Seismic Wave Velocities in Rocks I : Modeling Heterogeneous Media and their Elastic Wave Velocities

On the basis of the viewpoint that rocks are typical random heterogeneous media consisting of different minerals and micro-cracks, modeling techniques for predicting seismic wave velocities in crystalline rocks are reviewed. The term seismic velocity is sometimes unclear in its physical meaning in real media that contain heterogeneity and anisotropy. The physical meaning of seismic velocity is first discussed on the basis of wave fields in heterogeneous media. Elastic constants and phase velocity in an anisotropic medium are then introduced. Further, phase velocity and group velocity in transverse isotropy are discussed because transverse isotropy is considered to be a realistic case when we consider seismic wave propagation in the Earth's crust. In most cases in actual field observations, rocks are considered to be homogeneous materials because the wavelength of seismic velocity is always longer than the scale length of heterogeneity in rock. It is thus important to understand techniques used to model the macroscopic elastic properties of rocks, which are microscopically heterogeneous. Finally, modeling techniques are shown for anisotropic rocks having lattice-preferred orientations and micro-cracks. These techniques are useful for interpreting field seismic observations, as well as for interpreting experimental results in the laboratory.