JUt 7~"-'9§ “3 f;- i f3 " ‘u‘ ‘5: © Copyright by CARL WILLIAM ANDERSON 1977 LARGE SCALE VELOCITY ANISOTROPY AND THE Q-ELLIPSOID METHOD BY Carl W. Anderson A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Geology 1977 .1...i|u(.rll.l. I,’\.\\u( ABSTRACT LARGE SCALE VELOCITY ANISOTROPY AND THE Q-ELLIPSOID METHOD By Carl W. Anderson The purpose of this study was to test a technique for determining large scale seismic velocity anisotropy in the field based on the Q-ellipsoid method (Bennett, 1972). The technique was applied to three sites typifying metamorphic terrains: Marble Lake and Cross Lake, Ontario and Sugar Loaf Mountain. Marquette, Michigan. The Q-ellipsoid method was also applied ultrasonically to hand samples collected from each site for comparing with the field measurements. On the large scale seismic level, only the results for Cross Lake and Sugar Loaf supported the model (1.3. showed homogeneous anisotropy). At the ultrasonic level, homogeneous anisotropy was indicated only for the Marble Lake and Cross Lake hand samples. It was concluded that large scale seismic velocity measurements may be more reliable than ultrasonic velocity measurements from hand samples or from thin-sections for determining anisotropy in the field. It was also concluded that foliation may not be the dominant factor for determining the orientation of velocity anisotropy. ACKNOWLEDGMENTS I would like to thank Dr. Hugh Bennett for suggesting this thesis topic and for his help in completing the field and laboratory work. I would also like to thank him for his suggestions during the writing of this thesis. I would also like to thank Dr. Calbray and Dr. Hilband for being on my thesis committee. ii TABLE OF CONTENTS Introduction 0 e e PTOViOUB Work 0 e e e e e e e e e 0 Purpose 0 e e e e e e e e c e e e 0 Locations for Field Study . . . . . MOdBl e e e e e O o e e e e e e e e e e Q9E111P801d "OthOd e o c e e e e e Stratified Media and the Q—Ellipsoid Method Fifild Work 0 e e e e e e Instrumentation . . . . . . . . . . Field Procedure 0 c e e e e e e e e RBSUltS Of Field Work 0 e e e o e 0 Lab Uork o e o e e e e e e e e e e e e e Ultrasonic Velocity Measurements . Instrumentation e c e e e e 0 Preparation and description of samples Procedure and results . . . . Thin-section Analysis 0 e c e c e e D180“8810n e e e e e e e e e e e e e o 0 Velocity Data from Field Studies . Marble Lfikfl e e e e e o e e 0 Cross Lake 0 e e o e e e e e 0 Sugar Loaf e e e e e e e e e 0 Velocity Data from Ultrasonic Studie Conclusion 0 e o c e e e e e e e c e e 0 Comparison of Field and Lab Studies Marble Lflkfl e e e 0 Cross Lake . . . 0 Sugar Loaf e 0 Major Conclusions . Reconnendations for Future Study Appendix ‘ e e e e o o e e e e o e e e 0 Appendix B e e o o o e e e o e e e o e a Bibliography 0 e o e e e c e e e e e e 0 iii l. 2. 3. u. 5. 6. 7. 8. 9. 10. 11. 12. 13. 11.. 15. LIST OF TABIEB Calculated Velocities for Postma's Two Numerical Examples e e e e e e e e e e e 0 Normalized Q Values for Postma's Numerical Examples e e e e e e e e e e e e Summary of Range Switch, Timing Pulse, and Sampling Intervals e e e e e e e e e e Range Scale Used for Each Geophone Array . Propagation lengtm and Travel Times . . . Direction Cosines and Velocities . . . . . QValues................. Calculated Q Values and Statistics . . . . Q Surface Principal Axes and Major Axis Orientation e e e e e e e e e e e e e e e Directional Cosines, Distances, and Ultrasonic TIBV31.T1IOB e e e e e e e e e Propagation Directions and Ultrasonic V81001t108 e e e e e e e e e e e e e e e e Q values e e e e e e e e e e e e e e e e e Directional Cosines and Q Values . . . . . Statistical Data fbr Hand.Samples e e e e Principal Axes and Major Axis Orientation fbr Hand Samples e e e e e e e e e e e e 0 iv 10 11 1h 22 23 25 26 27 28 35 36 38 39 1. 2. 3. u. 5. 6. 7. 8. 9. 10. ll. 12. 13. 11$. 15. 16. 17. LIST OF FIGURES Regional locations for Marble Lake and Cross Lake teSt sites 0 e e e e e e e e e e e Regional location for Sugar loaf test site . Q surface and reference Q-ellipsoid . . . . . Q surfaces for Postma's two numerical examples e e e e e e e e e e e e e e e e e e Polarization modes for transversely oriented horizontal geophone . . . . . . . . Effect of hammer blows on signal . . . . . . Complex signal for propagation direction #6; Marble Lake (long array) e e e e e e e e e e Theoretical signal received at geophone . . . Signal for propagation direction #33 Marble Lake (long array) e e e e e e e e e 0 Finding the ropagation distance using equation (163 e e e e e e e e e e e e e e e e Q surface for Marble Lake (long array) . . . Q surface for Marble Lake (short array) Q surface fbr Cross Lakfl e e e e e e e e e e qurfaceforSugarLoaf ....... .. . Experimental set up for ultrasonic velocity leasurenents e e e e e e e e e e e e e e e e The determination of average Q values defining the planar section of the Q surface for the ultrasonic data 0 e e e e e e e e e e e e e e least squared Q surface for Marble Lalne hand salple e e e e e e e e e e e e e e e e e e e 1? 18 19 19 19 21 30 30 31 31 33 38 1+0 18. 19. 20. 21. 22. 23. 24. 25. Least squared Q surface for Cross Lake hand sample 0 O O O O I O I O 0 O O O O O O O O 0 Least squared Q surface for Sugar Loaf hand sample 0 O O O O O O O O O I O O O I O O O 0 Marble Lake: Photograph of thin-section perpendicular to xy-plane of the hand sample (“age 331) e e e e e e e e e e e e e e e e 0 Marble Lake: Photograph of thin-section parallel to xy-plane of the hand sample (Mag. 3:1) . . . . . . . . . . . . . . . . . Cross Lake: Photograph of thin-section perpendicular to xy-plane of the hand sample (“age 3:1) 0 I O O O O O I O O I O O O O O 0 Cross Lake: Photograph of thin-section parallel to xy-plane of the hand sample (Hag. 3:1) 0 I O O O O O O O l O O O O O O 0 Sugar Loaf: Photograph of thin-section perpendicular to xy-plane of the hand sample (M360331)eeeeeeeeeeeeeeeee Sugar Loaf: Photograph of thin—section parallel to xy-plane of the hand sample (Mag. 3:1) 0 O I O O O O O O O O O O O O O 0 vi #1 41 43 “3 45 45 I. INTRODUCTION A. PREVIOUS WORK Bennett (1972) has developed a simple seismic model for determining principal anisotropic directions within crystalline aggregates. His model uses a type of elastic stiffness figure referred to as the Q-ellipsoid. In general, three different body waves with orthogonal particle motions can propagate in anisotropic media in any prescribed direction. Thus, the Q which determines the theoretical surface of the Qpellipsoid is the sum of the squares of the three phase velocities for a given direction multiplied by the density. Bennett (1972) proved that the principal axes of the Q-ellipsoid are identical to the orthogonal crystallographic axes of a single crystal. He also postudated that the dellipsoid could be used as an indicator of structural and petrofabric patterns which can cause velocity anisotropy. As a test for the model, Tilmann and Bennett (1973a) applied the Qpellipsoid concept to each of three rock types: a quartzite, a marble, and a plastically defbrmed granitic boulder. The elastic velocities fer each sample were measured.and the results for the quartzite and the marble were compared to their respective optical petrofabric analyses and the results fer the granitic boulder to its shape axes. They found that each rock sample could be considered as a crystal aggregate behaving as a homogeneous pseudosingle crystal. They concluded that the orientations of the Qgellipsoids were controlled by crystal 1 2 orientations and structural effects, and that the shape axes of the plastically deformed granitic boulder closely coincided with the Qpellipsoid axes indicating that the Qpellipsoid method may be useful in describing regional tectonic ferces. B. PURPOSE The purpose of this paper is to extend the Qeellipsoid method to develop a method for testing large scale velocity anisotropy in the field. Testing for large scale velocity anisotropy may be important in the case where an area study is made to test for homogeneity and anisotropy. On the thin-section scale, this may require many thin- sections and involve a great amount of time and effbrt. Also, only a relatively small number of grains can be analyzed from the thin-sections. But if it is possible to test for large scale velocity anisotropy by means of the Qpellipsoid method, the time factor may be greatly reduced. The large scale test may also be more representative because it would be sampling many more times the number of grains than that sampled in thin- sections. The presence of large scale velocity anisotropy and the ability to detect it with the Qpellipsoid method may also be useful in determining regional structural trends relating such factors as stress fields, fracture orientations, structural layering, and preferred grain orientations. C. LOCATIONS FOR FIELD STUDY For this paper, three outcrop sites were selected. All three sites are in Pre-cambrian metamorphic terrains which have undergone one or more 3 periods of deformation and have some degree of foliation or layering (Appendix A: Gair and Thaden, 1968: Moon, 1942: Moore and Hutchean, 19x». Two sites are located in the general area approximately 50 miles north of Kingston, Ontario, Canada. One site is between Marble Lake and Hill Lake in Barrie Township. The other site is southwest of Cross Lake in Palmerston Township. Both townships are located in Frontenac County. Figure 1 gives the regional locations for both areas. 