Seismic Anisotropy: a Review of Studies by Japanese Researchers
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J. Phys. Earth, 43, 301-319, 1995 Seismic Anisotropy: A Review of Studies by Japanese Researchers Satoshi Kaneshima Departmentof Earth and Planetary Physics, Faculty of Science, The Universityof Tokyo, Bunkyo-ku,Tokyo 113,Japan 1. Preface Studies on seismic anisotropy in Japan began in the mid 60's, nearly at the same time its importance for geodynamicswas revealed by Hess (1964). Work in the 60's and 70's consisted mainly of studies of the theoretical and/or observational aspects of seismic surface waves. The latter half of the 70' and the 80's, on the other hand, may be characterized as being rich in body wave observations. Elastic wave propagation in anisotropic media is currently under extensiveresearch in exploration seismologyin the U.S. and Europe. Numerous laboratory experiments in the fields of mineral physics and rock mechanics have been performed throughout these decades. This article gives a review of research concerning seismic anisotropy by Japanese authors. Studies by foreign authors are also referred to whenever they are considered to be essential in the context of this article. The review is divided into five sections which deal with: (1) laboratory measurements of elastic anisotropy of rocks or minerals, (2) papers on rock deformation and the origin of seismic anisotropy relevant to tectonics and geodynarnics,(3) theoretical studies on the Earth's free oscillations, (4) theory and observations for surface waves, and (5) body wave studies. Added at the end of this article is a brief outlook on some current topics on seismic anisotropy as well as future problems to be solved. There have been a few recent reviews of seismic anisotropy, such as Kawasaki (1989), Karato (1989), and Takeshita and Karato (1989). The former emphasizes seismological observations, whereas the latter emphasizes deformation of rocks and petrological aspects of anisotropy. 2. Laboratory Measurementsof Elastic Anisotropy 2.1 Elastic constants of single crystals Determination of elastic constants of minerals and rocks is the basis of any studies on seismic anisotropy. Japan has played a leading role in developing technology for measuring the physical properties of material under high temperature and pressure. Collaborations between Japanese researchers and foreign researchers have also been ReceivedMay 19, 1992;Accepted May 20, 1993 301 302 S. Kaneshima fruitful in determining elastic constants. Techniques for measuring the elastic constants of minerals may be separated into two classes. The first measures propagation speeds of acoustic waves through mineral samples in various directions (Fig. 1(a)) and converts them to the elastic constants at the samples. Measuring ultrasonic wave velocities, for instance, Kumazawa determined the elastic constants of single crystal of olivine (Kumazawa and Anderson, 1969), and of orthopyroxene (Kumazawa, 1969). Kasahara and Kumazawa (1969) attempted to find relation between optical and acoustic anisotropies of crystals. The Brillouin spectroscopy method has also been used to measure velocities of elastic waves and to determine elastic constants for geophysically important minerals such as /3 (beta) phase of Mg2SiO4 (e.g., Sawamoto et al., 1984), y (gamma) phase of Mg2SiO4 (e.g., Weidner et al., 1984), and MgSiO3 perovskite (e.g., Yeganeh-Haeri et al., 1989). Compared with the first technique using body waves based on the approximation of geometrical optics, the second method, called the "resonance technique," directly applies the wave equation to the oscillation of samples. The resonance technique measures the eigenfrequencies of free oscillation (resonance) either of parallelepiped (e.g., Ohno, 1976) or of spherical samples (Suzuki et al., 1992) and converts them to the elastic constants using the variational principle. For instance, Oda et al. (1988) determined the elastic constants of spherical samples of anisotropic crystals applying the mathematical formulation of Mochizuki (1988 a). Details of the spherical resonance Fig. 1. (a) Variation of the quasi-P (qP) and the two quasi-S (qS1 and qS2) body-wave phase velocities for propagation in three ((001), (100), and (010)) orthogonal planes of symmetry of crystalline olivine. In each plane, qS1 and qS2 correspond either qSH or to qSV, where qSH and qSV represent the shear waves polarized nearly parallel and perpendicular to the propagation plane, respectively. (b) Schematic figure of shear wave splitting. A shear wave travelling through an anisotropic medium splits into two orthogonally polarized (quasi-)shear waves with different speeds (from Nicolas and Christensen (1987)). J. Phys. Earth Seismic Anisotropy: A Review of Studies by Japanese Researchers 303 technique are given in a recent article on measurements of elastic constants of olivine by Suzuki et al. (1992). Mochizuki (1987 a) presented a formula which can be used for resonance of parallelepiped samples. Aside from the papers cited above, a number of measurements have been performed for various single crystals. The contributions by Japanese researchers to the determination of elastic constants of minerals are discussed in a recent review article by Anderson et al. (1992). 