.09 2.50 2001.00 1151.40 323.21 1024.94 0.07269 2.62 6.57 16.92 2.62 2004.35 _1152.66 340.15 1024.94 0.07633 2.75 6.00 17.75 2.75 2007.09 1153.99 357.23 1024.94 0.07996 2.07 7.20 10.59 2.07 2091.64 1155.40 374.43 1024.94 0.00359 3.00 7.51 19.43 3.00 2095.6 1156.00 391.70 1024.94 0.00722 3.12 7.03 20.27 3.12 2099.77 1150.44 409.29 1024.94 0.09005 3.25 0.14 21.12 3.25 2104.17 1160.00 426.95 1024.94 0.09440 3.37 0.46 21.97 3.37 2100.79 1161.0 444.79 1024.94 0.09011 3.50 0.77 22.03 3.50 2113.66 1163.60 462.01 1024.94 0.10174 3.62 9.09 23.69 3.62 2110.77 1165.40 401.02 1024.94 0.10537 3.75 9.41 24.56 3.75 2124.14 1167.46 499.45 1024.94 0.109 3.07 9.72 25.44 3.07 2129.70 1169.53 510.10 1024.94 0.11263 4.00' 10.04 26.32 3.99 2135.70 1171.69 536.90 1024.94 0.11626 4.12 10.35 27.20 4.12 2141.92 1173.95 556.12 1024.94 0.11900 4.25 10.67 20.10 4.25 2140.44 1176.31 575.53 1024.94 0.12351 4.37 10.99 29.00 4.37 2155.29 1170.70 595.23 1024.94 0.12713 4.50 11.31 29.91 4.50 2162.40 1101.36 615.24 1024.94 0.13076 4.62 11.62 30.03 4.62 2170.02 1104.05 635.50 1024.94 0.13430 4.75 11.94 31.76 4.75 2177.95 1106.07 656.27 1024.94 0.13001 4.07 12.26 32.69 4.07 2106.27 1109.02 677.35 1024.94 0.14163 5.00 12:50 33.64 5.00 2195.03 1192.90 690.03 1024.94 0.14525 5.12 12.90 34.59 5.12 2204.23 1196.13 720.75 1024.94 0.14000 5.25 13.22 35.56 5.25 2213.93 1199.50 743.15 1024.94 0.1525 5.37 13.54 36.54 5.37 2224.14 1203.04 766.06 1024.94 0.15612 5.50 13.06 37.53 5.50 2234.91 1206.74 709.53 1024.94 0.15974 5.62 14.10 30.54 5.62 2246.20 1210.63 013.60 1024.94 0.16336 5.75 14.50 39.55 5.75 2250.31 1214.72 030.33 1024.94 0.16690 5.07 14.02 40.59 5.07 2271.04 1219.01 063.70 1024.94 0.17059 6.00 15.14 41.64 6.00 2204.54 1223.54 090.01 1024.94 0.17421 6.12 15.47 42.70 6.12 2290.00 1220.31 917.11 1024.94 0.17702 6.25 15.79 43.79 6.25 2314.15 1233.35 945.17 1024.94 0.10144 6.37 16.11 44.09 6.37 2330.43 1230.60 974.29 1024.94 0.10505 6.50 16.43 46.02- 6.50 2347.06 1244.34 1004.50 1024.94 0.10067 6.62 16.76 47.16 6.62 2366.55 1250.37 1036.19 1024.94 0.19220 D2 A-Velocity Profile PbP-P-P P-PwP-P Ray Path FROM P/B MOD-P/0 HOD-SONICS I DERART I INCOME I OUT I ARRlvE I TOTAL I TOTAL l HORIz I vERT I RAY I I RAY I RAY I RAY I RAY I DIST I TIME I DIST I DIST I PARM l I (DEB) I (0E8) l (DEG) I (DEG) I (H) I (MS) I (H) I (M) I I 1.00 2.50 6.23 0.99- 2053.20 1143.74 125.59 1024.27 0.02900 1.12 2.01 7.01 1.12 2054.45 1144.23 141.41 1024.27 0.03272 1.25 3.12 7.00 1.25 2055.05 1144.70 157.20 1024.27 0.03635 1.37 3.43 0.50 1.37 2057.40 1145.30 173.19 1024.27 0.03999- 1.50 3.75 9.37 1.50 2059.11 1146.05 109.15 1024.27 0.04362 1.62 4.06 10.16 1.62 2060.90 1146.70 205.10 1024.27 0.04726 1.75 4.37 10.95 1.75 2063.01 1147.57 221.27 1024.27 0.05009 1.07 4.69 11.74 1.07 2065.20 1140.42 237.43 1024.27 0.05453 2.00 5.00 12.54 1.99 2067.55 1149.34 253.67 1024.27 0.05016 2.12 5.31 13.33 2.12 2070.00 1150.31 269.99 1024.27 0.06179 2.25 5.63 14.13 2.25 2072.70 1151.36 206.40 1024.27 0.06543 2.37 5.94 14.94 2.37 2075.65 1152.47 302.91 1024.27 0.06906 2.50 6.26 15.74 2.50 2070.70 1153.65 