78 77 76 X ssm—ousssc ) i3 RENFRE ° ”’0 «W? \. f n. ‘n'der ’ O 44 'I I LAKE ow -RuL Scale, I Inch to so mlles ML Marble Lake CL Cross Lake Figure 1. Regional locations for Marble Lake and Cross Lake test sites. The third site is on a readout in the North-Central Marquette Quadrangle Just west of Sugar Loaf Mountain approximately three miles north of Marquette, Michigan along County Highway 550. Figure 2 gives the regional location for the third site. 9°. 89° 88' ~|\ e F 0 \° {‘6‘ , v -—r 9 ‘3 . tloughton 47H- .. “if, \r l 3 l— L'Anse L. . owrouAeow 35 . _; 3 Sugar Loaf , ._! I BARAGA Marquette a l_-_| , l : MARGUETTE a r..__-__] oncwmsow L db M Marquette Quadrangle S Sands Quadrangle Figure 2. Regional location for Sugar Loaf test site. Appendix A gives a brief description of the geology of each area and each outcrop. II . MODEL A. QLELLIPSOID METHOD From the equations governing elastic wave theory in anisotmpic media, Bennett (1972) derived the Q-ellipsoid, a simple elastic stiffness figure. The value of Q in the ith direction is defined by .03.. ,o where Q1 is the measured Q value (n1). ,0 is the density: v1, v2, 2 1 I 1 s a =(V, *V,+V, )‘.=|‘-¢g+m;~+n;°t”+2m- n,- °fn+2ll I; °§,+2|; m; ‘3‘... (U and V3 represent the pseudocompressional P wave phase velocity, the pseudo SH wave phase velocity, and the pseudo SV wave phase velocity: and (11, m1, n1) represent the directional cosines for a selected set of orthogonal axes x, y, and z. The density is not used in the calcu- lations because it is constant and therefore does not effect subsequent calculations. The alphas are elements of a symmetric 3 X 3 matrix. By referring to the principal axes, equation ( l ) becomes 0 . . z 7= I ’9, +m ain't-n °‘”= I Q'4- "‘20:" [130' (2) where 0(9- - O, i ,l 3. Therefore, the alphas (°(n .°(aa . “3 3) coincide with the major, intermediate, and minor axes. By setting s Q - 7- Hr (3) where (r) is the distance to the reference Q-ellipsoid from the origin, and by substituting l=x/r m =y/r n =z/r (4) equation (2) becomes x‘o‘ + y‘erz’Q, = I. (5) 6 Equation (5 ) is now in the fora of an ellipsoid whose principal axes have lengths of (alré, (q2)'%, and (Q3)'%. Pros equation (5 ), it can be shown tint the Q-ellipsoid is a reference Q-ellipsoid whose major, intermediate, and ainor axes have lengths of (alri‘, (q2)"1‘, and (c194. The q surface and the reference Q-ellipsoid are shown in Figure 3. +Y 1 Q = l/r (| r :(Q)'/1 (2 3 r +X (i) Q Surface (2) Unit circle of inversion (Nye, i957, p 47) (3) Reference Q-eiiipsoid Figure 3. Q surface and reference Q-ellipsoid. To find the elements of the best-fit °< -matrix for the Q surface, a least squares method is used described by Nye (1957). Is satrix fora, Q is defined by Q =e¢>< (6) where - 1 2 2 2 2m 2n 1 21 o< or Q "' Q1 ' 1 '1 n1 1‘1 1 1 1‘1 " u (7) _ _ 2 2 2 at“ Q2 12 "12 n2 2"2"2 2‘212 212% .93 Q 0 «I? e . «I! “a 2 2 2 - Qn - In an un Zmnnn 2nnln Zln'n n - number of propagation directions. The best-fit °< -matrix is determined by the matrix operation ‘I <>< =(e, e) 9.0. (a) This beet-fit O< -matrix is used to determine the calculated Q values (Me) by using equation ( I ). The calculated Q values define the surface of the least squared Q surface. From the best-fit °< -matrix, the principal axes are found by the successive approximation method described by Nye (1957). Here, unit vectors normal to the least squared Q surface are successively calculated until they converge on to the major axis. The minor axis is found by inverting the 0‘ -matrix and repeating the process. The intermediate axis is found by the cross-product of the major and minor axes. From the directional casinos, the magnitudes of the axes can be determined. For a more complete discussion of the two computational methods (least squares and successive approximation methods) see Nye (1957, pp. 158-168). After the least squared Q surface is determined, the measured and calculated Q values are statistically tested for homogeneous anisotropy. 8 In a purely isotropic body, the measured Q values have the same value in all directions. The Q-ellipsoid surface thus becomes a sphere. In an anisotropic body, the measured Q values vary with direction. Thus, when the measured Q values approximate an ellipsoid, anisotropy would be indicated. ' For the statistical test, the average data mean (i) and the average trace element of the symmetric matrix («[3 ) are first calculated. The average trace element (3) serves as the radius of a best-fit sphere for the data. Using i, s, and the measured and calculated q values (M1, NC), five standard mean-square deviations are calculated as shown below. 6% = Brim; - UV)” (9) 6's = ['33 $0“; - S 7]": (IO) ‘75: = [t gm. - “ii H“ u I) ‘5: = [1% gm. - s i']"’ (I2) a": = ffi.‘£(Mz - Mar-1": ('3) The standard deviations (‘45 . ‘E ) measure the deviation of the measured Q values from the mean and the best-fit sphere, respectively; the standard deviations (65¢ , Gig) measure the deviation of the calculated Q values from the mean and the best-fit sphere, respectively: and the standard deviation 6; measures the deviation of the measured Q values from the best-fit Q surface. 9 The uniformity of sampling will in part determine the reliability of the least squared Q surface. That is, i will approach S when the measurements are taken uniformily over at least 180 degrees. The percent ratio of K to S will serve as a measure of the uniformity of sampling. Thus, when the percent ratio is small, the sampling is uni- form. iihen the sampling is not uniform, the percent ratio will increase. Here, i will be weighed differently causing K to differ from s. The comparison of the standard mean-square deviations is used for establishing homogeneous anisotropy. The least squares process as described by Nye (1957) requires that Z(M¢ - Mi): be minimized. Because of this operation, 2(M‘ - M; )z< if“ - M‘- )2 and {(Mg-Mi)a<:(3 - M; )2 in most cases. Whenever the data is homo- geneous isotropic, CE = G} and 6-5 = G? . Therefore, G'e s67: Ge<6:. (l4) Homogeneous anisotropy is demonstrated whenever the eccentricity of the least squared Q surface is greater tlnn the data scatter from the same Q surface. The true eccentricity is not used because the least squared Q surface is not truly an ellipsoid. Therefore, 6:3 serves as the best measure of eccentricity and anisotropy. Also, whenever E approaches S (uniform directional distribution of measurements) 639 will approach <53} . The standard mean-square deviation 63 is the best measurement for the data scatter which includes inhomogeneity and errors in measurement. From this discussion, homogeneous anisotropy is demonstrated whenever 10 When 6'9 is greater than 53;. and 61-9 , inhomogeneous aniso- tropy is indicated. This would occur when the inhomogeneity and the errors in measurement exceed the degree of anisotropy. Because of this, the existence of true anisotropy would be uncertain. B. STRATIFIED MEDIA AND‘THE QgELLIPSOID METHOD Because each outcrop had some degree of fellation or layering, each outcrop can be approximated by a stratified medium consisting of two alternating homogeneous transversely isotropic layers. As a model for the application of the Qpellipsoid method to stratified media, I calcu- 1ated.the Q surfaces fer two of Postma's numerical examples from his study of wave propagation in stratified media (Postma, 1955, pp. 794- 799). Postma's numerical examples consisted of two alternating layers of sandstone and limestone with a thickness ratio of three to one, respec- tively. The second example had a thickness ratio of one to three, respec- tively. Table 1 lists the calculated V1, V2, and V3 velocities for each ample as a function of the angle ¢ relative to the xy-plane parallel to the layering (Postma. 1955. pp- 795. 797). Table 1 Calculated Velocities fer Postma's Two Numerical Examples fl V1(km/sec) V2(km/sec) V3(km/sec) Example 1 o 3.73 1.76 2.12 v /24 3.71 1.79 2.12 or /12 3.67 1.82 2.10 «v /8 3.62 1.87 2.07 air/6 3.52 1.91 2.01» sir/2n 3.u5 1.97 2.00 tar/u 3.36 2.00 1.95 71r/2h 3.29 2.00 1.89 «/3 3.24 1.94 1.86 ¢ V1(km/sec) V2(km/sec) V3(km/sec) 3 "/8 3.22 1.89 1.82 51r/12 3.21 1.84 1.79 liar/24 3.21 1.79 1.76 «/2 3.21 1.76 1.76 Example 2 0 4.90 2.32 2.79 11/24 4.87 2.34 2.79 7/12 4.82 2.39 2.77 v/8 4.74 2.45 2.74 1r/6 4.63 2.53 2.68 51/24 4.52 2.59 2.63 "/4 4.40 2.63 2.57 77r/24 4.31 2.63 2-51 "/3 4.24 2.57 2.45 37/8 4.22 2.51 2.39 sir/12 4.20 2.41 2.34 11 r/24 4.20 2.34 2.32 "/2 4.20 2.32 2.32 11 Table 1 (cont'd.) Table 2 lists the normalized measured Q values for each example. The Q values were normalized to the value at 9! s o for Example 2 to simplify plotting the Q surfaces and for comparing the two Q surfaces. Table 2 Normalized Q Values for Postma's Numerical Examples** ¢ Example 1 Example 2 0 0.57845 1.00000 1 /24 0. 57732 0.00462 11/12 0. 57002 0. 98496 11/8 0. 56181 0. 96775 11/6 0.54525 0.94200 51/24 0.53215 0.91605 1/4 0.51355 0.88448 7 7/24 0.48483 0.85519 «/3 0.47667 0.82270 3 1/8 0.46409 0.80214 5 1/12 0.45442 0.77801 11 w /24 0.44667 0.76632 1r /2 0.44381 0.76405 12 Figure ’4 displays the Q surfaces for each example. Ideally. the ujor axis should be parallel to the plane formed by the layering. In the field, this orientation may be alterred if other structural components with different orientations such as joints. fiastures. and folds are superimposed on the foliation or layering direction. In both examples. the layering is isotropic in the aq-plane. Therefore, the Q surface is a surface of revolution around the z-axis. +2 Ex.