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THESIS it! E ":4, w 5 This is to certify that the thesis entitled AZIMUTHAL VELOCITY-DEPTH DISTRIBUTION OF SEISMIC SHEAR AND COMPRESSIONAL WAVES IN THE ROSS ICE SHELF, 18 km EAST OF MINNA BLUFF, AND 96 km SSE OF MCMURDO STATION, ANTARCTICA presented by James B. NansTow has been accepted towards fulfillment of the requirements for M. 5; degree in __G£QI_OQ¥_ MQ/smj /Major professor Date 20/4“)! [(781 0-7639 OVERDUE FINES: 25¢ per day per Item RETURNING LIBRARY MATERIALS: Place In book return to remove charge from circulltton records AZIMUTHAL VELOCITY-DEPTH DISTRIBUTION OF SEISMIC SHEAR AND COMPRESSIONAL WAVES IN THE ROSS ICE SHELF. 18 km EAST OF MINNA BLUFF, AND 96 km SSE 0F MCMURDO STATION, ANTARCTICA By James B. Wanslow A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Geology 1981 \\ Ru 5.0.3.er (Q ABSTRACT AZIMUTHAL VELOCITY-DEPTH DISTRIBUTION OF SEISMIC SHEAR AND COMPRESSIONAL WAVES IN THE ROSS ICE SHELF. 18 km EAST OF MINNA BLUFF. AND 96 km SSE OF MCMURDO STATION, ANTARCTICA By James B. Wanslow This study was undertaken to determine the azimuthal seismic velocity-depth distribution in an area of known high shear stress. It was assumed that the effects of the shear stress field would be reflected in the azimuthal velocity- depth distribution because of the known response of ice fabric to shear stress. A site 18 km east of the Minna Bluff peninsula and 96 km SSE of McMurdo Station. Antarctica. was selected for the study due to the nature of the shear stress field in this region. Seismic data collected in 8 directions using a radial refraction array was analyzed to produce velocity-depth profiles. The distribution of SH-wave velocities was bimodal and centrosymmetric, with one maximum velocity set averaging 1 1 1 1 2056 ms' t 24 ms' . and the other 1830 ms' t 18 ms' . P- wave velocities displayed no centro-symmetry, and exhibited an average maximum velocity of 3671 ms"1 i 15 ms—l. The SH- wave results were attributed to a strong east-west ice crystal c-axis orientation with vertical basal planes below 37 m depth. The low P-wave velocity maximum was attributed primarily to fracturing. The importance of shear waves for velocity anisotropy studies was thus indicated. This work is dedicated to my wife Linda, whose assistance and tolerance helped make it possible. ii ACKNOWLEDGMENTS I would like to express my gratitude to Dr. Hugh Bennett, whose guidance and instruction made this thesis possible. Special recognition for typing assistance and moral support is also due my sister-in-law. Nancy Payne, and, most especially, my wife, Linda Wanslow. without whom this work might never have been completed. Lastly, I must acknowledge assistance and support of a different kind provided to me over many years by my mother, Lucille Wanslow. to whom I will always owe a large debt of grati- tude. iii TABLE OF CONTENTS Introduction........................................... Previous Seismic Work on the Ross Ice Shelf....... Pertinent Ice Petrofabric Research................ Pertinent Ultrasonic Research..................... Purpose........................................... Location of the Study Area........................ Pertinent Glaciological Aspects of the Ross Ice Shelf.. Surface Features.................................. Source Areas, Flow Direction. and Ice Thickness... Stratification.................................... Effect of Glaciological Parameters on Seismic Wave Propagation....................................... Field Procedures....................................... Field Season and Personnel........................ Description of Seismic Array, Equipment, and Procedures........................................ Distance and Time Measurement..................... Data Reduction: Time-Distance Curves................... Introduction...................................... Discussion of Time-Distance Curves................ Analysis and Interpretation............................ IntrOduCtionOOOOOIOO0....0......0....00......0.... iv H 00 «PFU N 10 1h 17 21 21 21 23 25 25 25 39 39 Velocity Determination and Error Analysis......... Velocity-Depth Profiles........................... Interpretation of Velocity-Depth Profiles: Developement of Model............................. Velocity Increase to 37 m Depth: Densification................................ Velocity Increase 37 m to 70 m Depth: Crystal Fabric............................... Heterogeniety in the Near Surface............ P-Wave Velocities Affected by Fracturing..... Proposed Model for the Minna Bluff Study Area..... Comparison of Velocity-Depth Profiles near Minna Bluff with Other Studies.......................... Importance of Shear Waves in Seismic Anisotropy Studies........................................... Appendix A: Transverse Isotropy........................ Appendix B: Derivation of Weichert-Herglotz-Bateman Integral............................................... Appendix C: Seismic Event Recognition and Arrival Time Determination.......................................... Appendix D: SH-Wave Time-Distance Data................. Appendix E: Seismic Velocities and WHB Depths.......... BibliographyOIOOOOOOOOOCOIOOOOOOOOOOOOOOO00.000.000.00. 39 45 57 57 59 61 62 65 65 67 7O 75 83 85 91 93 II III D-I D-II E-I LIST OF TABLES SH-Waves: Regression Lines and Maximum Velocities P-Waves: Regression Lines and Maximum Velocities. Error Analysis................................... SH;Wave Time-Distance Data....................... P-Wave Time-Distance Data........................ Seismic Velocities and WHB Depths................ vi 37 43 85 88 91 mmtwmp 8. 9. 10vA. 10-B. 10-C. 10-D. 10-E. 10-F. 10-G. 10-H. 11-A. 11-B. 12. 13-A. 13-B. LIST OF FIGURES Ross Ice Shelf, Minna Bluff Vicinity............. ERTS Photo, Minna BIUff Area.........o.....oo.... Crevasse Fields of the Ross Ice Shelf............ ThICkneSS Of the ROSS Ice Shelfeeeeoeeeeeeeeeeeee Velocity field of ice movement, Ross Ice Shelf... Density profiles at Byrd Station, Little America V, and Ellsworth.............o................... Temperature profile at Byrd and Little America V. T-X curve, T-X curve, T-X curve, T-X curve, T-X curve, T-X curve, T-X curve, T-X curve, T-X curve. T-X curve, P-Wave T-X P-Wave T-X SH waves Set A: 000-090 directions.... SH waves Set B: 0&5-135 directions.... non-linear non-linear non-linear non-linear non-linear non-linear non-linear non-linear 000 curve, curve, OAS part, Part: part, part, part, part, part, part, SH-OOO-D............. SH-OOO-R............. SH-Ohfi-D............. SH-045-R............. SH-O90-D............. SH—O90-R............. SH-lBS-D............. SH-135-R............. and 090 directions......... and 135 directions......... Best Fit Curves, Shear Wave Set A and B.......... Depth VS Error, SH-Waves......................... Depth vs Error, P-Waves.......................... vii 11 13 16 18 18 27 28 29 29 30 30 31 31 32 32 33 3h 35 b4 44 1u-A. 1n-B. 14-c. 1n-D. 1u-E. 14-F. 1u-c. 1u-H. 15-A. 15-3. 15-0. 15-9. 15-3. 15-F. 15-0. 15-H. 16. 17. 18. 190 20. 21. 22. Velocity-Depth Velocity-Depth Velocity-Depth Velocity-Depth Velocity-Depth Velocity-Depth Velocity-Depth Velocity-Depth Velocity-Depth Velocity-Depth Velocity-Depth Velocity-Depth Velocity-Depth Velocity-Depth Velocity-Depth Velocity-Depth Velocity-Depth Velocity-Depth Profile: Profile: Profile: Profile: Profile: Profile: Profile: Profile: Profile: Profile: Profile: Profile: Profile: Profile: Profile: Profile: Profile: Profile: Line SH‘OOO‘Deeoeeeeeeeeo Line SH-OOO-D............ Line SH-OhS-D............ Line SH—Oh5—R............ Line SH-O90-D............ Line SH’090-Reeeeeoeeeeee Line SH’135-Deeoeoeoeoeoe Line SH’lBS-Reeeoeoeeeeeo Line P-OOO-D............. Line P-OOO-R............. Line P-OAS-D............. Line P-OA5-R............. Line P-O90-D............. Line P-O90-R............. Line P-135-D............. Line P‘lBS‘Reeoeeeoeooeee SH-Waves Set A........... SH-Waves Set Booeeeeeeeoe Density vs P-wave velocity, linear plot, at Byrd StationCOIOOOOOO0.0.0....00.0.0000...00.0.00...O. P-wave and S-wave velocities and densities vs depth at Byrd Station............................ 0.0.0.0...COCOOOCIOCOOOOO00......OOOOOOOOOOOOOOIO Velocity-Depth Profiles at Byrd, at Little America v, and at EllsworthOOOOOOOOOIOOOOOOOOO00.......00 Ross Ice Shelf P and SH-wave Velocity-Depth PrefileSOIOOOOOIOIOOOOOCOOOOIOOOOOOOOOOCOOO00.0.. viii 1*? A? 48 us 49 49 so 50 51 51 52 52 53 53 54 5a 55 56 58 59 59 66 68 23. 24. 25. 26. 27. 