ELASTIC-WAVE UP DOWN DECOMPOSITION IN INHOMOGENEOUS AND ANISOTROPIC MEDIA - AN OPERATOR APPROACH AND ITS APPROXIMATIONS

A structural operator approach to the up/down decomposition of elastic waves in inhomogeneous and anisotropic media is presented. First, the up/down decomposition is carried out; next, a decomposition of the wave field into its polarization constituents is worked out. The procedure is discussed in detail for the class of orthorhombic media and includes lateral variations. The high-frequency approximation to the operator approach is shown to be amenable to matrix manipulations in the horizontal Fourier transform domain. Two-level parabolic approximations are carried out to find sparse matrix (finite-difference) representations of the relevant operators. Finally, the space-time peculiarities and artifacts associated with the parabolic approximation to the particle velocity of the wave motion generated by a point force in a homogeneous and isotropic solid are discussed.