We solve the elastic wave equation in spherical coordinates {r,&phgr;,&thgr;} by a high-order finite-difference (FD) scheme. The Earth model and the required fields are defined on a staggered grid, independent in &phgr;, and thus rotationally symmetric with respect to the axis &thgr;=0, &pgr;. This scheme allows us to model P-SV wave propagation in a heterogeneous two-dimensional Earth model. Since a uniform grid spacing in r and &thgr; is used, the maximum depth and epicentral distance that can be modeled is limited. Comparison with seismograms obtained by the Reflectivity Method (RM), and the Direct Solution Method (DSM), demonstrates the accuracy of the FD scheme. We use this algorithm to study the effects of heterogeneities in the core-mantle transition zone, the D″ layer, on long-period P-waves. Long-wavelength topography of a reflector in D″ produces significant focusing and defocusing. Random fluctuations (maximum perturbation ¿10%) in a D″ layer of 300 km thickness produce a wave-field similar to that of a sharp discontinuity only 200 km above the core-mantle boundary (CMB) at the dominant period considered (15 seconds). Maps of global variations of D″ thickness determined with long-period data may therefore be severely biased. ¿ American Geophysical Union 1996