28. SH-Wave identification: sample of corresponding overlaid traces.................................. ix 75 77 78 78 79 8h I . INTRODUCTION PREVIOUS SEISMIC WORK ON THE ROSS ICE SHELF The first intensive seismic reconnaissance program cov- ering the entire Ross Ice Shelf was performed during the years 1957 through 1960 as a part of the United States IGY activities in Antarctica. Three traverses were carried out: the Ross Ice Shelf Traverse of 1957-1958, the Victoria Land Traverse of 1958-1959, and the Discovery Deep Traverse of 1960 (Crary, et al.,1960) Seismic reflection and refraction surveys were carried out at stations along the traverse routes in conjunction with other glaciological studies. Goals of the seismic program included determination of ice thickness. mapping of water depth beneath the ice shelf, and measurement of seismic velocities within the ice. Results of the surveys included maps of ice thickness and water depth for the shelf as a whole. Seismic velocity was found to increase as an approximately logarithmic function of depth, with maximum velocity attained at a depth of 60 to 80 meters. 1 The velocity-depth profile at Little America V on the Ross Ice Shelf was constructed by seismic refraction work in conjunction with the deep core drilling project of 1958-1959 (Thiel and Ostenso, 1961). Comparison of the velocity-depth profile with the density-depth profile produced by the core drilling project indicated that to a first approximation the increase of velocity with depth reflected the increase of density with depth. Maximum compressional wave velocity was reached at 80 to 85 meters depth, as estimated from the 1 2 refraction survey. This compares well with the depth of 85 to 110 meters determined for maximum velocity from seismic logging of the deep drill hole. Maximum P-wave velocity was measured as 3839 ms"1 and maximum S-wave velocity as 1978 ms'l. PERTINENT ICE PETROFABRIC RESEARCH Crystal fabric studies of temperate and polar glaciers have demonstrated that the c-axes of ice crystals tend to be aligned perpendicular to the foliation plane (Rigsby, 1960: Taylor, 1963: others). Rigsby has further demonstrated that the alignment is strongest with high shear stress. Recrystal- lization during deformation with resulting c-axis alignment normal to applied shear stress has been observed by Rigsby during study of ice stressed under controlled laboratory conditions. Plastic deformation of ice is accomplished by translation gliding on the basal plane (Kamb, 1961). Glide direction and direction of shear stress correspond closely. Petrofabric studies of the deep drill core at Little America V have disclosed an increasing preferred orientation of c-axes with depth (Ragle, et al., 1960). In a study of ice fabrics from the Thule area in Greenland. Rigsby concluded that ice crystals in polar glaciers tend to be oriented with the basal glide plane parallel to the shear plane (Rigsby, 1955). PERTINENT ULTRASONIC RESEARCH Laboratory studies of ultrasonic wave propagation in single ice crystals have demonstrated the dependence of velo- city on propagation direction in a transversely isotropic manner (Appendix A). A difference of about 4% between P-wave velocity in the c- and a-axis directions has been observed. with a maximum difference of nearly 7% between pr0pagation in the c-axis direction and at 52° to the c-axis (Bennett, 1968). In a study of the effects of conic crystal distribu- tions, with a vertical axis of symmetry, a difference off< 2% in P-wave velocity between the vertical and horizontal direc- tions was found for c-axis distributions inclined at > 30° to the vertical (Bennett, 1972). Horizontal SH and SV-wave velo- cities were found to differ by at least 2% even for very slight preferred orientations. This, in conjunction with the ice petrofabric results cited above, implies that detection of preferred c-axis orientation in polycrystalline ice may be possible by determining the distribution of velocity with direction. If a preferred orientation is indeed present, then a directional dependency may be observable. It should be noted that velocity variations of a transversely isotropic nature may result from layering (Postma, 1955). Foliation often observed in glacier ice (Rigsby, 1960: Shumskii. 1964: Embledon and King, 1968), consisting of alternating layers of bubbly and clear ice or of microfracturing, which are believed to result from flow deformation (Embledon and King, 1968), would represent such a layering. Postma (1955) has )4. shown that in such a case the slow direction of P-wave propa- gation would be normal to the layering. PURPOSE The purpose of this study is to determine the distribu- tion of seismic velocity with depth and azimuth in an area of known high shear stress. It is assumed that the velocity distribution should be related to the direction of shear stress because of the response of ice fabrics to shear stress as discussed above. Thus, if the aggregate c-axis orientation is as indicated, the pattern of the seismic velocity distri- bution should be predictable. Therefore, determination of the velocity-depth profile as a function of azimuth should permit analysis of the effects of the stress field on the ice fabric. LOCATION OF THE STUDY AREA The study area is located on the Ross Ice Shelf, 18 km east of Minna Bluff and about 96 km SSE of McMurdo Station, Antarctica (Figures 1 and 2). The gross ice movement in the area is to the north. The ice movement is retarded by Minna Bluff, however. resulting in a zone of high strain rates in the shear stress field imposed by the movement past Minna Bluff (Crary, et al. 1962). Figure 1. Ross Ice Shelf, Minna Bluff Vicinity. Study area indicated by . fl . ‘ w (I "Foam It! _ -\ “$1,,thtn t“. F. 3‘"! h" ' . IN “ messmsmw: ’ .29 / @\ Ice ”rod (mth lunllhfl) 72 PM?“ Ea. ~19 Jcr Piedmuut RH /’ 575*"sfi-xu VICIOVII Leno Inverse 1958-5911959-60 -73 Figure 2. ERTS Photo, Minna Bluff Area. Study area indi- cated by 0 fl II. PERTINENT GLACIOLOGICAL ASPECTS OF T E RQ§S ICE S ___ SURFACEEEATURES Glaciological work of the IGY traverses listed in Chap- ter 1 included mapping of snow accumulation rates and sur- face density (Crary, et al., 1962). .Snow accumulation stud- ies employing surface stakes, pit studies, and drill core analysis indicated an average annual accumulation rate of 20 centimeters water equivalent per unit area for the entire Ross Ice Shelf. For most areas annual values ranged from 17 to 24 centimeters water equivalent per unit area (Crary, et al., 1962: Zumberge. et al., 1960). In the vicinity of Minna Bluff estimated annual accumulation ranged from 17.6 to 23.5 centimeters water equivalent per unit area. Bulk density measurements of the top two meters of the shelf indicated a range of 0.33 to 0.42 gm cm"3 for the entire ice shelf. A range of 0.40 to 0.41 gm cm-3 was observed in the vicinity of Minna Bluff. Sastrugi may be defined as a series of wavelike or domelike ridges formed by wind action. Well-developed sas- trugi with strong north-south orientation was observed in the study area (H. Bennett, personal communication). Mean peak to trough amplitude of the sastrugi was estimated to be 0.5 meters. Crevasses and fractures result from internal stresses exceeding certain parameters of the ice strength (Zumberge, et al., 1960). Thus, areas of high strain rates are implied by the locations of crevasse fields, as indicated 9 1 0 schematically in Figure 3. Note especially the crevasse field east of Minna Bluff indicated in Figure 3 and shown by ERTS photography in Figure 2. In crevasse fields, fractures ranging in width from several meters down to a few millimeters may be observable. In the case of extremely narrow fractures, it is not possible to determine the nature of the fracture at depth by visual observation alone. An attempt was made on the basis of preliminary aerial and ground reconnaissance to locate the study area completely outside the crevasse field adjacent to Minna Bluff. However, more detailed observation, during the course of the field work, revealed the presence of several very narrow but long fractures at the surface in the vicinity of the study area (H. Bennett, personal commun- ication). SOURCE AREAS, FLOW D;RECTIONS.AAND_ICE THICKNESS The major sources of the Ross Ice Shelf are the Marie Byrd Land Ice Sheet, the glaciers of the Transantarctic Moun- tains, and snow accumulation directly on the ice shelf (Crary, et al., 1962). The largest contribution is from Marie Byrd Land, as clearly seen from the isopachs of Figure 4. The glacial ice streams from the Transantarctic Mountains, form- ing the second largest ice source, are clearly discernable in the same figure. Snow accumulation on the ice shelf, dis- cussed above, was concluded by Crary (1962) to be the third largest source. In cores from the deep drilling project at Little America V, annual strata were discernable to at least 50 m depth (Ragle, et al., 1960). The stratification was 11 ." R035 SEA .: .4 Figure 3. Crevasse fields of the Ross Ice Shelf. (From Crary, et al.. 1962) 12 Figure 4. Thickness of the Ross Ice Shelf. (After Robin, 1975) : l/ \\ 0:0 /// \‘ Ifi 1‘ ’/ \\ / / I \6 ul‘ / lillll' mu "Will“ mu ROSS SEA w1ao°E i .3217? 