319.52 1024.27 0.07269 2.62 6.57 16.55 2.62 2001.94 1154.09 336.23 1024.27 0.07633 2.75 6.00 17.36 2.75 2005.36 1156.21 353.07 1024.27 0.07996 2.07 7.20 10.10 2.07 2000.90 1157.59 370.03 1024.27 0.00359 3.00 7.51 19.00 3.00 2092.00 1159.05 307.13 1024.27 0.00722 3.12 7.03 19.02 3.12 2096.03 1160.59 404.36 1024.27 0.09005 3.25 0.14 20.65 3.25 2101.06 1162.20 421.75 1024.27 0.09440 3.37 0.46 21.40 3.37 2105.52 1163.09 439.30 1024.27 0.09011 3.50 0.77 22.32 3.50 2110.20 1165.66 457.02 1024.27 0.10174 3.62 9.09 23.16 3.62 2115.12 1167.52 474.93 1024.27 0.10537 3.75 9.41 24.01 3.75 2120.20 1169.46 493.02 1024.27 0.109 3.07 9.72 24.06 3.07 2125.69 1171.40 511.33 1024.27 0.11263 4.00 10.04 25.72 3.99 2131.37 1173.60 529.05 1024.27 0.11626 4.12 10.35 26.50 4.12 2137.33 1175.02 540.61 1024.27 0.11900 4.25 10.67 27.45 4.25 . 2143.57 1170.13 567.62 1024.27 0.12351 4.37 10.99 20.33 4.37 2150.11 1100.55 506.09 1024.27 0.12713 4.50 11.31 29.21 4.50 2156.90 1103.07 606.45 1024.27 0.13076 4.62 11.62 30.11 4.62 2164.17 1105.70 626.31 1024.27 0.13430 4.75 11.94 31.01 4.75 2171.71 1100.45 646.49 1024.27 0.13001 4.07 12.26 31.91 4.07 2179.63 1191.32 667.02 1024.27 0.14163 5.00 12.50 32.03 5.00 2107.93 1194.32 607.92 1024.27 0.14525 5.12 12.90 33.76 5.12 2196.66 1197.45 709.22 1024.27 0.14000 5.25 13.22 34.70 5.25 2205.02 1200.73 730.95 1024.27 0.1525 5.37 13.54 35.64 5.37 2215.46 1204.15 753.14 1024.27 0.15612 5.50 13.06 36.60 5.50 2225.6 1207.74 775.03 1024.27 0.15974 5.62 14.10 37.57 5.62 2236.20 1211.49 799.06 1024.27 0.16336 5.75 14.50 30.56 5.75 2247.54 1215.42 022.07 1024.27 0.16690 5.07 14.02 39.55 5.07 2259.43 1219.55 047.31 1024.27 0.17059 6.00 15.14 40.56 6.00 2272.00 1223.00 072.45 1024.27 0.17421 6.12 15.47 41.59 6.12 2205.31 1220.44 090.34 1024.27 0.17702 6.25 15.79 42.63 6.25 2299.43 1233.24 925.06 1024.27 0.10144 6.37 16.11 43.69 6.37 2314.43 1230.3 952.69 1024.27 0.10505 6.50 16.43 44.77 6.50 2330.40 1243.66 901.33 1024.27 0.10067 6.62 16.76 45.07 6.62 2347.46 1249.33 1011.10 1024.27 0.19220 APPENDIX E P-P-P-S Ray Path Parameters El P-P-P-S F801 P /A HOD-SWA MOD-$014105 P-P-P-S Ray Path A-Velocity Profile I DERART I INCOHE I OUT I ARRIVE I TOTAL I TOTAL I HORIZ I VERT I RAY I I RAY I RAY I RAY I RAY I DIST I TIME I DIST l DIST I FARM I I (DEG) I (DEG) I (DEG) I (DEG) I (H) I (MS) I (H) I (H) I I 1.00 2.50 3.03 0.58 2053.37 1232.92 110.33 1024.94 0.02908 1.12, 2.81 3.41 0.65 2054.30 1233.35 124.21 1024.94 0.03272 1.25 3.12 3.79 0.72 2055.35 1233.83 138.1 1024.94 0.03635 1.37 3.43 4.17 0.79 2056.50 1234.36 152.03 1024.94 0.03999 1.50 3.75 4.55 0.87 2057.78 1234.95 166.00 1024.94 0.04362 1.62 4.06 4.94 0.94 2059.16 1235.58 180.00 1024.94 0.04726 1.75 4.37 5.32 1.01 2060.67 1236.27 194.05 1024.94 0.05089 1.87 4.69 5.70 1.09 2062.29 1237.01 208.14 1024.94 0.05453 2.00 5.00 6.08 1.16 2064.04 1237.81 222.28 1024.94 0.05816 2.12 5.31 6.46 1.23 2065.91 1238.66 236.47 1024.94 0.06179 2.25 5.63 6.84 1.30 2067.90 1239.57 250.72 1024.94 0.06543 2.37 5.94 7.22 1.38 2070.02 1240.53 265.03 1024.94 0.06906 2.50 6.26 7.61 1.45 2072.27 1241.55 