#2 Ex.“t I B A >-+x Q A = major axis B = minor axis Figure 4. Q surfaces for Postma's two numerical examples. 13 This particular treatment of Postma's numerical examples was applied to the field study because it was not practical to measure velocities in three dimensions in the field. Thus, the Q-ellipsoid method had to be modified to conform to a two-dimensional model. The value for Q in the ith direction then becomes 0. 7-0}— : (v: 4’ V:+ V:);= |¢?“n*nc‘1‘§s+2ni'i°‘no (I6) The least squares fit of the field data would be a planar section of the least squared Q surface (which contains the z-axis). The propa- gation directions are measured relative to the foliation or layering direction, and by using the successive approximation method, the orientation of the major axis from the foliation or layering is determined. III. FIELD WORK A. INSTRUMENTATION A portable ES-lOO Signal Enhancement Seismograph (hammer blow type) was used in this project. The seismograph was manufactured by Nimbus Instruments, Sacramento, CalifOrnia. The seismograph digitizes the signals received at the geophones and displays them on a cathode-ray oscilloscope (CRT). The seismograph has a 20 % duty cycle and has a switch for varying the sampling range, in milliseconds. The timing pulse and sampling intervals also vary with the sampling range (Table 3). Table 3 Summary of Range Switch, Timing Pulse and Sampling Intervals Range Switch Timing Pulse Sampling (ms) Interval Interval (ms) (ms) 10 0. 5 0.05 25 1.0 0.1 50 2.0 0.2 100 “.0 0.“ 200 8.0 0.8 400 16.0 1.6 The CRT has a time cursor connected to a millisecond counter for measuring the time picks for the first breaks of each wave type displayed. The timing pulse interval is the change in milliseconds for each setting of the time cursor. The seismograph also has a posi- tive and negative polarization switch. The use of the polarization switch is discussed in the section on field procedure. Vertical and horizontal geophones were used in orthogonal orien- tations along each propagation direction. The axis of the horizontal 14 15 geophone was placed parallel to the direction of propagation to detect the P-wave particle motion. To detect one of the shear wave particle motions, the axis of the horizontal geophone was transversely oriented to the direction of propagation. The vertical geophone axis was placed perpendicular to the horizontal plane to detect the other shear wave particle motion. Depending upon the orientation of the geophone, the hammer blows were directed so that the initial particle motion was parallel to the geophone axis. A transit and stadia were used for surveying the geophone locations relative to the target site (i.e. the elastic wave source) at each outcrop. B. FIELD PROCEDURE The outcrops for the field study were selected on the basis of outcrop exposure in metamorphic terrains. A large outcrop exposure was necessary in order that a sufficiently representative portion of an area could be tested. Metamorphic terrains were chosen so that the effect of foliation and/or layering on the least squared Q surface could be analyzed. The next step was to survey the outcrops for the locations of the geophones and the targets. From each transit position, horizontal angles (bearings), the elevation angles, and the straight-line distances along the elevation angles were recorded. The straight-line distances were determined by the stadia rod length intersected by a constant angle multiplied by 100. Later, the straight-line distances were converted to meters. The distance obtained from each reading is not the true distance because the stadia was not held perpendicular to the elevation angle sighting. Therefore, equation (I?) must be used to obtain the true l6 straight-line distance (dt) dt = (stadia reading” l00003¢ (I?) where g, is the elevation angle. At each geophone location, holes were drilled into the outcrop into which steel strips were cemented. The geophones were then attached to these strips. This ensured a firm couple of the geophones to the outcrop. This was done at Marble Lake and at Cross Lake, but not at Sugar Loaf because the outcrop was too resistant for the rock corer to drill. At the target site, a flat, round target made from armour plating was tested. Three holes at the apexes of a triangle were drilled through it. Holes were then drilled into the outcrop to coincide with the holes in the target. Two different methods were tested to attach bolts through the target into the outcrop: cementing the bolts and using expansion bolts. With either method, the target was bolted tightly against the outcrop to form a strong couple. For both methods, however, the target eventually worked itself loose with repeated blows of the hammer. This resulted in a weakened couple. So, periodically the target had to be retightened. In some cases, the target could not be kept tightened. Therefore, a number of rock faces had to be used.as targets. For the P-wave particle motion, a rock face was selected so that the hammer struck the rock face parallel to the propagation direction and the orientation of the horizontal geophone axis. The rock face for recording one of the shear wave particle motions was chosen so that the hammer blows were parallel to the transversely oriented horizontal geophone axis. For the other shear wave particle motion, the rock face was chosen so that 17 the hammer blows were parallel to the orientation of the vertical geophone axis. For each propagation direction, three such rock faces were selected. After the surveying at each outcrop was finished, the travel times for each wave type along the propagation directions were recorded. First, a range scale was selected depending upon the distance. For very long distances, a large range scale was used; for shorter distances, a smaller range scale was used. Then, a polarization mode was selected depending upon the orientation of the geophone axis. As an example for using the polarization modes, consider the transversely oriented horizontal geophone in Figure 5. {-4 Target Pro a otlon Dlrectlon J Geophone Axle (4') Orientation Figure 5. Polarization modes for transversely oriented horizontal geophone. If the positive polarization mode is chosen first, the first break of the signal displayed on the CRT screen would be downward when the hammer blows are in the same direction as the geophone axis. If the negative polarization mode is used, the first break would be reversed. The signal received at each geophone is continuously displayed on the CRT screen. With repeated hammer blows, the signal is built up in amplitude whereas the period remains the same. This enables the operator to locate each wave type more accurately. This is demonstrated in Figure 6. l8 Polarization ————-————— (__, _2_O home: blows_.v,WW 50 ms scale SV’ 37 ms W50 ms scqu (-) 4 SV 37.5 ms Figure 6. Effect of hammer blows on signal. The signal in Figure 6 is not drawn to true scale, but it does give a general idea on the result of repeated hammer blows on the signal. The signal pictured was received at the geophone location #7 from the long array at Marble Lake (#6 in the survey data, Appendix.B). The vertical geophone was used to record the SV wave particle motion. The time picks for the first breaks of each wave type had to be chosen very carefully for in many cases the signals received at the geophones were very complex. This complexity may have been due to noise or obstructions along the propagation paths. Figure 7 is one example showing the complexity of the signal received by the vertical geophone at the geophone location.#6 from the long array at Marble Lake (#5 in the survey data, Appendix B). Figure 7 is also not drawn to scale, but it does give a close representation of what the signal looked like on the CRT screen. l9 Polarization ('H W lOO me scale P SV ' 2| ms 36 me Figure 7. Complex signal for propagation direction #6; Marble Lake (long array). Ideally, the signal should look like Figure 8. Figure 8. Theoretical signal received at geophone. Another example for signal complexity is the signal received by the vertical geophone at the geophone location #3 for the long array at Marble Lake (Figure 9). Polarization 0+) W '00 m. 890.0 SV 53 ms Figure 9. Signal for pro ation direction.#3: Marble Lake (long arr§:§. 