44’s at} 400/ / Beardmore Glacl x' " \\ ..... 016$ LEGEND ISOIZHach (meters) Conjectured boundary oi ice shelf and streams Exposed rock margin I/Q Conspicuous crevassing ‘\ Direction of flow Kilometers J l J Imu‘ 14 attributed by Ragle, et al., to accumulation on the ice shelf, although it should be noted that annual strata are also recognizable in the ice sheet at Byrd Station (Gow, 1961). Ragle, et al., concluded that, due to melting at the bottom of the ice shelf, ice developed from annual snow accumulation may form a major fraction of the total shelf thickness near the terminus. It should be noted, however, that the whole question of melting at the base of the shelf is very controversial. Ice flow directions have been determined by observations of stake movements, mapping of thickness trends and visible flow lines, and surface leveling (Dorrer, et al., 1969: Stuart and Bull, 1963; Crary, et al., 1962; MacDonald and Hatherton, 1961). Recently, Robin (1975) has compiled a comprehensive map of velocity vectors and flow directions for the entire ice shelf (Figure 5). Note especially in Figure 5 the flow direction near Minna Bluff. Thickness of the Ross Ice Shelf has recently been mapped by airborne radio sounding techniques (Robin, 1975) (Fig- ure 4). Note in Figure 4 the damming effect of Minna Bluff as evidenced by the great ice thickness immediately behind and against it, and the rapid thinning adjacent to the east. STRATIFICATION During the traverses of 1959-1960, snow pit studies to 3 meters depth revealed annual strata readily discernable by textural variations (Crary, et al., 1962). Small ice lenses, probably formed by refreezing of meltwater, as well as crusts 15 Figure 5. Velocity field of ice movement, Ross Ice Shelf. (After Robin. 1975) W.180 E l LEGEND ,1300 Velocity isoline (rn per year) H‘ Conjectured flow line Visible stream line / /Conjectured boundary of .- lce shelf and streams //rw4<‘~c‘ Conspicuous crevassing 100 Mean speed between flow lines (m per year) Velocity vectors: BOOm/year L—————J Single, observed Mean Kilometers 290 Jerome 910ml)” O I; \ <00 \\\ \l \ li/ / /I \ . I». \ /\ / «oi / O , \ \. I / / / \ 1’ K \I / / / e o ’z o / Ag .0 \\ 31 _/(ll/ / >- La 0 \ / \\\\\ ////// / / S’le'g 9”) 7/ ll 1 l \\\\\\\\ WWW" ”ll/u - m“ “\i we, / H ”I, “WWW“ ”H ”IIW’I/l/II/llm l /I.\ \ - v, , “Ilium ,1” ’ NIH/m \ a .. { llj/I \ l/ \ J (H \ l L__/ ROSS SEA W11 \ \ i “HIS. / ll”, (Jalgulllnl/Il\ " 79 m ”ll/1 62 ’1 17 and layers of ice up to several centimeters thick were also observed. The crusts and layers were attributed to surface melting and refreezing followed by burial. Some of the thicker layers were correlatable over a relatively wide area. Borehole studies performed during the IGY included stratigraphic and density profiles. At IGY Camp Michigan, drill core was obtained to nearly 16 meters depth. Annual strata were observed as in the snow pit studies, with ice crusts, layers, and lenses often found to be vertically con- nected by ice pipes, implying vertical redistribution of meltwater (Zumberge, et al., 1960). Bulk density measure- ments showed an overall, although discontinuous in detail, increase in density with depth. Studies of four boreholes drilled to 20 meters depth during the traverse program yield- ed similar results (Crary, et al., 1960). Density-depth stu- dies to much greater depths were carried out at Little Amer- ica V on the Ross Ice Shelf, at Byrd Station on the mainland ice sheet, and at Ellsworth on the Filchner Ice Shelf (Thiel and Ostenso, 1961; Ragle, et al., 1960). A general logarith- mic increase of density with depth was observed, although the curves for the ice shelves exhibit anomolous zones from approximately 40 to 70 meters depth (Figure 6). EFFECT OF GLACIOLOGICAL PARAMETERS ON SEISMIC WAVE PROPAGATION. The density of the surface layers near Minna Bluff is high compared to the rest of the ice shelf, as indicated above. Therefore, somewhat shallower depth penetration 18 DENSITY (GM/6M3) TEMPERATURE ('6) a4 0.6 as /.0 -30 -20 #0 ' 20 20 4o 40 so 60 so 80 lOO IOO l20 ‘ l20 -\ v: 2 mo § ”0 é \. E E a mo & mo in Q Q l80 ISO zoo 200 220 220 240 240 260 260 280 280 300 300 Figure 6 Figure 7 Fig. 6. Density profiles at Byrd Station (solid), Little America V (dashed), and Ellsworth (dotted), (From Thiel and Ostenso, 1961). Fig. 7. Temperature profile at Byrd (solid) and Little Amer- ica V (dashed). (From Thiel and Ostenso, 1961) 19 should be expected for seismic refraction work since maximum density and hence maximum velocity should be achieved at shallower depth relative to the rest of the ice shelf. The effects of crevasses and fractures on seismic wave propagation in ice have been little investigated. However,. from theoretical considerations (Grant and West, 1965: Tel- ford, et al., 1976) certain effects are probable. Open cre- vasses could completely block seismic wave propagation. Shear waves could be blocked by water-filled crevasses with compressional waves being passed with little if any detect- able effect. The lower edges of crevasses entirely closed at depth could produce diffraction effects. To avoid such possible difficulties, the study area was chosen to be out- side the crevasse field located east of Minna Bluff (Figure 2), as mentioned above. Velocity anisotropy could be produced by stratification as discussed by Postma (1955) and in Appendix A. In this regard, Bennett (1968) detected velocity anisotropy in stratified ice from the Ross Ice Shelf, but no axis of sym- metry for the variation was identified. Lower density layers overlain by higher density ice could produce velocity reversals and hidden layers (Telford. et al., 1976). However, if there is a net density increase with depth, as observed, and the low density layers are very thin relative to seismic wavelength, then the effect should be negligible. Since such layers have been observed to be no more than several centimeters thick in the stratigraphic 20 studies cited above, and the wavelengths involved here are measured in several tens of meters, this is indeed the case. It should also be noted that seismic velocity in ice varies inversely with temperature (Thiel and Ostenso, 1961). As shown in Figure 7 temperature increases with depth in the ice shelf, an effect attributed to the underlying relatively warm ocean. Therefore, velocity reversal at depth should be expected to limit the depths of seismic refraction observa- tions, since density, the other principal factor in velocity, is nearly constant below about 90 meters (Figure 6). III. EIELD PROCEDURES FIELD SEASON AND_EERSONNEL The field work for this study was carried out from 26 December 1976 to 3 February 1977 during the Antarctic summer field season. Field personnel consisted of Dr. Hugh Bennett, Dr. Roger Turpening, Jim Adams, John Reed, Barry Prather, and Ron Jennings. DESCRIPTION OF SEESMIC ARRAYJ EQULPMENTi AND PROQEDUREE A radial seismic refraction array consisting of four geophone lines with angular separation of 45° was employed in this study. This pattern was chosen as it facilitates the detection of any directional dependency of seismic velocity. The geophone lines were designated 000, O45, 090, and 135 according to azimuth as measured counterclockwise from line 000, which was oriented east-west. Each line of the array consisted of 24 geophones spaced at 15.24 meter intervals. Three shotpoint locations were laid out in line with and at each end of the geophone lines in order to permit the record- ing of refraction profiles in both directions along the ar- ray. The shotpoints, numbered 1, 2, and 3, were located, respectively, 15.24 meters, 335.28 meters, and 685.80 meters from the ends of the geophone lines. The spacing was chosen to permit a three geophone overlap between seismic records from successive shotpoints on each line. Seismic records were identified by the array line, the shotpoint, and the letter D (Direct) or R (Reverse), 21 22 depending on which