279.41 1024.94 0.07269 2.62 6.57 7.99 1.52 2074.65 1242.63 293.85 1024.94 0.07633 2.75 6.88 8.37 1.59 2077.17 1243.76 308.38 1024.94 0.07996 2.87 7.20 8.76 1.67 2079.82 1244.96 322.98 1024.94 0.08359 3.00 7.51 9.14 1.74 2082.61 1246.21 337.66 1024.94 0.08722 3.12 7.83 9.52 1.81 2085.55 1247.53 352.44 1024.94 0.09085 3.25 8.14 9.91 1.88 2088.64 1248.90 367.31 1024.94 0.09448 3.37 8.46 10.29 1.96 2091.88 1250.35 382.29 1024.94 0.09811 3.50 8.77 10.68 2.03 2095.27 1251.85 397.37 1024.94 0.10174 3.62 9.09 11.06 2.10 2098.83 1253.43 412.57 1024.94 0.10537 3.75 9.41 11.45 2.18 2102.56 1255.07 427.89 1024.94 0.109 3.87 9.72 11.84 2.25 2106.46 1256.78 443.34 1024.94 0.11263 4.00 10.04 12.22 2.32 2110.53 1258.57 458.92 1024.94 0.11626 4.12 10.35 12.61 2.39 2114.80 1260.42 474.66 1024.94 0.11988 4.25 10.67 13.00 2.47 2119.25 1262.36 490.54 1024.94 0.12351 4.37 10.99 13.39 2.54 2123.91 1264.37 506.60 1024.94 0.12713 4.50 11.31 13.78 2.61 2128.78 1266.46 522.83 1024.94 0.13076 4.62 11.62 14.17 2.68 2133.87 1268.64 539.25 1024.94 0.13438 4.75 11.94 14.56 2.76 2139.19 1270.90 555.87 1024.94 0.13801 4.87 12.26 14.95 2.83 2144.76 1273.26 572.70 1024.94 0.14163 5.00 12.58 15.34 2.9 2150.57 1275.70 589.76 1024.94 0.14525 5.12 12.90 15.73 2.97 2156.66 1278.25 607.07 1024.94 0.14888 5.25 13.22 16.13 3.05 2163.04 1280.90 624.65 1024.94 0.1525 5.37 13.54 16.52 3.12 2169.71 1283.65 642.50 1024.94 0.15612 5.50 13.86 16.92 3.19 2176.71 1286.52 660.67 1024.94 0.15974 5.62 14.18 17.31 3.26 2184.06 1289.51 679.16 1024.94 0.16336 5.75 14.50 17.71 3.34 2191.78 1292.62 698.02 1024.94 0.16698 5.87 14.82 18.10 3.41 2199.89 1295.87 717.26 1024.94 0.17059 6.00 15.14 18.50 3.48 2208.44 1299.26 736.93 1024.94 0.17421 6.12 15.47 18.90 3.55 2217.46 1302.81 757.07 1024.94 0.17782 6.25 15.79 19.30 3.63 2226.98 1306.52 777.72 1024.94 0.18144- 6.37 16.11 19.7 3.70 2237.07 1310.41 798.93 1024.94 0.18505 6.50 16.43 20.10 3.77 2247.77 1314.49 820.77 1024.94 0.18867 6.62 16.76 20.50 3.84 2259.16 1318.78 843.30 1024.94 0.19228 6.75 17.08 20.91 3.92 2271.30 1323.31 866.62 1024.94 0.19589 6.87 17.41 21.31 3.99 2284.31 1328.09 890.82 1024.94 0.1995 7.00 17.73 21.72 4.06 2298.29 1333.16 916.01 1024.94 0.20311 7.12 18.06 22.12 4.13 2313.37 1338.56 942.36 1024.94 0.20672 7.25 18.39 22.53 4.20 2329.74 1344.33 970.03 1024.94 0.21033 7.37 18.71 22.94 4.28 2347.6 1350.53 999.25 1024.94 0.21393 P-P-P-S E2 Flam P ,9 Moo-SW8 mesmxcs P-P-P-SRay Path B-Velocity Profile I DEPART I INCOME I OUT I ARRIVE I TOTAL I TOTAL I HORIZ I VERT I RAY I I RAY RAY RAY RAY DIST I TIME I DIST I DIST I FARM I I (DEB) (DEO) (DEG) (DEG) (M) I (MS) (M) I (M) I I 1.00 2.50 3.46 0.58 2052.06 1216.31 111.47 1024.27 0.02908 1.12 2.81 3.89 0.65 2053.00 1216.74 125.48 1024.27 0.03272 1.25 3.12 4.32 0.72 2054.06 1217.22 139.52 1024.27 0.03635 1.37 3.43 4.76 0.79 2055.22 1217.76 153.59 1024.27 0.03999 1.50 3.75 5.19 0.87 2056.51 1218.35 167.70 1024.27 0.04362 1.62 4.06 5.62 0.94 2057.91 1218.99 181.84 1024.27 0.04726 1.75 4.37 6.06 1.01 2059.43 1219.69 196.02 1024.27 0.05089 1.87 4.69 6.49 1.09 2061.06 1220.44 