Numerical calculations of elastic waves in laterally inhomogeneous media

In most laterally inhomogeneous crustal structures, waves propagated away from the source can be constructed to first order without knowledge of any backscattered radiation. If this approximation is used, the second-order boundary-value problem for elastic waves in isotropic inhomogeneous media can be reduced to a first-order initial-value problem in space. Numerical solutions can then be economically obtained. Calculations for plane-layered structures agree quantitatively with exact solutions. Waves in more complicated structures agree qualitatively with intuition, observational experience, and model experiments.