A two-way parabolic equation for elastic media

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Abstract
The parabolic equation (PE) method is extended to handle wave propagation and scattering in range‐dependent elastic waveguides, which are approximated by a sequence of range‐independent regions. The two‐way elastic PE involves an efficient PE‐based scattering method for computing reflected and transmitted fields at the vertical interfaces separating range‐independent regions. The one‐way elastic PE is used to propagate the outgoing and incoming fields through the range‐independent regions with two‐way range marching. In addition to providing the backscattered field, the two‐way PE provides a correction to the outgoing field. The self‐starter is generalized to handle a source in a solid layer.

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