210.25 1024.27 0.05453 2.00 5.00 6.93 1.16 2062.82 1221.24 224.53 1024.27 0.05816 2.12 5.31 7.36 1.23 2064.70 1222.10 238.86 1024.27 0.06179 2.25 5.63 7.80 1.30 2066.71 1223.02 253.24 1024.27 0.06543 2.37 5.94 8.23 1.38 2068.84 1223.99 267.69 1024.27 0.06906 2.50 6.26 8.67 1.45 2071.11 1225.02 282.2 1024.27 0.07269 2.62 6.57 9.11 1.52 2073.50 1226.10 296.78 1024.27 0.07633 2.75 6.88 9.55 1.59 2076.03 1227.25 311.43 1024.27 0.07996 2.87 7.20 9.98 1.67 2078.70 1228.45 326.16 1024.27 0.08359 3.00 7.51 10.42 1.74 2081.50 1229.72 340.98 1024.27 0.08722 3.12 7.83 10.86 1.81 2084.45 1231.05 355.88 1024.27 0.09085 3.25 8.14 11.30 1.88 2087.55 1232.44 370.87 1024.27 0.09448 3.37 8.46 11.74 1.96 2090.80 1233.89 385.97 1024.27 0.09811 3.50 8.77 12.18 2.03 2094.20 1235.41 401.17 1024.27 0.10174 3.62 9.09 12.63 2.10 2097.77 1236.99 416.48 1024.27 0.10537 3.75 9.41 13.07 2.18 2101.49 1238.65 431.90 1024.27 0.109 3.87 9.72 13.51 2.25 2105.39 1240.37 447.46 1024.27 0.11263 4.00 10.04 13.95 2.32 2109.46 1242.17 463.14 1024.27 0.11626 4.12 10.35 14.40 2.39 2113.72 1244.04 478.97 1024.27 0.11988 4.25 10.67 14.85 2.47 2118.16 1245.98 494.95 1024.27 0.12351 4.37 10.99 15.29 2.54 2122.80 1248.00 511.08 1024.27 0.12713 4.50 11.31 15.74 2.61 2127.65 1250.10 527.38 1024.27 0.13076 4.62 11.62 16.19 2.68 2132.70 1252.29 543.87 1024.27 0.13438 4.75 11.94 16.64 2.76 2137.98 1254.56 560.54 1024.27 0.13801 4.87 12.26 17.09 2.83 2143.49 1256.92 577.41 1024.27 0.14163 5.00 12.58 17.54 2.9 2149.25 1259.37 594.50 1024.27 0.14525 5.12 12.90 17.99 2.97 2155.26 1261.92 611.83 1024.27 0.14888 5.25 13.22 18.44 3.05 2161.54 1264.57 629.39 1024.27 0.1525 5.37 13.54 18.90 3.12 2168.11 1267.32 647.23 1024.27 0.15612 5.50 13.86 19.35 3.19 2174.98 1270.18 665.34 1024.27 0.15974 5.62 14.18 19.81 3.26 2182.17 1273.16 683.76 1024.27 0.16336 5.75 14.50 20.27 3.34 2189.71 1276.25 702.52 1024.27 0.16698 5.87 14.82 20.73 3.41 2197.61 1279.48 721.62 1024.27 0.17059 6.00 15.14 21.19 3.48 2205.91 1282.84 741.11 1024.27 0.17421 6.12 15.47 21.65 3.55 2214.63 1286.34 761.02 1024.27 0.17782 6.25 15.79 22.11 3.63 2223.82 1290.00 781.39 1024.27 0.18144 6.37 16.11 22.58 3.70 2233.50 1293.83 802.26 1024.27 0.18505 6.50 16.43 23.04 3.77 2243.72 1297.83 823.68 1024.27 0.18867 6.62 16.76 23.51 3.84 2254.55 1302.02 845.70 1024.27 0.19228 6.75 17.08 23.98 3.92 2266.04 1306.43 868.39 1024.27 0.19589 6.87 17.41 24.45 3.99 2278.26 1311.07 891.84 1024.27 0.1995 7.00 17.73 24.92 4.06 2291.29 1315.95 916.13 1024.27 0.20311 7.12 10.06 25.40 4.13 2305.26 1321.13 941.37 1024.27 0.20672 7.25 18.39 25.87 4.20 2320.27 1326.62 967.68 1024.27 0.21033 7.37 18.71 26.35 4.28 2336.47 1332.46 995.25 1024.27 0.21393 APPENDIX F Computer Equipment F1 COMPUTER EQUIPMENT Apple II (48K) Apple III Monitor Sanyo Monitor Two Apple Disk Drives Apple DPM Printer Apple Graphics Tablet Grappler+ Buffered (16K) Interface Dithertizer and Sanyo Camera Apple II and Apple III are registered Trademarks of Apple Computer, Inc. Grappler+ Buffered is a registered Trademark of Orange Micro, Inc. Dithertizer is a registered