20 From Figures 7 and 9, it can be seen that the ability to choose the correct time pick can be very difficult at times. Therefore, care must be taken in order to select the correct time pick. In summary, to make a measurement, a propagation direction is chosen first. At the geophone location one of the geophone orienta- tions is selected. Next, a range scale is chosen based on the distance involved. After this, hammer blows are struck in the direction of the geophone axis until a readable signal is displayed on the CRT screen. From the signal, the travel times for the wave types being measured are recorded. This procedure is followed for each geophone orientation at each geophone location. C. RESULTS OF FIELD WORK At Marble Lake two different size geophone arrays were tested: one long and one short. The long array used only one target: the steel armour plate. The short array used the steel armour plate plus five rock faces for targets. The target sites at Cross Lake and Sugar Loaf also used the steel armour plate and rock faces as targets. Relative to the targets, seven geophone locations were surveyed. The survey data is given in Appendix B. The distance measurements had an estimated accuracy of approximately 1 %. The outcrop at Marble lake (long array) was surveyed in a loop consisting of five transit locations with a vertical closure of 7.32 cm over a distance of approximately 701.1“ m. This showed that the survey was accurate to an estimated O.h %iover a maximum vertical distance of 17.06 m. The short array at Marble Lake and the array at Cross Lake each had only one transit location. But Sugar Loaf, like the long array at Marble Lake, required more than one transit location to survey the outcrop. In this case, 21 three transit locations. The propagation distances at Marble Lake (long array) and Sugar Loaf were estimated by using the relative differences in the elevation between the targets and the geophone locations, and the horizontal angles and the horizontal distances from each transit position. The propagation distances for the small array at Marble Lake and for the array at Cross Lake were calculated by equation (i8) as applied to Figure 10. The angle 6 is a function of the dip and of the hori- zontal angle. 1 l dp =(b + 01- Zbc easel/2 (l8) +'Z .f‘Treneit Position $- ‘FY Geophone Locaflon Figure 10. Finding the ropagation distance using equation (I 8)’. 22 After surveying, the travel times for each wave type were recorded at each geophone location. For each array the longitudinal oriented horizontal geophone was used to record the P wave particle motion. At Marble Lake the transversely oriented horizontal geophone was used to record the SH wave particle motion. The axis of the geophone was oriented to the right when facing toward the target from the geophone position. The vertical geophone was used to record the SV wave particle motion. For Cross Lake (vertical foliation) the horizontal geophone was oriented transversely to the right to record the SV wave particle motion. The SH wave particle motion was recorded by the vertical geophone. At Sugar Loaf the transversely oriented horizontal geophone was used to record the SH wave particle motion, and the vertical geophone was used to record the SV wave particle motion. Table # gives the range scales used for each geophone array and the approximate accuracy in picking the first breaks for each wave type. Table h Range Scale Used for Each Geophone Array Geophone Array Range Scale Accuracy (millisec) (millisec) Marble Lake--Long Array eeoeeee 100 1.0 --Sh0rt AmYOeeeeee 25 0.2 --Short Array....... 50 005 Cross Lakeeeeeeeeeeeeeeeeeeeeee 25 002 Sugar Loaf..................... 100 loo Sugar loaf......o..........,... 50 0'5 For each geophone array, Table 5 gives the propagation lengths and the travel times for each wave type; Table 6 gives the directional cosines and the velocities for each propagation direction; Table 7 23 gives the measured and the normalized measured Q values for each propagation direction (the measured Q values were normalized to simplify the calculations): Table 8 gives the calculated Q values for each propagation direction and related statistics: and.Table 9 gives the principal axes for each least squared Q surface with their respec- tive orientation of the major axis. Table 5 Propagation Lengths and.Trave1 Times Propagation Path Length P SH SV (111) (ms) (ms) (ms) Marble Lake (Long Array) 1 lH-Target 185.62 36.5 65.0 68.5 2 Z-Target 157 e 52 27 e 0 57 e 0 55 e 0 3 3V-Target 175.20 32.0 53.0 53.0 4 4H-Target 146.30 26.5 40.0 51.5 5 4'-Target 1420014 1900 52.5 5200 6 S-Target 84073 1506 [4.5.0 3600 7 6-Target 98 e 15 23 e 0 “'1 e 5 37 e 5 ERROR ESTIMATE 1 76 2-5 76 0-3 % 0-3 % Marble Lake (Short Array) lJTarget l 55.87 29.5 l-Target 2 60.02 13.2 14Target 2a 59.22 27.0 2-Target 3 32.91 10.0 2-Target 2 36.32 7.5 2JTarget 1 32.05 13.0 3-Target ’4 38.95 13.6 3-Target 2a 37.88 9.3 34Target l 35.73 17.5 Lin-Target 2 33076 8e3 4-Target 2a 33.92 7.8 44Target l 32.65 13.0 54Target 2 40.54 15.0 S-Target 3 #1083 1002 5-Target 1 40.57 16.3 24 Table 5 (cont'd.) Propagation Path Length P SH SV (m) (ms) (ms) (ms) 6—Target 2 39. 95 11+. 8 6JTarget 3 42.39 9-3 6—Target 1 41.49 18. 6 74Target 2a 32.41 15.5 7-Target 5 34.30 7.4 7-Target 1 34.67 16.5 ERROR ESTIMATE l % 3-5 % 1-4 2 1-4 % Cross Lake l-Target 3 fleas 11 . 9 2- " 27.17 11.3 3- " 2’4, . 9O 13 . O 4- " 25.73 11.6 5. " 32.67 11.2 6— " [+8.09 17.0 7- n 61 0 87 22 on lJTarget 2 34.14 7.0 - " 27.05 6.0 3- " 24-97 5-7 4- " 25.95 6.2 5- " 33.17 6.7 6- " 48.68 10.0 7- " 62-39 12-0 lJTarget l 34.66 13.7 - " 27.58 11.0 3- " 25.45 9.0 4- " 26.36 9-5 5- " 33-32 10.7 6- " 48.66 14.5 7- " 62.36 22.2 ERROR ESTIMATE l 76 2-4 76 1-2 % 1-2 % Sugar Loaf l-Target 1 102.26 2.2.0 35.0 l-Target 2 101.03 15. 5 24Target 1 76.94 22.0 28.0 24Target 5 79.18 26.0 3-Target 3 61.44 13.0 24.9 34Target 4 56.56 36.0 25 Table 5 (cont'd.) Propagation Path Length m 4~Target 3 61.86 4~Target 60.99 (Steel Plate) 54Target 4 60.24 54Target 2 59.51 64Target 4 84.47 64Target 2 83.11 74Target 1 115.00 74Target 2 113.74 ERROR.ESTIMATE 1 % Propagation Direction \lmmpWNi-J \lChkh-PKJJNH Table 6 14.5 12.3 16.5 24.7 3-6:% SH sv (ms) (46) 30.0 23.0 33-5 35-5 28.0 41.0 40.0 39-7 2-3 5 2-3 % Directional Cosines and Velocities Directional Cosines Velocities (m/sec) v1 Marble Lake (Long Array) -1.00000, -0-93544. -0-58479. -0.47255, -0.27228, 0.56928, 0.98953. 0.00000 0-35347 0.80902 0.88130 0.96222 0.82214 0.14436 ERROR ESTIMATE 5100.34 5862.89 4636.10 5554-15 7529.54 5502.58 4332.40 2-5:% Marble lake (Short Array) -0-95528. -o.80386, 0.00000, 0.28569, 0.52547. 0.77715. 0.97030, 0.29571 0.59482 1.00000 0.95832 0.65081 0.62932 0.24192 ERROR.ESTIMATE 4544.17 4842.14 4072.77 4348.64 4101.08 4558.01 4634 . 91 2-61% v2 2864.05 2777-15 2799.16 3679.64 2724.97 1904.94 2401.09 0-31% 2193-37 3291.26 2864.05 4067.10 2702.97 2699.46 2090.71 0-51% V3 2720.80 2878.13 2799.16 2857.96 2751-19 2381.16 2657.22 0-3.% 1891.10 2465.01 2041.46 2511.92 2489.21 2230.62 2101.35 0-51% Propagation Direction VO‘sUK-P’WNH \ImknC'UNl-J 26 Table 6 (cont'd.) Directional Cosines -0.64945, -0-233“5. -0.03839, 0.21814, 0.70957. 0.88942 . 0.96363. Cross Lake 0.76041 0.97237 0.97592 0.99926 0.70463 0.45710 ERROR ESTIMATE -0.82413, .0.70711, -0.38430, 0-18395. 0.62115, 0.74314, 0.85806, Sugar Loaf 0. 56641 0.70711 0.92321 0.98294 0.78369 0.66913 0.51354 ERROR ESTIMATE Propagation Direction Table 7 Q values Velocities (n/sec) vl 4876.95 4508.75 4380.28 4185.51 4951-35 4867.75 5199-25 1-5 % 4848.14 3511.17 4726.26 4266.44 4897.92 5119.12 4655.91 2-5 % M1(.2/sec2) Marble Lake (Long Array) v2 2530.36 2507. 56 2827.72 2774-35 3114.26 3356-09 2809.13 0-3 % 2845.98 3045.44 1571.12 2651-73 1676.25 2027.16 2864.94 1-4 % M1(norlalized) VQMFVNH \IChkn'l-‘UNH Marble Lake (Short Array) 41619009.52 50369716.15 37164025.?6 52556308.53 71688403.45 39577149.20 31595702.88 29036638.01 40355028-59 28957795-26 41761715.59 30321084.56 33038198.97 30269165.99 0.58055 0.70262 0.51841 0.73312 1.00000 0.55207 0.44074 0.69529 0.96632 0.69341 1.00000 0.72605 0.79111 0.72481 V3 2894-99 2404.41 2963.81 2707.90 2916.97 2828.82 2762.10 0-3 % 2921.69 2758.78 2467.54 2062.09 1798-35 3016.61 2875.03 1-4‘% Propagation Direction \lmkn-F'UNH mGni—‘UNH Propagation Direction \lmmvP'WNi-J \lChUttF'KAJNl—J 27 Table 7 (cont'd.) M1(m2/secz) Cross Lake 38568346. 54 32397925-90 35967061.01 32548290.07 42723236.96 42960530.66 42552563-55 Sugar Loaf 383ll832.77 29213887.31 30894699-49 24838738.86 30033416.66 39414651.20 38151150-54 Table 8 0.89680 0.75413 0.83721 0.75763 0.99448 1.00000 0.99050 0.97022 0.74119 0.78384 0.63019 0.76199 1.00000 0.96794 M1(normalized) Calculated Q Values and Statistics M c Marble lake (Long Array) .3 '3 O . 17222 ‘3" = O . 10 932 ‘; 3 0.13293 ‘fif- 0.10968 ‘2 =3 0 . 17245 afig,<:vdfii «3;,‘¢s; “? 3"73 0.79196 0.83735 0.85923 0.82553 0.78957 0.75212 0.74112 “iil>”5; Statistics Ff - 0.64679 S 3 0.63761 lei-m Iii-5| S czf<63 “ GE. 13; Gib >“G; Sugar Loaf ._ 1 0.87472 «.1. .. 0.18428 M - 0.83648 2 0.80749 ‘5' .. 0.09802 3 - 0.82570 3 0.68295 6; 3 0.08114 3’: =3 4 0.66050 6:... 0.09487 I s l 1 7‘ 5 0.80135 0: = 0.13240 1.00994 6 0.86306 “3 Ms; “2.037 o< =- 0.64145 7 0.92881 6; >6; “7. (‘3 0.01821 Table 9 Q,Surface Principal Axes and Major Axis Orientation Axis Magnitude Directional Relative to Q,Surface Cosines Marble Lake (Long Array) Major 0.77931 E-0.29069, 0.95682; Minor 0.h7000 0.95682 , 0.29069 Marble Lake (Short Array) Major 0.87705 E-o.35402, 0.93524g Minor 0.73959 0.93524, 0.35402 Cross Lake Major 1.03543 é 0.99556, 0.09410; Minor 0.78272 -0.09th, 0.99556 Orientation of Major Axis ( From Foliation -73.1° -69.3° +5.4 fi) 29 Table 9 (cont'd.) Axis Magnitude Directional Orientation of Relative to Q,Surface Cosines Major Axis (g!) From Foliation Sugar Loaf , Major 1.01084 ( 0.99883, 0.04843g +2.8 Minor 0.64039 ( 0.04843,-0.99883 The travel time errors in Table 5 were estimated from the accuracy of each range scale used for each geophone array (Table 14). The velocity errors in Table 6 were estimated by equation (l8). V = x/t = xt" dV = dx/t - XI? 01/? = dx/t - th/t dV/V = dx/x - dt/t dV/V = -'-*— dx/x -— |dm| (I9) where dx/x 3" 1 5. Since we are testing for homogeneous anisotropy. the best estimate for the error in the seasured Q values would be given by 5'; . The value GE would incorporate errors due to inhomogeneity and errors due to measurement. Figures ll-lh show the least squared Q surfaces fer each geophone array. The foliation and the major axes are labeled, with the positions of the normalized measured Q values for each propagation direction marked by arrows . 