end of the array line the shotpoint was located. For example, if the shotpoint was the second on the west end of line 000, the resulting record would be designated OOO-2D. The record resulting from the corres- ponding shotpoint located on the opposite end of the line would be identified as OOO-ZR. Similarly, proceeding coun- terclockwise from 000 to 135 the shotpoints have D desig- nations, with those on the opposite ends designated R. The geophones used, produced by Mark Products, Inc., were characterized by a natural frequency of 4.5 Hz with essentially flat response from 7 Hz to over 100 Hz. Geophone orientation depended upon the seismic wave type whose detec- tion was desired, being vertical for P-wave records, hor- izontal and normal to the array line for SH-waves, and paral- lel to the array line for SV-wave records. The digital recording equipment was furnished by the Environmental Research Institute of Michigan (ERIM). The sampling rate employed for the seismic data was 480 samples per second, resulting in a sampling interval of approxi- mately 2 ms. Explosives were used to generate the P-wave records. Three pound charges of Nitromon, a product of E.I. DuPont de Nemours, were employed at a shot depth of 3 meters. For the shear wave records a 4.2 inch mortar, with its base plate seated on the ice, was employed as the seismic energy source. RegUIation propellant charges were used to fire plastic containers of a water and ethylene glycol 23 mixture. For the SH-wave records, the mortar was oriented normal to the geophone line with the barrel at a 35° eleva- tion. An orientation parallel to the geophone line and with the same elevation was used for the SV records. Pairs of seismic records having the first motion of the SH-wave first arrivals breaking in opposite directions (polarity reversal) were obtained for each shotpoint by reversing the direction of the mortar between consecutive shots. Since everything else was the same between shots, the arrival times for seis- mic events at the same geophone locations should likewise be identical. Therefore, positive identification of shear waves on the plotted seismic sections and increased accuracy of arrival time determination were made possible. The proced- ures for SV-waves were similar except for mortar and geo- phone orientation as noted above. EESTAEQE:§ND TIEE_MEASUREMEEE Distances were measured in the field by steel tape. Wooden dowels were used to mark measured locations. Arrival times were measured directly on seismic sections prepared by ERIM from digital field tapes. For a detailed description of the techniques followed in event recognition and time measurement, see Appendix C. Error estimates have been made for distance, time, and velocity measurement. The error in distance measurement was estimated in the field by triangulation and remeasurement to be i0.01% (H. Bennett, personal communication). 2L. Time-distance (T-X) curves prepared from arrival time data (Appendix D) exhibit linear and non-linear segments. Error was estimated for the linear segments by determining the standard deviation of the measured time values from the best straight line fitted to the data by least squares. For the non-linear segments, estimation of error in time measurement was by determination of the standard deviation of the mea- sured times from the visually best fitted curve. Estimated time error for both P and SH-waves is $0.8 ms for the linear segments and $1.0 ms for the non-linear segments. The re- sulting velocity error for the linear segments is estimated at i0.3% and i0.2% for SH and P-wave velocities, respectively (Chapter 5). Error in velocities for the non-linear segments is discussed in Chapter 5. Since the error in distance measurement is not more than 5% of the error in time measurement as estimated above, this error may be considered negligible for the purposes of this study. Distances will therefore be assumed to be accu- rate. All error is thus considered to arise in time measure- ment. IV. DATA REDUCTEON: TIME-QESTANCE CURVES INTRODUCTEQE Compressional and SH-wave records were chosen for this study on the basis of preliminary evaluation of the seismic sections prepared by ERIM. Time-distance (T-X) curves, discussed below, were prepared for both P- and SH-waves. The T-X curves were analyzed to produce velocity-depth curves (Chapter 5). DISCUSSION OF TEME-DESTANCE CURVES The T-X curves (Figures 8-12), initially non-linear, become linear with distance from the shotpoint. That point on the curve joining the linear and non-linear segments will herein be termed the breakpoint. The breakpoint for each curve was determined analytically. The data for each curve was fitted by least squares to a line of the form: T = mx + b where: T arrival time in seconds m = slope x = shotpoint-receiver distance b = T axis intercept Beginning with the T-X data point at X = 609.60m, points were successively fitted in the -X direction. The linear correlation coefficient (r) was computed after each succes- sive data point had been fitted. The correlation coeffi- cient defined (Crow, et al., 1960) by: 25 26 nEXT - (EXHZT) I‘ 3 ’I L [nzx2 - (3)2]? [nETZ - (2T)2 ‘3? where, in this case, X = shotpoint to receiver distance, T = arrival time, and n = number of data points, indicates how well the data points fit the least squares regression line. Hence, if successive data points are increasingly non-linear, then r should decrease in magnitude in a con- tinuous manner. The point at which such a decrease was ob- served to begin was selected as the breakpoint. Two sets of SH-wave data were thus indicated, one with the breakpoint at x = 140.97!!! at 14-59111 (Set A)(Figures 8 and 10-A,B,E,F), and one with the breakpoint at X = 297.18m.¢ 26.40m (Set B) (Figures 9 and 10-C,D,G,H). Set A, plotted in Figure 8, corresponds to the 000 and 090 array directions, with Set B, plotted in Figure 9, corresponding to the 045 and 135 direc- tions. One data set was indicated for the P-waves (Figures 11-A and 11-B with breakpoint at 106.68m i 8.15m. ' The reciprocal of the slope of a time-distance curve at a given distance from the shotpoint is the maximum velocity penetrated by the raypath from the shotpoint to a receiver at that location (Telford, et al., 1976). Since, in this case, the T-X curve slope is constant beyond the breakpoint, it is assumed that maximum velocity has been reached for the entire curve at this point. Maximum velocities were deter- mined for each curve by computing the reciprocal of the slope of the line fitted by least squares from the breakpoint to the end of the curve (Tables I and II). WHl 5001 0001 300‘ Time, ms 20 01 mm c0 91'.“ Figure 8. 27 45520 54634 64008 73fi52 ezéss Qimoo Distance, m .3188 27432 36175 T-X curve, SH waves Set A: 000-090 directions. l005.84 6004 $001 400* 3001 Time, ms 2001 I001 28 O 9E4e Figure 9. 62.88 27:32 355.75 457120 was: 640.08 73: 52 822.96 9.8.40 Distance, m T-X curve, SH waves Set B: 045-135 directions. coke: 29 0 98244 nus we: 0 :w nu a Distance, m Figure lo-A Figure 10-B Fig. 10-A. T-X curve. non-linear part, SH-OOO-D Fig. 10-B. T-X curve, non-linear part, SH-OOO-R 30' o 91- 2:7»,32 o 91-2-2 1.32.86 Distance, m Figure 10-C Figure 10-D Fig. 10-C. T-X curve, non-linear part, SH-045-D Fig. 10-D. T-X curve, non-linear part, SH-o45—R Time, ms F F 1g. 1g. lo-Eo lo‘F - x. .. .. 131...! in." we}; 0 - or.“ Distance, m Figure 10-E Figure lo-F T-X curve, non-linear part, SH-O90-D T-X curve, non-linear part, SH-090-R 174.37. 32 Time, ms 51.“ “1.33 1713?. - 3L” lea-t6 rm): 0 Distance, m Figure 10-G Figure 10-H Fig. 10-G. T-X curve, non-linear part, SH-135-D Fig. 10-H. T-X curve, non-linear part. SH-135-R 33 .meoapooede omo ecu ooo .o>p:o x-s m>m3-m .aaua onswam Asv sedan mom-go 2...: 8.03 v9.03 3:. Sum: 2w: 3 .3. 3...... oo foo. (S) amtm oo~ -OOn 34 «o «no. 0.2.15 .mcowpoouwo mna cam mac .o>hso xia o>mzsm Asv spoon 2...: 8mm. mod; «one; 3.»: 2M3 l 3.3m ~32. (P .m-HH enemas ovum 3 00. (S) emu, oo~ Gen 6001 500 400 200‘ 100 J 9144 Figure 12. 