Approximate 3 D Body - Wave Synthetics for Tomographic Models

We present a new method of generating analytical synthetics for tomographic-style models. These models are perturbations to a 1D layered model involving changes in block velocities producing 3D images. The procedure is broken into three steps: (1) construction of ray paths for the reference 1D layered model, (2) generation of perturbed paths and the construction of 2D synthetics in the plane containing the source and receiver, and (3) addition of out-of-plane contributions (2D) from virtual receivers weighted by diffraction operators. In step 1, the ray paths reflecting from the various interfaces are established with ray parameter (po) and travel time (to). Next, these values are corrected after adding the velocity perturbations where ray segments in faster blocks grow relative to slower blocks. This new set of ray parameters can be used to generate 2D Cagniard-deHoop synthetics or WKM synthetics. Contributions from virtual receivers at neighboring azimuths are added by convolving with diffraction operators that are defined by the source duration and travel time to the 3D structure. We suggest a particularly simple approximation based on four virtual receivers which produces synthetics in agreement with 3D numerical synthetics.