6 7 FOLIATION 0 55 g C’ o 1) s ‘ Z; m Figure 11. Q surface for Marble Lake (long array). 4. 5 2 6 ' 1 FOLIATION . 55 a 9 9» 7 y. S 7.0 Figure 12. Q surface for Marble Lake (short array). 5 6 7 \ FOLIATION MAJOR “‘5 68’ s Figure 13. Q surface for Cross Lake. 2 3 4 l .5 6 l 7 MAJOR 4,7,3 . ‘ FOLIATION ' 65" Figure 1“. Q surface for Sugar Loaf. IV. LAB WORK A. UDTRASONIC VELOCITY MEASUREMENTS l. Instrumentation The velocity anisotropy was measured for the rock samples collected from the field by means of ultrasonic shear wave birefringence at atmospheric pressure. In anisotropic media there are two orthogonally polarized shear waves which can propagate. In general, these two shear waves will propagate at different velocities. An ultrasonic generator is used in conjunction with the compressional P wave to shear 8 wave conversion technique (Tilmann and Bennett, 1973b; Jamieson and Hoskins, 1963) to test for this birefringence. With this technique, a compres- sional wave transducer converts an electrical energy impulse to mechan- ical energy which travels through a Pyrex glass wedge. The wedge is cut so that one angle is as close as possible to the critical angle. This is done so that the P wave will convert to a shear wave when reflected at a free surface. But it is observed that there is some P wave energy always present. The P and shear waves then propagate through the sample to another Pyrex glass wedge where the shear wave is reconverted and reflected back into another transducer. Here, the mechanical energy is converted back into an electrical energy impulse which is then displayed on a CRT screen. By rotating the sample, the two polarized shear waves can be measured. The experimental set up is shown in Figure 15. 32 33 RECEIVER COMPRESSIONAL TRANSDUCER TRANSDUCER PYR X PYREX \ EjGLASS SéprE GLASS.L2\V 1, Critical Angle Figure 15. Experimental set up for ultrasonic velocity measurements. 2. Preparation and Description of Samples Unoriented rock samples were collected from each outcrop. The rock samples were then cut to obtain propagation directions for measuring the travel times for each wave type by the P-S wave conversion technique. Each sample was cut in reference to an arbitrary set of orthogonal axes. But whenever possible, the (0,0,1) face was cut parallel to the foliation. The sample from Marble Lake was a pelitic schist with definite obser- vable foliation formed by the parallel alinement of ellipsoidal oolites less than two millimeters in diameter. The rock sample from Cross Lake was a hornblende-biotite schist with observable foliation formed from the parallel alinement of hornblende crystals. The rock contained very fine fractures. The rock sample from Sugar Loaf (gneiss) also contained very fine fractures, but it did not possess an observable foliation. 3. Procedure and Results For each pr0pagation direction, the P, SH, and.SV wave travel times were measured. The two polarized shear waves were measured by rotating the sample. The SH wave was measured when the particle motion was perpendicular to the (0,0,1) direction. The SV wave was measured for 38 the particle motion in the plane defined by the propagation direction and the (0,0,1) direction. Whenever there is no feliation or direction- al features present, the above two statements may not hold true for the two perpendicular polarized shear waves. Table 10 gives the directional cosines, the distances, and the travel times for each propagation direction. For some of the P and SV waves, the travel times could not be determined. Therefore, the travel times for these wave types were estimated by the averages of the other P and SV wave travel times. For Sugar Loaf it was difficult to measure both shear waves. With rotation of the hand sample, both shear waves were observed. But, one shear wave was better defined than the other. In fact, the less defined shear wave was masked so much by the total waveform that the first break for the second shear wave could not be determined. Therefore, the two shear waves were assumed to have equal travel times. Since the P wave travel times fer each propagation direction did not vary too much, equalizing the two shear wave travel times would in effect tend to reduce or minimize the eccentricity of the least squared Q surface. Table 10 Directional Cosines, Distances, and Ultrasonic Travel.Times Propagation Directional Distance P SH SV Direction Cosines (m) (’1 sec) (I sec) (’1 sec) Marble Lake (1,0,0 0.10381 17.6 27.8 37.0 (0,1,0 0.10274 17. 6 27.6 36.4 0,0,1 0.08433 19. 7** 28.6 28.6 -0.707,-0.707,0§ 0.14874 18.8 31.2 42.2 0.707,-0.707 0 0.11483 20. 8 30.4 41.0 0,-0. 719, 0. 645 0.10099 22.2 31. 0 35.4 0, 0. 707, 0. 707 0.09962 22.2 30. 2 36.8*** -0.719,0 ,-0.695g 0.10160 19.7** 30. 6 36.8*** 0.10132 19.7** 31.0 36.8*** \OGDVChUI-P’KJDNH 0. 713,0.-0 701 35 Table 10 (cont'd.) Propagation Directional Distance Direction Cos ines (:1) Cross Lake 1 1,0,0; 0.09936 2 0,1,0 0.09898 3 0,0,1 0.09835 4 -0.707,-0.707,0) 0.10404 5 -0.707,0.707,0; ------- 6 0,-0.707,0.707 0.10277 7 0,0.707.0.707) 0.10452 8 -0.707,0,-0.707g ....... 9 0.707,0.-0.707 0.10381 Sugar 1.an 1 1,0,0 0.10218 2 0,1,0 0.10144 3 0,0,1 0.10295 4 0.707,0.707,0) 0.10592 5 0.707,-0.707,0) 0.10467 6 0.-0.707,0.707) 0.10236 7 0,0.707,0.707) 0.10620 8 -0.707,0,-0.707; 0.10493 9 0.707,0,-0.707 0.10203 ** P (u sec) 17.6 17.4 18.3** 17.8 18:4 19.6 19.0 18.2 18.4 18.4 18.8 18.6 18.0 19.0 18.8 18.0 SH 9. sec) 28.8 28.8 31.8 29.2 29.6 31.0 31.4 29.8 30.0 30.“ 30.4 30.6 30.2 30.2 30.6 29.6 SV (’1- sec) 33-0 36.8 31.8 33-9*** 33-9*** 33-9*** 33-9*** 29.8 30. 30.4 30.4 30.6 30.2 30.2 30.6 29.6 Travel times were determined from the average of the P wave travel times measured. Travel times were determined from the average of the SV wave travel times measured. The SV wave travel times were assumed to be equal to those for the SH wave travel times. Table 11 Propagation Directions and Ultrasonic Velocities Propagation V V V Direction (m/sic) (m/sgc) (m/sZc) Marble Lake 1 5898.2 373h.1 2805.7 2 5880.9 3722.5 2822.6 3 4280.5 2948.5 2948.5 4 6316.2 3805.9 2813.9 Propagation Direction \O(D~Q‘; 63""; "0 >6; fie>‘3 Table 14 Statistical Data for Hand.Samples Marble Lake ‘7‘: - 0.12887 M - 0.72573 0.87536 ‘5..- 0.12356 3 - 0.70963 o< - 0.54382 ‘3 - 0.03081 “' -0.0389 6;. - 0.12215|'£12|' 2'3 5‘ 6'5 >6; 6?. > 6'3 _Cross Lake 6': . 0.03291 M - 0.90852 0.94200 ‘3'. 0.02881 8 - 0.90547 “ - 0.868% 6; - 0.01604 E-s -0.01748 4;}- c; . _Sugar Loaf ‘3 - 0.01003 M - 0.98025 0.9745 €3.- 0.00639 8 - 0.98247 °< - 0.9903 ‘5 - 0.00788 — | _ 0 2 a; 0.0032 ‘29- 0.00605 ' C; - 0.00982 GE J>t53 <fi§,,(i¢; ¢§§:>cs;, <:;,.:<=; 40 Table 15 gives the principal axes and the major axis orientation for each least squared Q surface. Table 15 Principal Axes and.Major Axis Orientation for Hand.Samples Axis Magnitude Directional Orientation of Cosines Major Axis (fl) From Foliation Marble Lake . Major 0.87988 (0.99351,-0.11379; -6.5 Minor 0.53938 0.11379, 0.99351 ' Cross Lake , Major 0.94596 20.92423,-0.20159; -12.3 Minor 0.81824 0.20159, 0.92423 Sugar Loaf 9 Major 0.99087 $040356, 0.99462) .84.1 Minor 0 . 971606 0 . 99*62 .CO .10356 Figures 17-19 show the least squared Q surface and the major axis orientation for each hand sample. *‘Z A FOLIATION °R : \ IXXIS \\\\\--‘_ 3D-~t X Figure 1?. Least squared Q surface for Marble Lake hand sample. 41 +-Z M Foumou (QR ,_ +x AXIS Figure 18. Least squared Q surface for Cross Lake hand sample. *2 FOLIATION AXIS MATOR AXIS Figure 19. least squared Q surface for Sugar Loaf hand sample. 42 B. THIN-SECTION ANALYSIS For each hand sample, photographs were taken from thin-sections parallel and perpendicular to the xy-plane. As already discussed under the section on the preparation and description of samples, each sample was out according to an arbitrary set of orthogonal axes. But when foliation was present, the aq-plane was cut parallel to the foliation. Figures 20 and 21 are photographs of thin-sections from the Marble lake tend sample perpendicular and parallel to the xy—plane. The magnification is approximately 331. There is a definite foliation formed by ellipsoids and very fine mineral banding parallel to the xy-plane. The thin-sections also display a very fine-grain textm'e. Figures 22 and 23 are photographs of thin-sections from the Cross Lake land sample parallel and perpendicular to the ity-plane. The magnification is approximately 3: 1. Very strong foliation and mineral banding can be seen parallel to the n-plane. The texture is also fine-grain but not as fine-grain as that for the Marble Lake hand sample. Figures 24 and 25 are also photographs of thin-sections parallel and perpendicular to the xy-plane for the Sugar Loaf hand sample. The magnification is also approximately 3:1. If there is foliation revealed by the thin-sections, it is very subtle. But there are two fractures on the thin-section perpendicular to the xy-plane. The texture is coarse grain with grains many times larger tram those for the Marble Lake or Cross Lake hand sample. h l FOLIATION Figure 20. Marble lake: Photograph of thin-section perpendicular to ity-plane of the hand sample (Mag. 3:1). \\\ raunnow Figure 21. Marble lakes Photograph of thin-section parallel to icy-plane of the hand sample (Mag. 381) . +— «_ FOLIATION Figure 22. Cross Lake: Photograph of thin-section perpendicular to xy-plane of the hand sample (Mag. 3:1). N0 FOLIATION Figure 23. Cross Lakes Photograph of thin-section parallel to xy-plane of the hand sample (Mag. 3:1) . 