35 «8238 27931 36176 ASIZO S‘Sfi‘ 5¢Ofl8 73L52 62236 Depth (m) Best Fit Curves. Shear Wave Set A and B. 9ILdO lOOiB‘ 36 Maximum SH-wave velocity thus computed varied in a centro—symmetric fashion about the array. Two data sets were apparent, corresponding to Sets A and B above, with Set B velocities greater than those of Set A. As seen from Table I, the greatest difference in maximum SH-wave velocity for the array is 276.7ms'1, or about 15.3% occurring between the OOO-R and 135-D directions. Mean velocity for Set A is 1829.5ms"1 i 14.86ms-1, while that of Set B is 2056.4ms'"1 i 24.2ms-1, or about 12.4% greater. Composite T-X curves for the two sets, prepared by fitting all data in each set by least squares beyond the breakpoint and visually fitting the non-linear segment, are plotted in Figure 12, with maximum velocities given in Table I. Compressional wave maximum velocities (Table II) varied with direction, but did not exhibit centro-symmetry. How- ever, the P-wave data exhibits shingling in the linear part of all curves except 135R. Successive linear segments (shingles) having the same slope are shifted down 2 ms with respect to the preceeding linear segment. This results in the overall slope of the line decreasing, and hence the velocity increasing, with each additional shingle. The num- ber of shingles per curve varies from zero to 4. Thus, it would be expected that the maximum velocities computed from' the raw data depend significantly on the shingling (Table II A). By applying successive 2, 4, 6, and 8 ms corrections as needed, the shingles may be shifted back into one line. Maximum velocities thus computed were found to be nearly 37 SH-NAVES: REGRESSIoN LINES AND MAXIMUM VELOCITIES TABLE I Break- m b V point 0.0001656848 0.0370882034 1839.6 0.999991 137.16 0.000168308 0.0319356488 1810.9 0.999927 152.40 0.0001653559 0.0339135756 1843.3 0.999869 121.92 0.0001670867 0.0328314292 1824.2 0.999974 152.40 0.0001501921 0.0465203385 2029.4 0.999905 274.32 0.000148703 0.0486235916 2049.7 0.999908 274.32 0.0001459978 0.0517536593 2087.7 0.999885 320.04 0.0001480648 0.0466262903 2058.6 0.999953 320.04 P-NAVES: REGRESSION LINES AND MAXIMUM VELOCITIES TABLE II-A. (SHINGLING PRESENT) Break~ m b V ___£;___- point 0.0214274878 0.0000802895 3796.3 0.999902 121.92 0.0218468894 0.0000793171 3842.8 0.999908 91.44 0.0204982104 0.0000796083 3828.7 0.999940 106.68 0.0168963888 .0.0000811375 3756.6 0.999949 106.68 0.018222967 0.0000816989 3730.8 0.999904 106.68 0.0000836222 0.0157131531 3645.0 0.999940 106.68 0.019456133 0.0000813077 3748.7 0.999894 106.68 (no shingling observed) TABLE 11-3 (SHINGLING NOT PRESENT) Break- m b V’ r point 0.0000829497 0.0187043464 3674.5 0.999991 121.92 0.000082862 0.0168198662 3678.4- 0.999980 91.44 0.0000823795 0.0173331??? 3699.9 0.999995 106.68 0.0000829898 0.0145586475 3672.7 0.999998 106.68 0.0000827115 0.0169785599 3685.1 0.999997 106.68 0.0000833153 0.0164307294 3658.4: 0.999969 106.68 0.0000835575 0.0158197548 3647-8 0.999919 106.68 0.0000833862 0.0184724438 3655-3 0.999874 106.68 38' the same. with a maximum difference of 52.1 ms"1 (z1.4%), and a mean velocity for the entire array of 3671.3 t 18.1 ms"1 (Table II B). The variation in velocity with direction ap- pears random. As to the causes of the shingling phenomenon, a full discussion and analysis is beyond the scope of this report, but certain conjectures may be made. Spencer (1965) showed that such an effect in a P-wave refraction profile may result from multiple reflections within a high-speed layer. Accord- ing to this theory, where such a layer is present and is several wavelengths in thickness, the refracted arrival may consist of a series of events separated by a constant time interval. Each such shingle is produced by superposition of P-S converted waves multiply reflected the same number of times within the layer while in the shear mode. Such a layer within the ice shelf could be visualized as forming at the surface during a time of warmer climate in the past. Fairly extensive melting and refreezing of surface layers into a thick, dense ice layer, later buried by annual snow accumu- lation. would be required. However, as no other evidence for such a layer has been found, and as the thickness of the layer would at least have to approach that of the wavelengths involved, here about 80 m, such a model should be considered very tentative and quite Questionable. V. ANALYSIS AND INTERPRETATION INTRODUCTION SH and P-wave velocity—depth (V-Z) profiles are pre- sented in this chapter for each array direction. The pro- files are discussed and a model proposed to explain the re- sults in Chapter 6. The Weichert-Herglotz-Batemann (WHB) integral method (AppendixB) was used to compute the V—Z profiles. This method requires a knowledge of the increase of velocity with distance up to the maximum velocity for each curve. Therefore, the velOcities were determined at evenly-spaced consecutive points along the non-linear portion of each T-X curve. The method of velocity determination is discussed in the following section, and error is estimated for both velocity and depth. VELOCITY DETERMINATION AND ERROR ANALYSIS The velocities for the non-linear portions of each T-X curve were determined graphically. A T-X plot was constructed for each non-linear segment with the data points plotted to a precision of i 0.1 ms. A smooth curve was then visually fitted to each plot (Figures lo-A to lo-H. for example). The velocity was determined along the curves every 15.24 m, corresponding to geophone spacing, as follows. A straight- edge was visually aligned tangent to the curve at each such point. The tangent line was fitted first without optical aids, then the fit at and near the point was examined under 5X magnification, to verify precise placement of the 39 4o straight-edge, and adjusted if necessary. The velocity at each point was computed by the formula: xi in = tXi - to where: xi = distance from the origin txi = time intercepted by the tangent line at xi to = the T-axis intercept time The times, txiand to were read directly from the graph to i 0.1 ms precision. Error in the velocities thus determined, as well as error in maximum velocity, has been estimated and is dis- cussed in the following paragraphs. The resulting error in depths computed by the WHB method will also be evaluated. . Error in time measurement was estimated to be i 0.8 ms for the linear portions of the T-X curves (Chapter 3). The resulting error in maximum velocity may be estimated as follows, where v, x, and t are velocity, distance, and time respectively. v=-—.— therefore: dv = dt _ x dt tdt t2 - _Q§_ _ xdt dv ‘ t t dV = dx . t _ xdt . t v t x t2 x dv _ dx dt #1 For Av, Ax, At very small, this may be approximated by: Av _ Ax At v x t Since distance is assumed accurate with respect to timing errors (Chapter 3). the first term on the right can be neglected, and Therefore, where Av is velocity error, and At = i Ate = time error, the % error in velocity is given by: _ AV _ Ate Ev - V 100 - i t o 100 Average velocity V = —%— , 7; —%— = —%_ VAte thus: Ev - _ X . 100 (1) where v is the velocity determined by least squares for the linear segment of a T-X curve and x.is the length of the linear segment, (1) gives the percent velocity error. The application of this formula to the T-X curves yielded an error in maximum velocity of i 0.3% for the P-waves, and i 0.2% for the SH-waves. The velocities determined for the non-linear portions of the T-X curves were used to compute the WHB profiles, as stated above. For velocities less than maximum velocity (Vm), error was estimated by determining the standard devi- ation of velocity at selected depths on the V-Z profiles. Percent velocity error was estimated as J%%- , where Vi = mean velocity at depth 2, and 02 = standard deviation of #2 velocity at depth 2. The associated depth error was similar- ly estimated by standard deviation of depth at selected velocities on the V-Z profile. Percent error in depth was (Tv Zv occurs, and.0y = standard deviation of depth at which that estimated as , where Zv = mean depth at which velocity v velocity is reached. This is thought to represent a reason- able estimate of total error, since the computed V-Z profile incorporates all errors affecting velocities from V0 to Vm. The results of the error analysis appear in Table III and Figures 13A and 13B. SH-wave velocity error ranges from i8.8% at the surface to i0.2%, as noted above, at maximum depth. fiepth error for SH-waves exhibits a range of 125.0% for a velocity of 500 ms"1 to i7.5% and i5.3% at maximum velocity for Set A and Set B, respectively. P-wave velocity error ranges from i25.h% at the surface, to 10.3%, as noted above, at maximum depth. Error in P-wave depth was estimated at i40% at 1000 ms‘l, with an error of :6.8% at maximum velocity. For depths greater than 20 m, P and SH-wave velo- city error is less than 4%, while depth error is not more than 2%. It is readily concluded from Table III and Figures 13A and 13B that velocity error decreases with depth, while accuracy of depth determination increases with velocity. The large magnitude of the estimated error in both velocity and depth for P and SH-waves above 20 m is largely attribut- able to the inhomogeneous nature of the near-surface layers of the ice shelf, such as described in snow-pit studies by Crary. et. al., (1963). 