Trademark of Computer Stations, Inc. Sanyo is a registered Trademark of Sanyo Corporation APPENDIX G Events a and b Frequency Analysis Gl 1 I Record DO I of I II II 'III IIII III III VIII' -1 lllllllllllllll lLllEllllllIl'lllllllllI 1 H Record D45 0 ' II .IIIIII.' IIII' III.' -1 l 1 .I.I.I.I.I.I.I.I.I..I.I.I.I.I.I.I.I.I. ..I,.I .I .I .I.I_.1 .I .I .I .1 1|, .I.I.I.I.I.I.I III III. .II. III III. II... I ' ' I ' .IIII.. . L1,.J .I .J .l .1 .1 .1 .1 .I .I .I .1 Record D90 .IIII IIIII .III' II “III. ...... .I.I.I.I.l.I.1.I.I.I.I.I.I.I.I.I.I. 1.1. , I.I.. Record D135 .1. 1.1.1.1. 1.1l.1. 1 .I. 1,.1 0 looms 0 50 100 Hz CZ III II. V II I III III. III I V . v V . .I.1.l.1.1.1.1. IIII .I.1.1.I.I.I.I.ILI.I.1.L .I..' " I III .-II. II I I. ‘ .I.I.I.L.l.|.|.|.I.I.I'I.L.l.1.l.|.1. .|.I..|.I.II.I.1.1 .1.I..1.1 hl.Ll.Ld.L. .|.|.ILI.ILL.I.L.1.I.1.1 III III .III III MIMI V V 0 IOOms IIIIII so 0 100 Hz I APPENDIX H P—P and P-S Ray Path Parameters H1 2R3! P/A-P/A-smxcs P—P Ray Path A—Velocity Profile I DEPART I INCOME I OUT I ARRIVE I TOTAL I TOIAL I HORIZ I UERT I RAY I I RAY I RAY I RAY I RAY I DIST I TIME I DIST I DIST I RARM I I (DEG) I (DEG)' I (DEG) I (DEG) I (H) I (MS) I (H) I (M) I I 3.00 19.43 19.43 3.00 635.04 183.18 200.69 300.94 0.08722 3.12 20.27 20.27 3.12 638.13 184.02 210.08 300.94 0.09085 3.25 21.12 21.12 3.25 641.4 184.90 219.63 300.94 0.09448 3.37 21.97 21.97 3.37 644.85 185.83 229.33 300.94 0.09811 3.50 22.83 22.83 3.50 648.49 186.82 239.19 300.94 0.10174 3.62 23.69 23.69 3.62 652.34 187.86 249.23 300.94 0.10537 3.75 24.56 24.56 3.75 656.39 188.96 259.46 300.94 0.109 3.87 25.44 25.44 3.87 660.66 190.11 269.89 300.94 0.11263 4.00 26.32 26.32 3.99 665.17 191.33 280.54 300.94 0.11626 4.12 27.20 27.20 4.12 669.92 192.62 291.41 300.94 0.11988 4.25 28.10 28.10 4.25 674.93 193.97 302.53 300.94 0.12351 4.37 29.00 29.00 4.37 680.22 195.40 313.92 300.94 0.12713 4.50 29.91 29.91 4.50 685.79 196.90 325.59 300.94 0.13076 4.62 30.83 30.83 4.62 691.67 198.49 337.57 300.94 0.13438 4.75 31.76 31.76 4.75 697.88 200.16 349.87 300.94 0.13801 4.87 32.69 32.69 4.87 704.44 201.93 362.52 300.94 0.14163 5.00 33.64 33.64 5.00 711.38 203.80 375.56 300.94 0.14525 5.12 34.59 34.59 5.12 718.72 205.78 389.00 300.94 0.14888 5.25 35.56 35.56 5.25 726.49 207.87 402.89 300.94 0.1525 5.37 36.54 36.54 5.37 734.72 210.09 417.26 300.94 0.15612 5.50 37.53 37.53 5.50 743.46 212.44 432.16 300.94 0.15974 5.62 38.54 38.54 5.62 752.75 214.94 447.62 300.94 0.16336 5.75 39.55 39.55 5.75 762.63 217.60 463.71 300.94 0.16698 5.87 40.59 40.59 5.87 773.16 220.43 480.48 300.94 0.17059 6.00 41.64 41.64 6.00 784.41 223.45 498.00 300.94 0.17421 6.12 42.70 42.70 6.12 796.44 226.68 516.35 300.94 0.17782 6.25 43.79 43.79 6.25 809.34 230.14 535.61 300.94 0.18144 6.37 44.89 44.89 6.37 823.20 233.86 555.9 300.94 0.18505 6.50 46.02 46.02 6.50 838.14 237.86 577.32 300.94 0.18867 6.62 47.16 47.16 6.62 854.28 242.19 600.02 300.94 0.19228 6.75 48.34 48.34 6.75 871.79 246.87 624.16 300.94 0.19589 6.87 49.54 49.54 6.87 890.85 251.97 649.94 300.94 0.1995 7.00 50.77 50.77 7.00 911.68 257.54 