45 in: 2 9333371.; /' // FOLIATION? Figure 24. Sugar Loaf: Photograph of thinpsection perpendicular to n-plane of the land sample (Mag. 3:1). / // FOLIATION? Figure 25. Sugar loaf: Photograph of thin-section parallel to aw-plane of the land sample ("l-8e 311). V. DISCUSSION A. VEIDCITY DATA FROM FIELD STUDIE 1. Marble Lake Both geophone arrays at Marble Lake displayed inhomogeneous anisotropy (Table 8). The 6:" are larger than those for Sugar Loaf or Cross Lake. This indicates that the Q, values are much nore scattered than those for Cross Lake or Sugar Loaf. Therefore, the reliability of the least squared Q surfaces may be questionable even though the percent differences between i and S (i.e. the difference between i and 3 divided by s) are small. The large data scatter may be the result of large errors in measurement and/or inhomogeneity in the outcrop as indicated by the fact that 6? is greater than 679 and 6:5 . The anisotropy defined by equation (20) is about 1&9. 5 i for the long array and about 17.0 75 for the short array. Anisotropy - (a-b)/S (20) a - Major axis b - Minor axis The differences in anisotropy are probably due to changes in lithology since the long array sampled two different lithologies (netavolcanics and pelitic schist) while the short array sampled only one (pelitic schist). Because of the indicated inhonogeneity, the aetml degree of anisotropy say be unreliable. The orientations of the major axes are not parallel to the observed foliation on the outcrop. This result does not fit the nodal. The orientations of the najor axes are roughly 90 degrees from the foliation (long array: -73.1. 3 short arrays -69.3. ). The major axis orienta- tions nay be related to the isoclinal folds mapped in the area which #6 a? have their fold axes trending to the northeast (Meen, 19%, p. 25). The foliation on the outcrop is parallel to the fold axes, but this relationship can not be observed on the outcrop itself. Therefore, even though there is a distinct foliation direction observed on the outcrop, the least squared Q surface orientations may be reflecting the effects of folding. The Q surfaces may thus be indicating an area which has undergone more than one deformation period. In fact, at least three stages of defamation have been described for the Marble Lake area (Moore and Hutchean, 1973. p. 939). 2. Cross Lake The outcrop at Cross Lake displayed homogeneous anisotropy (Table 8) . The percent difference between if and s is small and ‘1. and 67,-. are both larger than ‘5 . Therefore, the outcrop is homogeneous aniso- tropic. The anisotropy is approximately 27.8 76 The orientation of the major axis is approximately 5.1+ degrees from the foliation again indicating that there may rave been an uncomplicated deformation history at this site. 3. Sugar Loaf The standard deviations for the outcrop at Sugar Loaf indicated homogeneous anisotropy (Table 8). Also, the percent difference between E and s is approximately 1 x shoring direction sampling uniformity. The least squared Q surface can he therefore considered to indicate homoge- neous anisotropy because of the small '9‘?) value and because ‘7" and ‘3: are larger than ‘3 . The anisotropy is approximately “4.9 5‘. The orientation of the major axis from the foliation is approximate- ly 2.8 degrees showing good agreement with Postma's model for velocities 1&8 in layered media. This orientation may indicate an uncomplicated defor- mation history at this site. B . VELOCITY DATA FROM ULTRASONIC STUDIE For Marble Lake the ultrasonic velocity measurements indicated homogeneous anisotropy (Table 11+) . Even though the measurements were taken uniformin and the 6; is small. the data may be biased because not all of the P-nve and shear wave velocity measurements could be measured (Table 10) . The thin-sections showed a fairly strong foliation parallel to the ity-plane for the hand sample. The orientation of the major axis was approximately 6.5 degrees from the foliation plane. Thus. the least squared Q surface fits Postma's model fairly well. The aniso- tropy was approximately 1&8.0 S. The ultrasonic velocity measurements for Cross Lake also indicated homogeneous anisotropy (Table 1h) . The small percent difference between H and s and the small 6; indicated good data. Again, the data may be biased for the same reason as for Marble lake. The thin-sections revealed a strong foliation and mineral banding parallel to the xy-plane. The orientation of the najor axis was approximtely 12.3 degrees from the foliation plane. Therefore, the least sqmred Q surface for the Cross Lake hand sample also fits the model. The anisotropy is about lll.5 %. For stgar Loaf inhomogeneous anisotropy was indicated (Table 11+) . The inhomogeneity may be due to the random orientation or spacing of fractures and to the large grain also observed in the land sample. The thin-sections showed little or no foliation, some fracturing, and a coarse grain texture. If the grains are comparable to the wavelengths used in measuring the travel times. distortions in the signal received 49 may result, causing the measurements to be inaccurate. The orientation of the major axis is about 81+.l degrees relative to an arbitrary set of axes since no foliation is observed from the hand sample. But the indication of a unique major axis is unreliable because the eccentricity shows that the least squared Q surface is practically a sphere reducing the ability to determine an unique set of oriented principal axes. Figure 19 also supports this by graphically showing the least squared Q surface to be almost a sphere. The anisotropy is about 1.7 95. VI. CONCLUSION A. COMPARISON OF FIELD AND LAB REUITS 1. Marble Lake The seismic field data and the ultrasonic data did not yield similar results concerning homogeneous anisotropy. The long and short arrays both indicated inhomogeneous anisotropy indicating that the outcrop is heterogeneous (Table 8). This was expected for the long array since it sampled two different lithologies (metavolcanics and pelitic schist). The short array, however, displayed the same result as the long array even though only the pelitic schist was sampled. The ultrasonic velocity measurements from the hand sample revealed homogeneous anisotropy (Table It). This discrepancy between the seismic field data and the ultrasonic data may be due to the nature of the hand sample. The hand sample represents only a small portion of the outcrop and.may not be a true representative of the outcrop. .Also the ability to determine the P-wave velocities from the ultrasonics indicate that the propagation paths contained little or no cracks whereas the outcrop may have been highly fractured, Thus, even though the hand.sample showed homogeneous anisotropy, this is not representative of the outcrop as shown by the field measurements. Another significant result was the orientations of the major axes for the seismic field.and ultrasonic data. The model predicted.that the major axis orientation would be parallel to the foliation. The ultrasonic velocity measurements and the thin-sections, together, supported the model. The thin-sections revealed strong foliation parallel to the xy—plane of the hand sample. The ultrasonic data showed a major axis orientation approximately 6.5 degrees from the foliation plane. 50 51 The seismic field data yielded a completely different result which was unexpected. The orientations of the major axis for both the long and short arrays were almost perpendicular to the foliation. This result differed significantly from Sugar Loaf and especially Cross Lake where the orientations of the major axes supported the model. Since the foliation is known from the literature to be parallel to the fold axes of isoclinal folds in the outcrop at Marble Lake (the folding could not be observed on the outcrop itself), the orientation of the least squared Q surfaces may be reflecting the presence of the isoclinal folds or of different periods of deformation superimposed upon one another. The orientations of the major axes for the seismic field and ultrasonic data suggets that the use of large scale seismic field measurements are more important than measurements which rely only on single hand samples or thin-sections. The orientation of the major axes for the two seismic arrays, which are similar (Table 9), may be signi- ficant in that the long array sampled two different lithologies while the short array sampled but one. In this case, the orientation of the least sqmred Q surface appeared to be independent of lithologic change. This observation, however, needs further study. The eccentricity and the anisotropy for the ultrasonic data were greater than that for the seismic field data. The 67. for the short array was 0.0413 5 (Table 8) . The 67. for the ultrasonic data was 0.12215 (Table 1a). The anisotropy was 17.0 S for the short array and 148.0 x for the ultrasonic data. The anisotropy and the eccentricity may be greater for the ultrasonic data than for the seismic field data because of the difference in wavelingths used and because of the fine grain texture and fine foliation revealed by the hand sample and 52 thin-sections. The ultrasonic velocity measurements used much higher frequencies than that for the seismic field measurements (four orders of magnitude greater). Thus, the wavelengtm for the ultrasonic data were much smaller than those for the seismic field data. Because of the much smaller wavelengths used for the ultrasonic data, the foliation and the grain size may rave a more pronounce effect on the velocity measurements. The larger wavelengths used for the seismic field measurements would tend to average the effect of the fine grains, micro- fractures , and foliation. 