Ultrasonic shear wave birefringence as a test of homogeneous elastic anisotropy

Abstract

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...

A Sonic Method for petrographic analysis

“…The baraboo quartzite, a Grenville marble, and a plastically deformed granitic boulder -were analyzed according to the Q ellipsoid technique. The measuring apparatus used for determining the elastic velocities is described by Tilmann and Bennett [1973]. In addition, optical petrofabric analyses were performed on the quartzite and marble.…”

Shear‐wave velocity anisotropy in sedimentary rocks: A laboratory study

“…From time to time, we have seen a resurgence in interest concerning velocity anisotropy in rocks. In the early 1970s, a number of studies dealing with velocity anisotropy in rocks were reported (e.g., Nur and Simmons, 1969;Christensen and Ramananantoandro, 1971;Gupta, 1973;Tilmann and Bennett, 1973;Todd et al, 1973;Bonner 1974). Most of these studies were on low-porosity crystalline igneous rocks.…”

Laboratory measurement of elastic anisotropy on spherical rock samples by longitudinal and transverse sounding under confining pressure

“…The anisotropy of rocks may be caused by: (1) lattice (or crystallographic) preferred orientation (LPO), (2) preferred morphological or shape-preferred orientation of inclusions (SPO) [1,2], (3) preferred orientation of micro-cracks/pores, (4) thin layers of isotropic materials with different elastic properties [3], or (5) the combination of the above mentioned parameters. The anisotropy of mechanical properties also depends on the stress level and on the system of acting forces -uniaxial force, confining pressure, etc.…”