677.59 300.94 0.20311 7.12 52.04 52.04 7.12 934.56 263.65 707.41 300.94 0.20672 7.25 ‘53.34 53.34 7.25 959.83 270.39 739.74 300.94 0.21033 7.37 ‘54.68 54.68 7.37 987.91 277.88 775.04 300.94 0.21393 7.50 -56.06 56.06 7.50 1019.34 286.26 813.85 300.94 0.21754 7.62 57.50 57.50 7.62 1054.82 295.7 856.90 300.94 0.22114 7.75 59.00 59.00 7.74 1095.28 306.46 905.15 300.94 0.22475 7.87 60.56 60.56 7.87 1141.96 318.86 959.89 300.94 0.22835 8.00 62.21 62.21 8.00 1196.63 333.37 1022.91 300.94 0.23195 H2 :33" P,A_SWA_WICS P-S Ray Path A—Velocity Profile I DERART I INCOME I OUT I ARRIVE I TOTAL I TOTAL I HORIZ I VERT I RAY I I RAY I RAY I RAY I RAY I DIST I TIME I DIST I DIST I RARH I I (DEB) I (0E8) I (DEG) I (DEB) I (H) I (MS) I (H) I (H) I I 3.00 19.43 9.14 1.74 622.06 272.51 146.57 300.94 0.08722 3.12 20.27 9.52 1.81 623.91 273.10 153.24 300.94 0.09085 3.25 21.12 9.91 1.88 625.87 273.73 159.99 300.94 0.09448 3.37 21.97 10.29 1.96 627.93 274.38 166.83 300.94 0.09811 3.50 22.83 10.68 2.03 630.11 275.08 173.75 300.94 0.10174 3.62 23.69 11.06 2.10 632.4 275.80 180.78 300.94 0.10537 3.75 24.56 11.45 2.18 634.80 276.57 187.90 300.94 0.109 3.87 25.44 11.84 2.25 637.34 277.37 195.13 300.94 0.11263 4.00 26.32 12.22 2.32 640.00 278.21 202.47 300.94 0.11626 4.12 27.20 12.61 2.39 642.80 279.09 209.94 300.94 0.11988 4.25 28.10 13.00 2.47 645.74 280.02 217.55 300.94 0.12351 4.37 29.00 13.39 2.54 648.84 280.99 225.29 300.94 0.12713 4.50 29.91 13.78 2.61 652.10 282.00 233.18 300.94 0.13076 4.62 30.83 14.17 2.68 655.52 283.07 241.24 300.94 0.13438 4.75 31.76 14.56 2.76 659.13 284.19 249.46 300.94 0.13801 4.87 32.69 14.95 2.83 662.93 285.37 257.88 300.94 0.14163 5.00 33.64 15.34 2.9 666.93 286.61 266.49 300.94 0.14525 5.12 34.59 15.73 2.97 671.15 287.90 275.32 300.94 0.14888 5.25 35.56 16.13 3.05 675.60 289.27 284.39 300.94 0.1525 5.37 36.54 16.52 3.12 680.30 290.71 293.7 300.94 0.15612 5.50 37.53 16.92 3.19 685.27 292.22 303.30 300.94 0.15974 5.62 38.54 17.31 3.26 690.53 293.82 313.18 300.94 0.16336 5.75 39.55 17.71 3.34 696.10 295.51 323.40 300.94 0.16698 5.87 40.59 18.10 3.41 .702.02 297.29 333.96 300.94 0.17059 6.00 41.64 18.50 3.48 708.31 299.18 344.92 300.94 0.17421 6.12 42.70 18.90 3.55 715.02 301.18 356.30 300.94 0.17782 6.25 43.79 19.30 3.63 722.18 303.31 368.16 300.94 0.18144 6.37 44.89 19.7 3.70 729.83 305.58 380.54 300.94 0.18505 6.50 46.02 20.10 3.77 738.05 308.01 393.51 300.94 0.18867 6.62 47.16 20.50 3.84 746.89 310.60 407.13 300.94 0.19228 6.75 48.34 20.91 3.92 756.43 313.39 421.48 300.94 0.19589 6.87 49.54 21.31 3.99 766.76 316.39 436.68 300.94 0.1995 7.00 50.77 21.72 4.06 778.01 319.64 452.83 300.94 0.20311 7.12 52.04 22.12 4.13 790.30 323.18 470.08 300.94 0.20672 7.25 53.34 22.53 4.20 803.80 327.84 488.60 300.94 0.21033 7.37 54.68 22.94 4.28 818.74 331.29 508.62 300.94 0.21393 7.50 56.06 23.35 4.35 835.37 338.99 530.43 300.94 0.21754 7.62 57.50 23.76 4.42 854.05 341.25 554.37 300.94 0.22114 7.75 59.00 24.17 4.49 875.25 347.17 580.94 300.94 0.22475 7.87 60.56 24.58 4.57 899.58 353.93 610.77 300.94 0.22835 8.00 62.21 25.00 4.64 927.93 