2. Cross Lake The seismic field and ultrasonic data and the thin-sections were comparable. Both the field data and the ultrasonic data showed homoge- neous anisotropy (Table 8 and Table 14, respectively). The thin-sections indicated strong foliation and mineral banding parallel to the xy-plane of the hand sample (Figure 22 and 23). The ultrasonics showed that the major axis was approximately parallel to the foliation plane (Table 15). The seismic field data also showed a major axis parallel to the foliation (Table 9). These results exhibited good agreement with Postm's model. The seismic anisotropy for the outcrop was greater than the ultra- sonic anisotropy for the hand sample. This was probably due to more pronounce fracturing parallel to the foliation in the outcrop than in the land sample. 3. Sugar Loaf At Sugar Loaf the seismic field data and the ultrasonic data were not comparable. The seismic field data indicated homogeneom anisotropy while the ultrasonic data exhibited inhomogeneous anisotropy (Table 8 53 and Table 11+, respectively). This discrepancy was probably due to the comparatively larger grain size in this hand sample (Figures 2“ and 25). For the hand samples, very high frequencies and thus very small wave- lengths were used for testing the samples ultrasonically. As previously mentioned, when the grain size and the wavelengths are comparable, dis- tortions in the signal can result causing inaccuracies in the measure- ments. The thin-sections showed that the hand sample for Sugar Loaf was composed of very large grains as compared to the fine grains for Marble Lake and Cross Lake (Figures 20-23). The major axis orientation for the seismic field and the ultrasonic velocity measurements could not be adequately compared for the Sugar Loaf sample, because of the very low anisotropy for the ultrasonic measurements (1.7 S) as compared to “4.9 S for the seismic field meas- urements. Because of this large difference, the actual major axis orientation for the hand sample is not reliable. In support of the very low anisotropy indicated by the ultrasonic velocity measurements on a single hand specimen, the thin-sections showed little or no foli- ation (Figures 2h and 25). The small anisotropy may have been due to several reasons. First, the thin-sections showed that the grain size (i.e. diameter) was com- parable to the wavelengths used for the ultrasonic velocity measurements, thus reducing the effect of the foliation. Secondly, became of the large grain size, fewer grains were sampled which would again tend to deemphasize the foliation and mineral orientation. Thirdly, the degree of anisotropy may vary between hand size specimens (i.e. the outcrop was heterogeneous on a small scale). Finally, as noted earlier, the SV velocities were chosen to be identical to the measurable SH velocities. 51+ Because of this , the ultrasonic velocity measurements would tend to approach a sphere, thus reducing the eccentricity and the anisotropy. The effect of the inadequate number of ultrasonic velocity meas- urements mist be taken into account when comparing the above seismic field and ultrasonic measurements. Not all of the P and shear wave measurements were able to be measured (Table 10). Therefore, the ultrasonic data statistics are not as reliable as the seismic field data statistics. B. MAJOR CONCLUSIONS Two major conclusions can be made from this study. First, snll scale seismic field measurements for determining velocity anisotropy in the field by the Q-ellipsoid method appear to be more reliable than measuring single land samples ultrasonically or by using thin-sections. This conclusion is based on the results for the Compeau Creek Gneiss from Sugar Loaf, Marquette, Michiganand for the Flinton Group (pelitic schist) from Marble lake, Ontario, Canada. Four reasons may possibly account for the results at Sugar Loaf and Marble lake. Major fracturing in the outcrop and slight heterogeneity may be two of the reasons. The hand samples were collected specifical- ly without major fractures in order to be measured ultrasonically. Also, the hand samples may have been collected from areas which were either homogeneous or heterogeneous on a small scale while the seismic field measurements averaged together areas with varying degrees of heterogeneity. It is also possible that in situ stress may be a contributing factor. But this is difficult to evaluate. At Sugar Loaf, specifically, the disagreement may also be related to large grain size at the ultrasonic level which may interfer with the ultrasonic 55 signals and which would also result in fewer grains being sampled. The second conclusion is that foliation may not necessarily be the dominant controlling factor for determining the orientation of velocity anisotropy. Velocity anisotropy can be caused by any number of factors such as stress fields, fracture orientations, structural orientations, and preferred grain orietations. The foliation at Cross Lake and Sugar Loaf showed good correlation with the major axes of the least squared Q surfaces (i.e. the major axes were parallel to the foliation plane). Marble Lake, however, showed poor correlation between the seismic field and ultrasonic velocity data. At Marble Lake, the least squared Q surface orientation for the seismic field data was approximately perpendicular to that predicted by Postma's layering model and to that observed ultrasonically. The Q surface may be reflecting the presence of isoclinal folds found in the Marble Lake area where the foliation is parallel to the fold axes (Meen, l9h2, p. 25 and Map No. 51d). As a final observation, it was noticed that the ultrasonic veloci- ties tend to be faster than the small scale seismic field velocity measurements (Table 6 and 11). This observation may be due partly to material dispersion of the body waves because of large differences in frequencies used for the seismic and ultrasonic velocity measurements. Fracturing may also be a major factor. A greater amount of fracturing in the outcrop would decrease the elastic modulus, thus reducing the velocity as compared to that for the hand sample. The collecting of the hand samples may also be a factor. The outcrop may be composed of different areas with greater or lower elastic moduli (i.e. slightly heterogeneous). As a whole, the small scale seismic velocity 56 measurements will average these areas together. Therefore, a hand sample collected from an area with a comparatively large elastic modulus as compared to the outcrop as a single unit would tend to have higher velocities. VII. RECOMMENDATIONS FOR.FUTURE STUDY For future investigations, permanent hard copy records, photographs, ink recordings, etc. of each signal should be recorded for further study at a later time. The signals could then be compared with each other to select the travel times for each wave type more consistently and accu- rately. Also, fer each geophone orientation, signals for polarization pairs (i.e. compression, rarefaction: 180 degree phase change) should be recorded. Later, the signals can be compared with each other to check for reversals (180 degree phase change). By comparing the reversals, the P-wave travel times can be determined.more readily and.accurately. It is also recommended that an improved method of anchoring the target be found. In this study, the target became loose with repeated blows of the hammer, thus reducing the effectiveness of the target. Because of this, additional targets (rock faces) ind to be used to measure each wave type. The use of several targets instead of only one can introduce errors in the final determination of the measured Q values. Therefore, the use of only one target will remove this source of error and give a more accurate determination of the measured Q values. Also, a more detailed study of an area should be made to compare the structural geology with the least squared Q surface, to further investigate the effects of structural components on the orientation of the least squared Q surface. 5? APPEN DI APPENDIX A GEDIOGIC SUMMARY OF EACH STUDY AREA 1. Marble lake In the Marble Lake area, three groups of rocks were found: marbles , metavolcanics , and metasediments. The metavolcanics are the oldest (1310 1 15 m.y.) and are mafic to felsic in composition. The marbles lie in a belt trending northeast bounded on the north by gneiss and metavolcanics and on the west and south by metavolcanics. The marbles also lie confombly over the metavolcanics. After the marbles were laid down, the gneisses were intruded into the area. later, these rocks were uplifted to form open folds trending to the northeast. The Flinton Group (1250-1050 m.y.) was then unconformably deposited over the metavolcanics , marbles , and gneisses in a continental or shal- low marine environment. The Flinton Group consists of mica schists, marbles , sulfide bearing pelitic schists with or without graphite, calc- schists, and quartzite- or marble-pebble metaconglomerate. There is also a metamorphic facies orange eastward from chloritoid-staurolite to staurolite-Iqanite. later, the Flinton Group was uplifted to form a narrow band of isoclinal folds with northeast trending fold axes. The axial planes dip steeply to the northwest. The Marble lake area thus underwent three stages of metamorphism: first, contact metamorphism; then lower to mid-amphibolite facies regional metamorphism: and then retrograde metamorphism. 