2.2 Elastic anisotropy of polycrystalline rocks The elastic constants of polycrystalline rocks are determined by the first of the above class of techniques for measuring body wave speeds. Kasahara et al. (1968 a, b), analyzed the petro-fabric of dunite samples which are composed mostly of olivine, and also measured the compressive and shear velocities of ultrasonic waves in various directions through the samples. They observed anisotropy-related phenomena, indicating azimuthal dependence of body wave propagation speeds as well as splitting of body shear waves. They also confirmed that the elastic anisotropy of dunite is closely related with the preferred alignments of a- and b-axes of olivine crystals (LPO) in the directions parallel and perpendicular to the lineation, respectively. Elastic anisotropy of amphibolite, a typical metamorphic rock in the lower crust, was measured and related to the LPO of hornblende by Siegesmund et al. (1989). For upper crustal rocks such as granite, on the other hand, experimental studies are mainly on the anisotropy due to preferred alignments of cracks. Intensive measurements of the elastic constants of granite have been performed, confirming the presence of three sets of orthogonal cracks, which are commonly known as "rift" and "grain" in quarries (e.g., Sano et al., 1992; Kudo et al., 1987). Since Nur and Simmons (1969) showed azimuthal variation of seismic wave speeds and splitting of shear waves on uni-axially stressed samples, seismic anisotropy of crustal rocks has been related to dilatancy, which is the stress induced opening of cracks before failure of rocks. A number of studies have been performed on anisotropy caused by preferred alignments of microcracks for crustal rocks like granite under deformation due to non-hydrostatic stress (e.g., Soga et al., 1978; Takahashi et al., 1984). The experiment by Soga et al. (1978) was on the velocity anisotropy of uni-axially stressed samples, whereas Takahashi et al. (1984) examined the same phenomenon in triaxially stressed rock samples. Such studies always need a theory for the computation of effective elastic constants of materials that include cracks. The theories are classified into two approaches. The first one applies scattering theory under the assumption of a long wavelength of the incident waves compared with the size of the cracks, and requires the distribution of crack to be sparse so that interaction between the cracks can be neglected (e.g., Hudson, 1981). The second class of methods evaluates the elastic energy due to the presence of an elliptical inclusion under a static stress field (Eshelby, 1957). Using the second approach, Nishizawa (1982) presented a numerical method to compute the effective elastic constants of isotropic materials including non-randomly aligned cracks, which can be applied even to dense distributions of thick cracks. Nishizawa and Yoshino (1991) attempted to extend Nishizawa's method to the case of crack alignment in generally anisotropic materials. Vol. 43, No. 3, 1995 304 S. Kaneshima 3. Deformation of Rocks and the Origin of Seismic Anisotropy: Implications for Geodynamics 3.1 Origin of seismic anisotropy As described in the last section, mantle and crustal rocks are usually anisotropic. This means that if elastic anisotropy of in situ rock is uniform within a large enough volume, it can be detected through seismological observations. The anisotropy of in situ rocks has great importance for our understanding of geodynamics. The mechanisms which cause elastic anisotropy of in situ rocks include: (1) lattice preferred orientation (LPO) of the minerals composing the rocks, (2) preferred orientation of pockets of melts in partially molten materials, and (3) preferred orientation of brittle tensile cracks filled with liquid such as water. LPO of olivine is widely believed to be the dominant cause of upper mantle anisotropy and reflect the geometry of flow or stress orientation depending on the ambient condition such as temperature and strain rate. Brittle tensile cracks play a principal role in the upper crust as they are predominantly aligned parallel to the maximum compressive stress, while they are unlikely to pervade in the lower crust and mantle. Partial melting may prevail in the part of the asthenosphere where the geotherm is close to the solidus, and may exist in the mantle beneath island arcs,