One-way wave equations for seismoacoustic propagation in elastic waveguides

Abstract

One-way or parabolic wave equations for time-harmonic propagation in two-dimensional elastic waveguides are considered. It is shown that the direct application of a rational linear approximation with real coefficients to the elastic wave propagation case results in exponential growth in the numerical solutions. Elementary analysis demonstrates that this kind of approximation does not treat properly the modes with complex wavenumber which can exist in elastic waveguides. A new bilinear square-root approximation with complex coefficients is introduced that accommodates all mode types and leads to stable numerical solutions. In the case of thick elastic layers (such as sea-bottom sediments), this new approximation gives accurate total field prediction. When thin elastic layers (such as ice on the sea surface) are present, however, the method introduces excessive damping to modes with wavenumbers significantly different from a reference wavenumber.