Elastic wave propagation in inhomogeneous anisotropic media

Plane wave decomposition is a convenient and effective method in the study of wave field. Various complex wave fields can be obtained by using plane wave composition. In this paper, the method of plane wave is used to study elastic wave propagation in inhomogeneous and anisotropic media. The f k transformation is applied to time space domain wave equation in inhomogeneous anisotropic media. As a result, the frequency wave number domain wave equation (Christoffel equation) can be obtained. Using the relation between elastic parameters or its spatial derivatives and Christoffel matrix elements, a method for solving the Christoffel matrix in inhomogeneous anisotropic media is formulated and applied to inhomogeneous TIV as well as inhomogeneous EDA media. The results obtained show that directional derivative of wave amplitude in continuum is negative, so amplitude is reduced, when propagating direction directs to velocity increasing direction; and directional derivative of wave amplitude is positive that means amplitude enhanced when propagating direction directs to velocity decreasing direction. Thus, wave amplitude depends on propagation direction (even in isotropic medium), but does not always attenuate. The conclusion that in continuum wave amplitude attenuates does not apply to all propagation direction.