P-SV WAVE-PROPAGATION IN THE EARTHS MANTLE USING FINITE-DIFFERENCES -APPLICATION TO HETEROGENEOUS LOWERMOST MANTLE STRUCTURE

We solve the elastic wave equation in spherical coordinates {r, rho, t heta} by a high-order finite-difference (FD) scheme. The Earth model a nd the required fields are defined on a staggered grid, independent in cp, and thus rotationally symmetric with respect to the axis theta = 0, pi. This scheme allows us to model P-SV wave propagation in a heter ogeneous two-dimensional Earth model. Since a uniform grid spacing in r and theta is used, the maximum depth and epicentral distance that ca n be modeled is limited. Comparison with seismograms obtained by the R eflectivity Method (RM), and the Direct Solution Method (DSM), demonst rates the accuracy of the FD scheme. We use this algorithm to study th e effects of heterogeneities in the core-mantle transition zone, the D '' layer, on long-period P-waves. Longwavelength topography of a refle ctor in D'' produces significant focusing and defocusing. Random fluct uations (maximum perturbation +/-10%) in a D'' layer of 300 km thickne ss produce a wave-field similar to that of a sharp discontinuity only 200 km above the core-mantle boundary (CRIB) at the dominant period co nsidered (15 seconds). Maps of global variations of D'' thickness dete rmined with long-period data may therefore be severely biased.