Recent studies of deep mantle structure indicate strong heterogeneity. To conduct high-resolution waveform modelling of these structures, we have developed a new method to construct 2-D synthetics directly from block-style tomographic models. Unlike the WKBJ approximation, which utilizes rays overshooting and undershooting receivers, our method (WKM approximation) uses rays that arrive at the receiver. First, the ray paths from the 1-D layered reference model are used to localize each ray segment, where the anomalous velocities are applied by overlay, as in tomography. Next, new p_i (t_i) (p_i ray parameter, ti traveltime) are computed to satisfy Snell’s law along with their numerical derivative (δp/δt), which is used to construct a synthetic seismogram similar to the WKBJ method. As a demonstration of the usefulness of this method, we generated WKM synthetics for the D″ region of high velocities beneath Central America based on Grand’s tomography model. Reasonable fits to broad-band data are obtained by condensing his distributed anomalies into his lowermost mantle layer; such a 2-D model predicts synthetics containing a laterally varying S_cd triplication similar to observations
