General elastic wave scattering problems using an impedance operator approach – II. Two‐dimensional isotropic validation and examples

SUMMARY Highly accurate solutions to general wave scattering problems can be calculated using an impedance operator to factorize the wave equation by direction of energy flow. The classical second‐order partial differential wave equation for a heterogeneous region bounded in the vertical direction is recast as a set of two first‐order initial value problems: a spectral expansion converts these to ordinary differential equations, which can then solved to a very high degree of precision. We demonstrate this technique for both P ‐ SV and SH problems and validate our results by comparison with a finite‐difference calculation. In its most straightforward form, when the wavefields inside and outside the heterogeneous region are matched using a common Fourier expansion, the method is computationally expensive; a reformulation in which the coupling is carried out via a boundary integral technique is much more efficient, however.