3(3) 2222 2222 2252 0 305.7 10 995 20 1&10 30 1665 40 50 60 112211 2222 500 2.6 1000 10.1 1500 23.3 Vm(A) 33-7 Vm(8) .2121 2222 0 601.7 10 2090 20 2780 30 3280 312211. 2222 1000 1 3 2000 9.1 3000 24.2 7m 40.0 * Columns OOOD through 135R are velocities in me- 287.5 1100 1563 1775 0903 612.0 2060 2850 3270 F ‘0‘0 9 O :0 UN NN C‘UFN 305.h 1075 1550 1663 1785 1875 1955 0252 680.4 2150 2555 3405 O 1‘: U o e O\U\\I|"\) UN MNCOH “3 $3393 ANAL2§IS TABLE III SH-HAVES: ggpgggg; 23202 * v 9.252 2920 29.08 11.112 1.2.53 220; 338.? 325.2 350.3 326.0 363.7 327.8 2 26.3 1115 1035 1040 1150 1175 1085.6 2 61.2 1495 1490 1490 1515 1525 1494.8 2 51.2 1690 1720 1700 1695 1715 1702.9 2 35.7 1800 1800 1820 1801.3 2 14.4 1585 1897 1895 1880.0 2 10.1 1962 1975 1963 1964.8 2 8.3 $8-8Ay§§. 02213 3589399 2.1.“ R 2222 2228 11112 115.8 2" t ‘3’ 1.5 2.2 2.0 1.6 1.2 2.0 2 0.5 7.8 9.4 9.3 7.5 7.0 8.5 2 1.0 20.2 20.3 20.4 18.3 19.0 20.0 2 1.8 36.3 38-9 37.2 2 2.8 6702 7401 72.5 7001 t 307 P-flA!§§: 2;;00123 23393 9 'V 9.24 8 29.9.2 2.2.9 R 1122 25.1 R z * ‘7'- 677.3 762.0 1172.3 655.5 937.8 729.9 2 184.3 2225 2115 2495 2035 2185 2169.4 2 145.9 2920 2845 3020 2895 2795 2870 2 76.2 3&00 3373 3450 3“75 3295 3393-5 2 7h-5 P-NAVE§: 08223 3330899 0458 0900 0998 1350 1353 2" t ‘3' 1.6 1.4 1.3 0.3 1.5 2 0.6 8.0 8.9 4.9 9.7 7.8 8.3 2 1.5 21.4 22.7 19.6 21.4 24.0 22.3 2 1.5 34.7 36.0 32.9 33.8 36.2 35.2 2 2.4 1 at depth 2. " Columns 000D t rough 1352 are depths in m at velocity V. .p maxroo -u \ ax ' pa 0 g... ‘2 ‘5‘ I. ‘0 ‘3 n N .wo>azum ON .uounm m> :pnoa .m-nH ouswem m2 62 m o A>M\>v gonna hvwooao> % (m) umdaa .m0>031:m .houum m> gamma .M\$V gonna hpnooao> m 45 VELOCITY-DEPTH PRCEILES The WHB integral, derived in Appendix B, was used to compute P and SH-wave velocity-depth profiles for all array directions. The integral is defined as: Vxn X - zn=--1Tl---fon cosh 1( in ) dx, where: Vxn = -%%— = maximum velocity sampled by the x=Xn raypath from shotpoint to receiver at range xn. -_2_X_ = ~ . . VXi - dt x=xi veloCIty at x1, 0 s l s n. Zn depth at which Vxn is penetrated. The integral is obviously of such a form that it may be directly computed numerically (Grant and West, 1965). Numerical computation may be implemented by: .Ax: Vx n .2 cosh'1( V n ) l=0 Xi V V 5 A x n xn { xn _, } (2) where : A x Zn spacing between V-x data points n number of data points Zn, Vx and in are as above. n! In the calculation, Vxn is fixed for any given raypath, and in ranges from V0 to Vxn' Thus, for any given Vxn' all previous in determined from the T-X curve are used in the integration. For this study, a program for the automatic computation of the integral using equation (2) was written A6 for a Texas Instruments Ti-58 programmable calculator with PC-100A printer, with which all profiles were calculated. The tabulated results appear in Appendix E. The velocity-depth profiles are presented in Figures 14-A to 14-H for P-waves, and in Figures 15-A to 15-H for SH-waves. It is readily observed that the SH-wave curves fall into two groups, corresponding with T-X data Sets A and B of the preceeding chapter. For Set A (Figures 15-A, B, E, F & 16) maximum velocity is reached at a mean depth of 37.2 m i 2.8 m, whereas for Set B (Figures 15-C, D, G, H, & 17), Vm occurs at a mean depth of 70.1 m.i 3.7 m. Depth to P-wave maximum velocity is nearly the same for all array directions, with a mean of 35.2 m i 2.4 m. The implications of these results are discussed in depth in the next chapter. 47 Velocity (ms-1) 0 1000 2000 0 1000 2000 Depth (m) Figure 14-A Figure 14-B Figure 14—A. Velocity-Depth Profile: Line SH-OOO-D. Figure lh-B. Velocity-Depth Profile: Line SH-OOO-R. Depth (m) #8 Velocity (ms‘l) q 1000 2000 O 1000 2000 10 20 30 40 50 60 70 Figure lh-C Figure lh-D Figure lb-C. Velocity-Depth Profile: Line SH-OAS-D. Figure lh-D. Velocity-Depth Profile: Line SH-045-R. Depth (m) “9 Velocity (ms‘l) O 1000 2000 0 1000 2000 10 N O u 0 1+0 50 Figure lh-E Figure 14-F Figure lh-E. Velocity-Depth Profile: Line SH-090-D- Figure lb-F. Velocity-Depth Profile: Line SH-090-R- Depth (m) 10 20 30 40 50 60 70 Figure 14-0. Figure lh-H. 50 Velocity (ms‘l) 0 1000 2000 0 1000 2000 Figure lh-G Figure lh-H Velocity-Depth Profile: Line SH-135-D. Velocity-Depth Profile: Line SH-135-R. 51 coon .m-oooum mafia .0anmoum :pgmauswfiooam> .ouoooum 0:22 .oanmocm canonuspflooflm> m-mH muswflm ooom oooH o ooom AHImEV hpwooam> .m1mfi .wflm .<-mH .mfim .oumH .wnm o-mzo-m mafia .maflmoum gpmwolspflooao> .oumH .mam 61mg 022022 o-mH mnsmflm Depth (m) ooom .oobm oooH o. . _ ooom ooom Good 0 Aaamev hpwooao> 53 ooom .m-omo-m mean .0afimopm gpgmn-spfiooam> .nuoao-m mafia .mafimogm 2060a-spfiooao> mind ohzmflm ooom oooa o ooom aaumsv hpwooaw> .2-mfi .022 .man .mmm mumfi muzmflm OOON ooo~ Depth (m) 5h ooom .msmnfinm mafia .oafimonm gpdmo-sefiooao> .nummfium mafia .maflmogm nvawouspfiooam> mind muswam ooom oooa o , ooom Afiumsv spfiooam>,. .xumfi .022 .u-mH .wflm u-mH mwzmflm ooom oooH Depth (m) 55 Velocity (ms-1) O 1000 2000 10 20 30 1+0 Depth (m) 50 60 70 Figure 16. Velocity-Depth Profile: SH-Waves Set A. 0 SH-OOO-D D SH—OOO-R A SH—O90-D V SH—O90-R 56 Velocity (ms'l) O 1000 2000 Depth (10) Figure 17. Velocity-Depth Profile: SH-Waves Set B. ‘3 SH-O’JvS-D D SH-OlPS-R A SH—135-D V SH-135-R 57 INTERPRETATION OF VELOCITY-DEPTH PROFILES: DEVELOPMENT OF MODEL A. VELOCITY INCREASE T0137 M DEPTH: DENSIFICATION Compressional and SH-wave velocities are, on the average, 60% of their maximum value at 10 m depth, and 80% of maximum velocity is attained at 20 m depth (Table III). Maximum velocity for both wave types is reached at about 37 m, con- sidering only the Set A shear wave maximum velocity. Thus, velocity increases very rapidly with depth, with the rate of increase falling quickly below about 15 m depth, as is read- ily seen in Figures 14 through 17. Studies on the Ross Ice Shelf at Little America V and along the IGY traverses, at Ellsworth Station on the Filch- ner Ice Shelf, at Byrd Station on the Marie Byrd Land Ice Sheet, in Greenland, and elsewhere have repeatedly demon- strated the rapid initial increase of density with depth (Robin, 1958: Crow, 1960; Ragle, et. al., 1960; Thiel and Ostenso, 1961: Crary, et. al., 1962; Kohnen and Bentley, 1973). Densification of snow in general initially proceeds rapidly with depth by mechanical repacking of grains as load increases, until a density of 0.55 gm cm"3 is reached, which represents the limit below which further porosity reduction is not possible by repacking alone (Paterson, 1969). Crary, et. al. (1962) found that this density was reached at depths ranging from about 9 m to 14 m at various sites on the Ross Ice Shelf. At depths below that at which this density is attained, densification proceeds at a decreasing rate by 58 recrystallization until permeability is reduced to zero at a density of about 0.85 gm cm“3 (Paterson, 1969). Below this level, density increases only very slowly with depth by compresSion of air bubbles in the ice (Shumskii, 1964; Pater- son, 1969). Seismic P-wave velocity has been shown experimentally to increase in direct proportion to ice density (Robin, 1958: Thiel and Ostenso, 1961: Kohnen and Bentley, 1973) (Figure 18). Kohnen and Bently (1973) found that shear wave velo- city at Byrd Station also appears to increase with density (Figure 19). The form of the velocity-depth increase in the Minna Bluff study area as described above is thus attribut- able to increasing density with depth. It is therefore con- cluded that the increase in P-wave and SH-wave velocity to a depth of about 37 m results from snow densification. no J” ,I g\ 8 £0.75 x k v) 2 ‘4: Q 0 5 e "’ . I "- / e NEW'EYRD‘ _ / + OLD'BYRD' 025 I L 11 o 1.0 2.0 3.0 4.0 VELOCITY (km/s) ‘ Figure 18. Density gs P—wave velocity, linear plot, at Byrd Station (From Kohnen and Bently, 1973). 59 4.0 3.0 2.0 m VEL ocxrr (km/s) l < M 5 P o 2 ‘2 0.5 3 . 8 —- NEW'BYRO' 2 s 3' ----- OLD'BYRO‘ - ‘9 l l l 1 I o so 100 :50 200 DEPTH(m) Figure 19. P-wave and S-wave velocities and densities gs depth at Byrd Station (From Kohnen & Bently, 1973)- B. VELOCITY INCREASE 37 M TO 70 M DEPTH: CRYSTAL FABRIC The distribution of shear wave maximum velocity with depth and direction in the study area is strongly bimodal as observed above. The velocity-depth distribution is also centro—symmetric (Figure 20). Centro-symmetry characterizes velocity distributions in anisotropic media (Kusgrave, 1970). 