361.76 644.76 300.94 0.23195 8.12 63.94 25.41 4.71 961.56 370.98 684.23 300.94 0.23555 8.25 65.8 25.83 4.78 1002.42 382.12 731.14 300.94 0.23915 8.37 67.79 26.25 4.85 1053.61 395.98 788.66 300.94 0.24275 8.50 69.98 26.66 4.93 1120.54 414.00 862.30 300.94 0.24634 8.62 72.41 27.09 5.00 1213.81 438.94 962.78 300.94 0.24994 8.75 75.23 27.51 5.07 1357.90 477.24 1114.84 300.94 0.25353 P-P FROM P/B-P/B-SONICS H3 P-P Ray Path B-Velocity Profile I DERART I INCOME I OUT I ARRIVE I TOTAL I TOTAL I HORIZ I UERT I RAY I I RAY I RAY I RAY I RAY I DIST I TIME I DIST l DIST I FARM I I (DEB) I (DEG) I (DEB) I (DEB) I (M) I (MS) I (M) I (M) I I 3.00 19.00 19.00 3.00 632.24 185.35 196.03 300.27 0.08722 3.12 19.82 19.82 3.12 635.19 186.16 205.16 300.27 0.09085 3.25 20.65 20.65 3.25 638.30 187.02 214.43 300.27 0.09448 3.37 21.48 21.48 3.37 641.58 187.93 223.84 300.27 0.09811 3.50 22.32 22.32 3.50 645.04 188.89 233.41 300.27 0.10174 3.62 23.16 23.16 - 3.62 648.68 189.89 243.13 300.27 0.10537 3.75 24.01 24.01 3.75 652.53 190.95 253.03 300.27 0.109 3.87 24.86 24.86 3.87 656.58 192.07 263.12 300.27 0.11263 4.00 25.72 25.72 3.99 660.84 193.25 273.40 300.27 0.11626 4.12 26.58 26.58 4.12 665.33 194.49 283.90 300.27 0.11988 4.25 27.45 27.45 4.25 670.06 195.79 294.62 300.27 0.12351 4.37 28.33 28.33 4.37 675.04 197.17 305.58 .300.27 0.12713 4.50 29.21 29.21 4.50 680.29 198.61 316.80 300.27 0.13076 4.62 30.11 30.11 4.62 685.82 200.14 328.30 300.27 0.13438 4.75 31.01 31.01 4.75 691.65 201.74 340.09 300.27 0.13801 4.87 31.91 31.91 4.87 697.80 203.44 352.2 300.27“0.14163 5.00 32.83 32.83 5.00 704.29 205.22 364.65- 300.27 0.14525 5.12 33.76 33.76 5.12 711.14 207.11 377.47 300.27 0.14888 5.25 34.70 34.70 5.25 718.38 209.10 390.69 300.27 0.1525 5.37 35.64 35.64 5.37 726.04 211.21 404.34 300.27 0.15612 5.50 36.60 36.60 5.50 734.15 213.44 418.46 300.27 0.15974 5.62 37.57 37.57 5.62 742.74 215.80 433.08 300.27 0.16336 5.75 38.56 38.56 5.75 751.86 218.31 448.25 300.27 0.16698 5.87 39.55 39.55 5.87 761.56 220.97 464.01 300.27 0.17059 6.00 40.56 40.56 6.00 771.87 223.80 480.43 300.27 0.17421 6.12 41.59 41.59 6.12 782.87 226.82 497.57 300.27 0.17782 6.25 42.63 42.63 6.25 794.62 230.04 515.50 300.27 0.18144 6.37 43.69 43.69 6.37 807.19 233.48 534.30 300.27 0.18505 6.50 44.77 44.77 6.50 820.68 237.18 554.07 300.27 0.18867 6.62 45.87 45.87 6.62 835.19 241.15 574.92 300.27 0.19228 6.75 46.99 46.99 6.75 850.84 245.43 596.97 300.27 0.19589 6.87 48.13 48.13 6.87 867.76 250.06 620.38 300.27 0.1995 7.00 49.30 49.30 7.00 886.14 255.08 645.32 300.27 0.20311 7.12 50.50 50.50 7.12 906.17 260.55 672.01 300.27 0.20672 7.25 51.73 51.73 7.25 928.10 266.53 700.70 300.27 0.21033 7.37 52.99 52.99 7.37 952.24 273.11 731.72 300.27 0.21393 7.50 54.30 54.30 7.50 978.95 280.39 765.45 300.27 0.21754 7.62 55.64 55.64 7.62 1008.70 288.49 802.38 300.27 0.22114 7.75 57.03 57.03 7.74 1042.11 297.58 843.13 300.27 0.22475 7.87 58.47 58.47 7.87 1079.96 307.87 888.53 300.27 0.22835 8.00 59.98 59.98 8.00 1123.29 319.63 939.65 300.27 0.23195 8.12 61.56 61.56 8.12 1173.56 333.27 997.99 300.27 0.23555 