SCATTERING OF ELASTIC-WAVES FROM DEPTH-DEPENDENT INHOMOGENEITIES

Scattered pulse shapes are studies by modeling inhomogeneities as a sequence of infinitesimally thin homogeneous layers. With oblique incidence of plane P of SV waves, the reflected-converted-transmitted waves are obtained by taking the calculus limit for the sum of primary interactions of the incident wave with all layer boundaries. The resulting scattered waves thus present themselves naturally in the time domain. The method is accurate when compared with methods in which higher-order boundary interactions are also retained (i. e. Haskell methods and an adaptation in the time domain which also keeps all multiples). In specific studies of P-waves incident (up to 30 degrees away from the vertical) upon a 5 km thick crust-mantle transition, between materials having impedance ratio 1:2:8, the scattered pulse shapes are given adequately by the theory, for the passband of short-period seismometers. The theory remains remarkably accurate even for long periods, being in error by only 8 percent at zero frequency.