3‘ B \\ \ / \ \ I (Figure 20.) A 4,, 7 \ U) m 6O Hexagonal ice crystals exhibit transverse isotropy (Appendix A), with the c crystallographic axis parallel to the axis of elastic symmetry (Bennett, 1968). In an investigation of ultrasonic wave propagation in ice, Bennett (1968) found that, in a single ice crystal, the shear wave with particle motion in the plane containing the c-axis exhibits maximum velocity (2185 ms-l) for propagation at an angle of #5.5° to the c-axis, with minimum velocity (1827 ms'l) occurring for propagation in the direction of the c-axis. This is a variation of 18% of the mean velocity. The shear wave having direction of particle motion normal to the c-axis exhibits maximum velocity (1920 ms'l) for propagation normal to the c-axis, with minimum velocity (1827 ms-l) occurring for propagation in the direction of the c-axis, a variation of 6% of the mean velocity. Since the c-axis is the vertical axis in the standard crystallographic orientan tion, the shear wave with direction of particle motion in the plane containing the c-axis is an SVewave, and the shear wave having direction of particle motion normal to this plane is a SH—wave. Laboratory and field investigations of ice petrofabrics under conditions of known shear stress, as discussed in Chap- ter 1, show that ice crystal c-axes tend to reorient normal to the direction of applied shear stress with basal planes aligned parallel to shear stress. The average maximum velo- 1 1 cities for the two shear wave sets, 1830 ms- and 2056 ms' , differ by 11.6%. From Bennett's results stated above, if the 61 ice in the study area exhibits an aggregate c-axis alignment, then direction of particle motion for the two shear wave velocity sets is inferred to be in the plane containing the c-axes. Further, since minimum shear wave velocity for single ice crystals (above) occurs along and perpendicular to the c-axis, the distribution of SH-wave maximum velocity about the array implies an aggregate horizontal East-WeSt or North-South c-axis orientation, with vertical basal planes oriented North-South or East-West, respectively. It is concluded, from the petrofabric results cited above and the direction of shear stress as inferred in Chapters 1 and 2, that the probable c-axis orientation is East-West. The maximum shear wave velocity in the study area (2056 ms-l) is significantly greater than that determined by Bennett (1968) for pure isotropic ice (1940 ms'l). The minimum velocity for shear wave propagation in.a single ice crystal with particle motion in the plane of the c-axis (1827 ms'l), as stated above, is virtually identical to the Set A shear wave maximum velocity (1830 ms'l). Therefore, it is further concluded that velocity anisotropy resulting from aggregate c-axis alignment, as presented in the above discussion. is primarily responsible for the observed shear wave velocity distribution from 37 m to 70 m depth. C. HETEROGENIETY IN THE NEAR SURFACE The error in both velocity and depth determination for compressional and shear waves (Figure 13 and Table 3) appears 62 excessively large above 20 m, and increases towards the surface. Vertical inhomogeniety in the near surface layers of the Ross Ice Shelf. as evidenced by the discontinuous nature of the overall density increase with depth, has been noted by Crary, et. al., (1962). P-wave and SH-wave velo- cities at the surface were observed to range from about 1 1 1 to 1172 ms-l, respec- 287 ms- to 36h ms' , and 612 ms- tively. in this study (Table III). Thus, it is concluded that areal heterogeniety is also important in the near surface layers of the ice shelf. Furthermore. the large error estimates noted above are thus largely attributable to areal heterogeniety in the layers above 20 m depth. D. P-WAVE VELOCITIES AFFECTED BY FRACTURIEQ Maximum P-wave velocity in the study area was found to be about 3671 ms"1 (Chapter #). Bennett (1968) found that compressional wave velocity for a single ice crystal varied 1 to #077 ms‘l. with propagation direction from 3803 ms- Crary. et. al. (1962), found the maximum P-wave velocity in various areas of the Ross Ice Shelf to range from about 3750 ms-1 to 3814 ms'1 1 about 3780 ms“ . Thus, maximum P-wave velocity observed , with an average maximum velocity of near Minna Bluff is abnormally low. However, the velocity at 37 m depth is about 5% to 10% higher than that reported elsewhere on the ice shelf at this depth. This implies that density is unusually high at 37 m depth. At Little America V, the density at 37 m is about 0.7 gm cm"3 (Figure 6). well within the firn zone 63 (Paterson, 1969). The bimodal maximum shear wave velocity distribution observed in this study has a mean of 19h3 ms'l, very close to the isotropic shear wave velocity of pure ice (19h0 ms'1)(Bennett. 1968). Since maximum velocity for both the P-waves and Set A of the SH-waves, as discussed above, is reached at about 37 m depth. it is inferred that bubbly ice of at least normal glacial ice density (20.85 gm cm'3, Paterson, 1969) is present at this level. Further- 1 more, the average maximum P-wave velocity is 3671 ms- in the study area (Chapter IV). This corresponds to a density of 0.85 gm cm-3 on the P-wave velocity-density curves given in Robin (1958). The pattern of the isopachs of Figure h suggests that the major source of the ice in the Minna Bluff vicinity is Byrd Glacier. As observed above, bubbly ice rather than firn is believed to be present at about 37 m depth in the study area. At this depth, P-wave velocities are high rela-' tive to other locations on the ice shelf, as noted above. Shear wave velocities also are somewhat high near Minna Bluff. being about 2% higher than most other areas at 37 m depth, and about 7% higher at 70 m depth, as discussed below. Therefore, it is proposed that to a depth of approx- imately 37 m. the velocity increase reflects normal densifi- cation of snow accummulation, as discussed above. Below 37 m the unusually high velocities in the study area may be explained by the presence of dense glacial ice derived from the Byrd Glacier. 64 Fractures were observed at the surface in the vicinity of the study area (Chapter 2). One seismic effect of small fractures oriented randomly within a rock mass is to isotro- pically reduce the velocities from those of the unfractured rock (Crampin, McGonigle. and Bamford, 1980). If a zone of very fine fractures. which might be termed microcrevasses, was present in the ice below about 37 m, it is conceivable that the effect on seismic wave propagation through the fractured zone could be to both reduce the velocity and lengthen travel paths, thus resulting in a lower maximum velocity as observed at the surface. It should be recalled that the observed maximum P-wave velocity ( 3671 ms'l) is low compared to maximum velocity in pure ice and in other areas of the ice shelf, as noted above. Thus, true maximum P-wave velocity has probably not been reached. Fracturing at depth could also be the reason why anisotropy was not observed in the P-wave studies. Crevasses are known to close with depth in the Ross Ice Shelf (H. Bennett, Personal com- munication). If the inferred micro-crevasse zone also closes with depth, then higher velocities. and perhaps anisotropy in the deeper layers, might be observed with a sufficiently long refraction profile. The SH-waves were apparently not affected by the proposed fracture zone. This suggests that the zone may consist of dry fractures, since if a water sat- urated fracture zone were present, a reduction of shear wave velocity, along with possible severe attenuation, might be anticipated. Several crevasses 5 km West of the study area were entered by the field party and found to be dry 65 (H. Bennett, Personal communications). PROPOSED MODEL FOR T§§~MINNA BLQFF_§TQQI_AR§A In the model developed in the above discussion, the increase of velocity with depth in the first 37 m is attri- buted to densification. The increase in shear wave velocity from 37 m to 70 m depth results from increased preferred orientation of c-axes. In the study area, a strong fabric is developed below 37 m, with c-axes oriented horizontally East-West, and basal planes vertical with North-South orien- tation. Areal and vertical heterogeniety characterize the near surface layers above 20 m depth. At 37 m, density and velocity appear to be abnormally high. This is attributed to a possible dense layer of glacial ice originating in the Byrd Glacier. A dry microcrevasse zone may exist in the glacial ice layer, explaining why P-wave maximum velocity was probably not reached. COMPARISON OnggLOCITY—DEPTH PROFILES NEAR MINNA BLUFF fllTH OTHER STUDIES Crary, et. al. (1962), obtained velocity-depth profiles at various stations along the IGY traverse routes. P-wave profiles for Stations in and 58 (see map, Figure 3) are plot- ted in Figure 22, along with shear wave profiles at Station 58 and at Little America. P-wave profiles at Little America V, Byrd Station, and Ellsworth appear in Figure 21. Comparison of these to Figures 14-17 indicate that to the common depth of sampling shear wave velocities are Figure 21. 