8.25 63.22 63.22 8.25 1232.82 349.33 1065.63 300.27 0.23915 H4 P-S I DEPART I INCOME I OUT I ARRIVE I TOTAL I TOTAL I HORIZ I UERT I RAY I I RAY I RAY I MY I RAY I DIST I TIME I DIST I DIST I PAM I I (0E8) I (0E8) I (DEG) I (0E8) I (M) I (MS) I (M) I (M) I I 3.00 19.00 13.89 1.74 620.95 256.02 149.88 300.27 0.08722 3.12 19.82 14.48 1.81 622.82 256.62 156.68 300.27 0.09085 3.25 20.65 15.07 1.88 624.78 257.26 163.55 300.27 0.09448 3.37 21.48 15.67 1.96 626.86 257.93 170.51 300.27 0.09811 3.50 22.32 16.26 2.03 629.04 258.63 177.55 300.27 0.10174 3.62 23.16 16.86 2.10 631.33 259.37 184.68 300.27 0.10537 3.75 24.01 17.46 2.18 633.74 260.15 191.91 300.27 0.109 3.87 24.86 18.06 2.25 636.27 260.96 199.25 300.27 0.11263 4.00 25.72 18.66 2.32 638.93 261.81 206.70 300.27 0.11626 4.12 26.58 19.27 2.39 641.72 262.7 214.26 300.27 0.11988 4.25 27.45 19.87 2.47 644.65 263.64 221.95 300.27 0.12351 4.37 28.33 20.48 2.54 647.73 264.62 229.77 300.27 0.12713 4.50 29.21 21.09 2.61 650.96 265.65 237.74 300,27 0.13076 4.62 30.11 21.71 2.68 654.35 266.72 245.85 300.27 0.13438 4.75 31.01 22.33 2.76 657.92 267.85 254.13 300.27 0.13801 4.87 31.91 22.94 2.83 661.66 269.03 262.59 300.27 0.14163 5.00 32.83 23.57 2.9 665.60 270.27 271.23 300.27 0.14525 5.12 33.76 24.19 2.97 669.74 271.57 280.08 300.27 0.14888 5.25 34.70 24.82 3.05 674.10 272.94 289.14 300.27 0.1525 5.37 35.64 25.45 3.12 678.69 274.37 298.43 300.27 0.15612 5.50 36.60 26.08 3.19 683.53 275.88 307.97 300.27 0.15974 5.62 37.57 26.72 3.26 688.64 277.47 317.78 300.27 0.16336 5.75 38.56 27.36 3.34 694.03 279.14 327.89 300.27 0.16698 5.87 39.55 28.01 3.41 699.74 280.90 338.32 300.27 0.17059 6.00 40.56 28.66 3.48 705.78 282.76 349.10 300.27 0.17421 6.12 41.59 29.31 3.55 712.20 284.72 360.26 300.27 0.17782 6.25 42.63 29.96 3.63 719.01 286.80 371.83 300.27 0.18144 6.37 43.69 30.62 3.70 726.26 289.00 383.87 300.27 0.18505 6.50 44.77 31.29 3.77 734.00 291.35 396.41 300.27 0.18867 6.62 45.87 31.96 3.84 742.28 293.85 409.52 300.27 0.19228 6.75 46.99 32.63 3.92 751.16 296.51 423.26 300.27 0.19589 6.87 48.13 33.31 3.99 760.71 299.37 437.70 300.27 0.1995 7.00 49.30 33.99 4.06 771.02 302.44 452.94 300.27 0.20311 7.12 50.50 34.68 4.13 782.18 305.74 469.08 300.27 0.20672 7.25 51.73 35.38 4.20 794.33 309.33 486.26 300.27 0.21033 7.37- 52.99 36.08 4.28 807.61 313.22 504.62 300.27 0.21393 7.50 54.30 36.79 4.35 822.22 317.48 524.38 300.27 0.21754 7.62 55.64 37.50 4.42 838.39 322.18 545.77 300.27 0.22114 7.75 57.03 38.22 4.49 856.42 327.38 569.11 300.27 0.22475 7.87 58.47 38.95 4.57 876.71 333.2 594.81 300.27 0.22835 8.00 59.98 39.68 4.64 899.78 339.79 623.4 300.27 0.23195. 8.12 61.56 40.42 4.71 926.36 347.32 655.65 300.27 0.23555 8.25 63.22 41.17 4.78 957.47 356.09 692.58 300.27 0.23915 8.37 64.98 41.93 4.85 . 994.63 366.50 735.76 300.27 0.24275 8.50 66.87 42.70 4.93 1040.17 379.17 787.56 300.27 0.24634 8.62 68.91' 43.47 5.00 1097.98 395.15 851.94 300.27 0.24994 8.75 71.16 44.26 5.07 1175.09 416.33 936.04 300.27 0.25353 8.87 73.71 45.06 5.14 1286.08 446.62 1054.61 300.27 0.25713 APPENDIX I Transverse Records