58 59 The outcrop which was studied between Marble Lake and Hill lake consisted of the Flinton Group. The foliation trended N 55 E with a 70 degree dip to the northwest (Meen, 19142, p. 25 and Map No. 51d, Grimsthorpe-Kennebec area) . 2. Cross Lake In the vicinity of Cross lake, there are two narrow bands of biotite-hornblende schists between masses of Gross lake biotite granite gneiss. There is a distinct northeast lineation in both groups of rocks caused by the parallel alinement of elongated quartz or feldspar grains in the gneiss and by hornblende needles in the schist. The schist is thinly laminated which may suggest that they were originally tuffs. But, this is not for certain. The laminated layers have a northeast trend with southeast dips. The outcrop under study consists of biotite-hornblende schists with thinly laminated layers trending northeast with a 50 degree south- east dip (Smith, 1956, Map No. 1956A). The lineation trends slightly farther northeast than the lamination and plunges five degrees to the northeast (Smith, 1956, Map No. 19564»). 3. Sugar Loaf Gair and Thaden (1968, p. 18) named the gneiss found in the northern part of the Marquette Quadrangle the Compeau Creek Gneiss. The Compeau Creek Gneiss is Lower Pre-cambrian and is typically light colored, foliated, tonalitic, and granodioritic. North of the Marquette syncli- norium, the gneiss consists mainly of the dark, chloritic, biotitic, and hornblende varieties. The dark layers in the gneiss may represent relict sedimentary bedding, but Gair and Thaden (1968, p. 26) defined part of 60 the gneiss as siliceous igneous material which intruded into the Mona Schist. Throughout the Compeau Creek Gneiss, there is a general east-to- east-southeast trend of foliation and layering. The trends generally dip steeply to the north. Folds are rare, but small folds in the foliation of isolated outcrops can be found with amplitudes and lengths of only a few feet or less. There are also isolated outcrops with foliation and layering trending fro. the southeast to nearly south. Also, nuch of the biotite and hornblende grains have preferred alinement parallel to the layering. The origin of the Conpeau Creek Gneiss is not well known. Some of the gneiss appears to be for-ed has the intrusion of felsic nagna or solutions into the Mona Schist. But, a substantial portion of the gneiss seens to be the result of the intrmion of siliceous igneous material into one or acre types of pre-existing layered or foliated country rock. The pro-existing country rock was netanorphosed up to the amphi- bolite facies before the intrmion of the siliceous igneous material. This occurred during pre-Anilike tine. During post-Anisike and pre-Ke- weenawan tine, widespread orogeny and netanorphisn took place below the level of the alphibolite facies. Retrograde netanorphisn also occurred in some of the less stable minerals. The outcrop under study is bounded on the east and the southwest by faults. There are also snall qmrtz veins with a general trend in approxintely the same northwest trend as the foliation. The quartz veins range up to a few inches in thickness. The foliation direction trends to the northwest and is approximately parallel to County 61 Highway 550. Also, in the general area, there are joints trending north with a 75 degree dip to the west (Gair and Thaden, 1968, Plate 1). Transit Position Location Stadia Break in Point Turning Point #0H #3v #2 #1” #1H #lv #2 Target Structure Transit Pen 0 #2 Transit Pan 3 Turning Point Road.Sign Road.Sign Turning Point Transit Pan 5 #3 APPENDIX B SURVEY DATA Angle Angle* Marble Lake (Long Array) Structure 265.758 255-633 189.975 311.567 310.150 360.000 125.502 360.000 5-633 16.921 136.392 3-379 139.183 139.088 360.000 82.983 80.779 0.000 6.279 201.729 237.596 229.908 202.583 251.813 72.917 269.038 -l0.083§5'§ 1.925 +7.917(5'g 3.510 +3e5l7(5' 2.160 +1.550(5' 0.212 -6.000E5' 0.725 +1.533 7' 3.150 +0.199g5'; 0.650 +0.350 5' 2.700 -1.500(5') 1.670 -0-533 5' -0.067 5' +0.050 5' -1.067 5' +0.608 5' +0.750 5' 1.090 0.885 2.360 2.525 0.610 0.900 +0.650 +0.050 5' 5.080 5' 5.600 +6.933(5') 0.000 +0.77526'; 2.100 +0.900 0' 0.371 -o.750(5') 2.005 -0.325(5') 2.180 -0.958(5'; 1.810 -1.525(5' 1.670 -0.117(7') 0.376 -0.100(5') 0.886 62 105.98 65.71 6.03 21.98 95.98 101.73 83.51 50.88 05.01 26.9? 71-93 76.95 100.50 109.30 56.91 150.83 171.90 121.03 65.22 11.31 62-33 66.05 55.16 50.88 11.06 27.01 Horizontal Vertical Transit Corr.** Vert. Reading Reading Dist. +10.60 +0.03 +0.17 -2.30 +1.96 +0.25 +0.51 -1-33 -0.02 -0.03 +0.06 -1.03 +1.09 +1e95 -l3.85 +1.76 +1.35 +10.61 +0.58 +0.08 -0.82 -O.38 -0.92 -1-35 -0.63 -0.05 Horiz e Dist. 105.13 65.59 6.06 21.85 95.96 101.73 83.51 50.87 05.01 26.97 71.93 76.90 100.09 109.33 55.20 150.82 171.90 120.15 65.22 11.30 62.32 66.05 55-15 50-87 11.00 27.01 63 Transit Stadia Horizontal Vertical Transit Corr.M Vert. Horiz. Position Location Angle Angle* Reading Reading Dist. Dist. 1. Marble lake (Long Arm , cont'd.) 2 Turning 208.025 +0.350( 5' 2.700 83. 51 +0. 51 83.51 Point Road 81871 211+0975 *006‘2 5' 2.700 83051 +0.9} 83e50 #6 82.900 +0.083 5' 0.650 101.73 +0.20 101.73 Transit 82.183 +0.908 5' 5.350 163.05 +2.58 163.02 Pen 1 1 Structure 0.000 +7.883é5'; 3.500 105.67 +10.93 100.67 TranS1t 53.621 ~00975 5' 5.360 163.35 +2e78 163032 Pen 2 2. Marble lake (Short Array) #1 0.000 -3.002 8' 1.890 57.50 -0.37 57.00 #2 5.208 -2.667 8' 0.990 30.10 -2.26 30.11 #3 83.806 40.000 9' 0.655 19.96 -1.39 19.96 #0 115.592 +0.000 8' 0.502 16.52 -0.90 16.52 #5 137.383 +0.00E11' 0.852 25.97 -1.92 25.97 #6 165.029 +0.00 12' 1.020 31.09 -2.06 31.09 #7 197.238 -7.05038' 1.005 31.58 -0.99 31.32 Target 1 283.850 +0.000 9' 0.535 16.31 -1.29 16.31 Target 2 270e750 -Oe00 12' 00592 18.“ -2e12 18.00 Target 3 282.783 +0.00 11' 0.583 17.77 -1-82 17.77 Target 0 278.883 -l.7l 11' 0.600 19.09 -2.10 19.09 Target 5 2780667 -1e87 10' 0e620 18e89 -2ell" 18088 30 Cross Lake 1 #1 279.902 +1.910 0' 1.502 05.75 +3.05 05.72 #2 275.075 +2.255 0' 1.100 33.50 +2.80 33.07 #3 269.096 +3.300 0' 0.807 25.79 +3.01 25.76 #0 263.833 +3.300 0' 0.600 19.08 +2.66 19.05 #5 196.850 +3.332 0' 0.307 10.55 +2.10 10.52 #6 139.550 +6.515 0' 0.770 23.32 +0.17 23.16 #7 130.233 +3.925 0' 1.300 00.75 +0.31 00.66 Turning 229.783 410.592 1+. 1.325 39e08 +10015 37083 Point 2 Turning 80.617 +16.100(7') 1.325 38.80 +10.15 37.28 Point Target 1 80.150 +15.000 7' 1.000 01.21 +10.06 39.81 Target 2 815.817 +1ue758 7' 14390 00.97 +Oe83 39.62 Target 3 80.192 +15.000 7' 1.380 00. +10.16 39.08 60 ** The number in the parentheses is the height at which the transit is sited on the stadia. The transit reading is corrected to obtain the true distance and then converted to meters. and horizontal distances are also expressed in meters. The vertical Transit Stadia Horizontal Vertical Transit Corr.“ Vert. Horiz. Position Location Angle Angle* Reading Reading Dist. Dist. he Sugar loaf Turning 0.000 +0.000(9') 1.120 30.10 -1.16 30.10 Point Steel Plate Target 2%.000 40.000 6. 0.030 1.07 -0.20 1.00 Target 1 130e500 +0.000 5' 00035 1.07 +0.00 1.07 Target 2 58.000 +0.000 2' 0.083 2.53 +0.91 2.53 Target 3 210.000 +0.000 7. 0006‘ 1095 -Oe55 1e95 Target 0 2.500 +0.000 3' 0.132 0.02 +0.53 0.02 Target 5 130.006 +0.000 5' 0.112 3.01 -0.10 3.01 Target 6 12100006 +0.000(6' 0e155 4.72 ~0e20 0.72 Steel Plate Target 0.000 +3.650E8'g 1.105 30.83 -1.23 30.76 Transit 258.867 -l9.950 6' 2.225 63.75 +21.05 59.92 Pan 3 Turning 0.000 +20.083(5') 2.370 67.67 +23.68 63.39 Point #1 32.125 1+0.00(11' 3.700 113.99 -1.69 113.99 ‘#2 26.267 +0.000(5' 2.810 85.65 +0.03 85.65 #3 19.188 +0.0é0.6' 1.870 56.99 +1.35 56.99 #0' 2.625 +0.0 0.5' 0.900 27.03 +1.36 27.03 #5 299.271 '+10.062(1' 0.855 25.63 1+5.86 25.20 ‘#6 208.571 1+0.02-0.5' 1.088 33.16 1+1.69 33.16 #7 230.233 +0.0 12.1' 2.150 65.53 -l.80 65.53 BIBLIOGRAPHY BIBLIOGRAPHY Bennett, H. F., A simple seismic model for determining principal anisotropic direction, J. Geophys. Res., 77, 3078-3080 , 1972 . Gair, J. E., and R. E. Thaden, Geology of the Marquette and Sands Quadrangle Marquette County Michigan, USGS, 197, 1968. Jamieson, J. D., and H. Haskins, The measurement of shear wave velocities in solids using axially polarized ceramic transducers, Geophysics, 28, 82-90, 1963. Meen, V. B., Geology of the Grimsthorpe-Barrie area, Ont. Dept. Mines, 51, pt. 0, 1902. Moore, J. M., and I. Hutchean, The tremolite isograd near Marble Lake, Ontario, Can. J. Earth Sci., 10, 936, 1973. Nye, J. F., Physical Properties of Crystals, London: Oxford, Clarendon Press , 19570 Postma, G. W., Wave propagation in a stratified medium, Geophysics, 20, 780-806 g 1955. Prather, B. W., Seismic anisotropy in the Vaughan Lewis Glacier Juneau Icefield1¥Alaska,_l969, Michigan State UniVersity: Unpublished Masters Thesis, 1972. Smith, B. L., Geology of the Clarendon-Dalhousie area, Ont. Dept. Mines, 65, Pt. 7, 1J6, 1956. Tilmann, S. E., and.H. F. Bennett,.A sonic method fer petrographic analySiS, Jo GeOEhySe ReSe' 78, 8063-8069, 19733. , Ultrasonic shear wave birefringence as a test of homogeneous elastic anisotropy, J. Geophys. .1125}! 78’ 7623-76299 1973b- 65