66 VELOCITY {m/sec/ 3000 [000 N...“ 2000 4000 ‘\ 1‘ \k \ 40 c; Q 0". all" ’ . at". cocoa-p.000... Q) C) DEPTH (meters) /00 EU /40 /60 Velocity-Depth Profiles at Byrd (solid line), at Little America V. (dashed line), and at Ellsworth (dotted line). 67 similar in most areas. Compared to the profile at Little America Station (Figure 22), shear wave velocity increases somewhat more rapidly after 37 m near Minna Bluff, being about 7% greater at the 70 m depth. This is interpreted as reflecting the influence of crystal fabric and, possibly. dense glacial ice in the study area, as discussed above. P-wave velocities appear similar at all other sites on the Ross Ice Shelf to about 30 m depth, increasing more rapidly thereafter in the study area. At 37 m depth, velocity near Minna Bluff is in general 5% to 10% greater than elsewhere, even though maximum P-wave velocity as determined in this study is abnormally low, as compared with pure ice. The difference observed between V-Z profiles in different areas are thus attributed to differences in density structure, fracturing, and crystal orientation. as suggested by the above model. IMPORTANCE OF SHEAR WAVES IN SEISMIC ANISOTROPY STUDIES Bennett (1968, 1972) found P-waves to be affected less strongly by crystal fabric than shear waves, as noted in Chapter 1, for conic distributions of c-axes. For single ice crystals, he also found the variation of velocity with direction to be only about 7% for P-waves. versus as much as 18% for shear waves. Hence, it would be expected for shear waves to be better indicators of anisotropy than P-waves. The results of the present study tend to confirm this conclu- sion. It is also noted that shear waves may be characterized by better propagation in dry fractured zones than P-waves. 68 Velocity (ms-1) 800 1600 2400 3200 4000 Figure 22: Ross Ice Shelf P and SH-wave Velocity-Depth Profiles. P-waves IGY Traverse Station 1“ IGY Traverse Station 58 SH-waves IGY Traverse Station 10 Little America Station (Data from Crary, et. al., 1962) 69 Of course, the presence of such a fracture zone in the study area is not conclusively established. However. regardless of whether or not the ice is fractured as proposed, the shear wave results show the presence of anisotropy while the P-wave results do not. Similarly, during the IGY Ross Ice Shelf traverse studies, Crary, et. al. (1962) attempted to detect anisotropy with P-wave refraction profiles, but none was detected. Thus, it is concluded that shear waves are a more important indicator of velocity anisotropy than P-waves. Furthermore, anisotropy may thus not have been detected in previous studies because P-waves were used primarily or exclusively. APPENDICES APPENDIX A APPENDIX A TRANSVERSE ISOTROPY The following brief discussion of transverse isotropy is based primarily on Postma. 1957. A A medium in which the elastic properties are symmetri- cal with respect to a fixed axis is termed transversely iso- tropic. Since in the case of ice and other hexagonal crystals this axis parallels the c crystallographic axis. the c-axis will be presumed to correspond with the z-axis. defined above as the fixed axis of symmetry, in the ensuing discussion. Hooke's law (Love.193h) may be stated in matrix form as follows: °11 °12 °13 C11; c15 °16 exx x1] 021 °22 °23 C24 C25 °26 eym Yy °31 °32 °33 °3t+ °35 °36 an z 22 (1) °u1 °u2 .cug °uu °u5 °u6 eyz Yz °51 °52 °53 °5u °55 °56 92x zx 361 C62 C:63 C61} c:65 C66 .fxy Lxfl in which: cij = Oji R2. Therefore, the wave having the largest normal velocity resembles a p-wave, and the slower wave resembles a shear wave. In the 0 = 0 and 0 = w/2 directions the waves are purely longitudinal or purely transverse, but not in other directions in general. APPENDIX B APPENDIX B DERIVATION 0F WEICHERT-HERGLOTZ-BATEMAN~ G The following derivation is outlined in Officer (1958). Let velocity be assumed to increase as a continuous function of depth, e.g. Figure 23: Figure 23. Then both the horizontal range x along a given ray path, say xn, and the travel time t can be expressed parametrically in terms of depth 2 and angle of inclination 6 as follows (Figure 2’4 ) x . Z n xn = f0 tan 6 dz (1) s z t - f0 1! ' f0 v cos 9 (2) The ray parameter p is defined as p = Si: 9 , 5 sin 0 = pv(z) For sin x = a, tan x = -—§-- , cos x = (1-a2)%, hence (1-a2)é tan a ... __221.2.L_ (3) (1-p2v2(z))2 75 76 cos 9 = (1-p2v2)% (4) Substituting (3) and (4) in (1) and (2), respectively. _ f2 vdz x 0 (1-p2v2)5 Z dz 1; : ° V(1-p2VZ)§ Rearranging. z vdz x = —_—_—I 0 v(1/v2-p2)2 (5) t = 1‘2 ——;dz ’ <6) 0 v2(1/v2_p2) Defining u = 1/v, and substituting in (5) and (6), x = D $2 --5-—; (7) o (u 2-pz) 2 I“ —L——5dz <8) Assume that the ray under discussion returns to the source depth. The horizontal range xn and the travel time t are therefore: 2 X'n = 2p f0 n -—-7 (9) -p2) z Zdz t = 2 f n u - (1o) 0 (HZ'PZ) where zn is the depth of maximum penetration of the ray path. Let two adjacent rays, penetrating to some depth 2. be defined by ray parameters p and p+dp. Draw wave surfaces S1 and 32 normal to them (Figure 24). $1 and 82 will be sepa-~ rated by range interval dx and time interval dt. 77 x From Figure 24, . _ vdt Sin 9 - E;- But: sin 9 = pv, -9l-1 p'dx’v Since a = g = 9xi at the vertex of a given ray, where V=in. =l or (11) P ”Xi' P=Hxi Note that vxi, attained at the depth of maximum penetration 21. is the greatest velocity reached along the ray path. A ray emergent at horizontal range xi will exhibit the same angle of inclination that it had at the source, since, from Snellfis Law sin 90 = sin 9 = p (12) V0 V 78 The reciprocal slope of the T-X curve at xi is the velocity ‘V with which the associated wave front travels along the surface 2 = 0. Referring to Figure 25, k—th Figure 25. sin 90 = 210:9 vdt ?’= v0 sin 90 Referring to Equations (11) and (12), a v = in Hence, the reciprocal slope of the T-X curve at xi is the velocity at the depth of maximum penetration for the ray emergent at xi (Figure 26). I T 1 slope=-- vx. 1 I l I 2 z X X1 Figure 26. 79 Equation (9) may be rewritten as an integration along the ray path as follows: x : 213.141on “0 (112-132)% Applying the operator I:Xn\(p2-u§ )‘fidp to both sides: 0 n fuxn lm_ g fuxn d, fuxn m (,3, “0 (pZ-ugn)% “0 “ (pz-ufin) (uZ—p2>% This operation is an integration across the rays from the ray at x = 0 to the ray at xn whose vertex is at a depth where Vxn = 1/uxn. The integration limits have the relation: P0 = (1pc = [-10 3 1/V0 pxn = uPxn= ”Kn = l/yxn (Hxnvuo) (”0:30) Figure 27. Referring to Figure.27. the order and limits of integration of (13) may be readily changed to the following: nx _ 4x “x d d 2 d J‘nLgf nduf néw (14) ”0 (pg-ugn)% “0 “ p(-p“+(u2+u§n)pz-u§nu2)% Observing that, for the integral on the left-hand side: 80 fuxn xdp = fuxn x gp_ ”0 (pZ-u§n>% ”0 (pZ/uin - 0% uxn $an ——xfiP—- = 1:" xufig— - 1529—) (15) ”0 (Dz-ufin)% uxn uxn Since dcosh’1(z) = (zZ-l)‘%dz, where z'= p/uxn. the integral on the right of (15) is of the form fudv. where v = cosh’1(P/hxn). It is readily seen that the integral may be evaluated by parts. since fudv = uv - fvdu + c. Hence: ”X ”x “X u n--£gE--'= xcosh'1(-2') u n‘fu n g£°°8h-1(‘E‘)dp (16) 0 (Dz-(132m)§ Hxn 0 0 dp “xn Evaluating the first term on the right of (16): DX ”x “ xcosh‘1(-2-) u n = xcosh'1(—-2)-xcosh'1(-2-) uxn ° uxn uxn ”0 xcosh‘1(1)-xcosh'1(-—-) llxn “0 -xcosh‘1(—-) uxn Observing that when p = ”0: x = O, P “x xcosh‘1(--) n = 0 uxn #0 Thus. ux . 4 In n 44-3-3 =-.+qu“ g<:osh-1<-P-) <17) 0 (pz-uxn) ° dp uxn Referring to the first integral on the right side of (14): 81 uxn (dZ/du)2pdp dz uxn Zpdp nuz)it du u (-p“+(u2+u§n)p2-u§npz)§ u (-pu+(u2+u§n)p2-u§ Letting a>= -u§n 2. b = u2+u§n. c = -1. u = p2. it is readily seen that the integral on the right above is of the form: I du % -2¢u-b f = (-o)‘ sin'1( i)' c < o (a*bu+cu2)% (b2-4ac) Thus: uxn ZPdP u (-u§n92+(u2+u§n)p2-pu)é sin-1 -2(-1)