A description of the floating Ross ice shelf in Antarctica, determined from miscellaneous studies between 1957 and I960, is provided by contoured maps giving values of ice thickness, ocean floor depth, surface snow density, average annual temperature, and average annual snow accumulation. The low surface densities and low average annual surface temperatures encountered in the central part of the shelf are explained by meteorological parameters. The thickness of the ice varies from about 700 meters in the southeastern area of the shelf to about 250 meters near the barrier edge, and it is demonstrated from theoretical strain values for floating ice that the main portion of the shelf must be under abnormally large horizontal stresses which prevent the ice from thinning more rapidly, thus accounting for its presence over such a large area. Snow densities at 40 meters depth, derived from an empirical relation between seismic refraction velocities and densities, vary widely over the shelf areas, and these differences can be explained in part by variations in the strain rates. The horizontal velocity components of the ice particles are obtained from the amount of accumulation and the area of the ‘snowshed,’ on the assumption that elevations are not changing in time. In order for these inferred velocities to conform to observed values near the shelf barrier, considerable melting is required at the ice‐water boundary at the bottom of the shelf. This melting is confirmed by local data and is shown to increase from east to west. Vertical velocities of ice particles with respect to the surface are determined from snow accumulation and strain rates. These velocity components are combined in a numerical‐integration method to allow the ice particle paths to be followed forward or backward in time or in space. The method is illustrated by reference to the area of Little America station, where a 250‐meter hole was drilled in 1957. Ice cores from this hole, which include three large ash layers, have a maximum age of about 4500 years.

The evaluation of finite strain in naturally deformed rocks is restricted by the limited occurrence of good natural strain indicators which are also homogeneous with respect to the matrix. This problem is overcome by establishing the relation between measured finite strain and those physical behaviour characteristics of rocks that are dependent upon the anisotropy resulting from deformation. Accordingly, the strain measured from natural indicators is calibrated against ( degree of preferred orientation, (b) magnetic susceptibility anisotropy, and (r) seismic anisotropy. This _ will permit three approaches to be used independently for the evaluation of strain, provided that a minimal number of actual strains are available. The relation between measured strain and the degree of preferred orientation of layer silicates as revealed by X-ray transmission goniometry is established for a group of fine grained tectonites of dominantly planar fabric which have an average deformation ellipsoid of form 1.6:1 :,0.26. The strains measured from the degree of preferred orientation are in remarkable agreement with those measured from natural strain indicators. The measured deformation ellipsoids for a wide range of strains are also compared to the correlative ellipsoids of magnetic susceptibility anisotropy. The axes of both sets of ellipsoids are coincidental and the shape relationship between deformation and magnetic susceptibility ellipsoids is established by linear regression. Finally, the anisotropy of seismic velocities is determined by measuring the pseudocompressional velocity and two orthogonally polarized pseudo shear wave velocities for each of a minimum of nine non-coplanar directions. The velocity surfaces thus obtained define an elastic or seismic velocity anisotropy ellipsoid, the axes of which are also precisely coincidental with those of the finite deformation ellipsoid. The influence of rock fabric upon seismic velocities is such that for a rock which has undergone a principal finite extension of 135 % and a finite shortening of 65 %, the difference of compressional and shear wave velocities between these two directions is in the ratio 1.26:1 for P waves and 1.33:1 for S waves.

A simple elastic stiffness figure called the Q ellipsoid is derived from the basic equations for elastic waves in anisotropic media. Here Q is the sum of the squares of three velocities for a given direction multiplied by the density. This surface can be used (1) to show that only 18 independent elastic constants are necessary to describe the most general anisotropic case (triclinic), (2) to orient sonically a material through a least‐squares fit of the seismic data, (3) to test statistically for velocity anisotropy, (4) to provide a constraint on velocity measurements, and (5) perhaps to estimate the variation in directional properties of second‐rank tensor properties, such as thermal and electromagnetic properties. In general the measurement of velocity anisotropy may provide a means of estimating petrofabric and structural patterns in the crust and upper mantle and act as a constraint on petrologic models. The method requires measurement of the pseudocompressional velocity and two pseudo shear‐wave phase velocities.

Ultrasonic shear wave birefringence is used as a positive indicator of elastic anisotropy. Polarized shear waves are generated by conversion of a compressional P wave to a shear S wave at a free surface (Jamieson and Haskins, 1963). The P-S conversion technique is preferred over the direct use of AC-cut quartz shear wave transducers because the wave amplitudes are considerably greater in the conversion technique. Even though the P/S wave amplitude ratio for the P-S conversion transducers is 1/80, the P wave has sufficient amplitude for recognition. The rotation of the sample allows identification and measurement of the travel times of two orthogonally polarized shear waves. Relative difference in the two shear wave travel times positively establishes homogeneous anisotropy, even though the sample may be nearly isotropic in the P wave mode. Thus P wave velocity and travel path distance need not be known in order to detect elastic anisotropy. Shear wave birefringence is not restricted to any particular scale, and a minimum of one propagation direction may be used to establish anisotropy. A suite of 20 rock samples of various lithologies was measured according to this technique. All samples were found to be anisotropic. These results point out that elastic anisotropy is probably the rule rather than the exception in describing the elastic behavior of rock materials of hand sample size. It is therefore of interest to determine at which scale, if any, elastic anisotropy is no longer the rule but the exception. The use of shear wave birefringence may aid in answering this question.The theory of elastic wave propagation in a homogeneously anisotropic material (e.g., single crystals) was originally developed by Lord Kelvin in his Baltimore lectures [Kelvin, 1904]. At that time he described the three types of body wave velocity surfaces and the nature of the particle displacement vectors. A more recent treatment of the problem by Musgrave [1954] shows that the particle displacement vectors form an orthogonal set and the two pseudo-shear waves have orthogonal vibrations. Since in the general case the three roots of the velocity equations are different, the two pseudoshear waves will propagate with differing velocities. This phenomenon of two orthogonally polarized time-separated shear waves is referred to in this paper as shear wave birefringence. Shear wave birefringence has been observed in the antarctic ice sheet by Bentley [1964], whose studies show a 1.8% time difference between early SV (vertically polarized shear wave) arrivals and late SH (horizontally polarized shear wave) arrivals over a 12x/2-km refraction line. Bennett [1968, 1972] observed shear wave Copyright (•) 1973 by the American Geophysical Union. birefringence in single ice crystals and ice cores. He also observed that the polarized shear wave amplitude varies as a cosine function of the angle between the polarization plane and the crystallographic c axis in single ice crystals. Shear wave birefringence in rocks of hand sample size has been observed an...

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