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.

Deep seafloor arrivals: An unexplained set of arrivals in long-range ocean acoustic propagation

“…The point of this paper is that the arrival structure on the seafloor geophone is distinctly different from the arrival structure on a hydrophone 750 m above the seafloor. Future analysis will include modeling that considers the additional elastic waves ͑shear and interface waves͒ and scattering from seafloor roughness and sub-seafloor heterogeneity ͑Collins, 1989Stephen and Swift, 1994;Swift and Stephen, 1994;Wetton and Brooke, 1990͒.…”

Discrete Transparent Boundary Conditions for Wide Angle Parabolic Equations in Underwater Acoustics

“…Finally, we add a small remark on the coupling of the SPE with an elastic parabolic equation (EPE) for the sea bottom [13,22,47]. In [36,37] a TBC for this coupling was derived.…”

The One-Way Wave Equation: A Full-Waveform Tool for Modeling Seismic Body Wave Phenomena

“…The bilinear approximation is modified by replacing the real coefficients with complex coefficients. In [58] the authors show that their bilinear approximation not only propagates the complex modes within the waveguide more accurately, but also allows for improved numerical stability of ordinary waves. Unfortunately, all of the above approaches are limited when applied to elastic media.…”

“…The coefficients a 0 , a 1 and b 1 are real and chosen to fit optimally the square-root function. In [58] the authors demonstrate that the real coefficients of this rational linear approximation improperly treat the evanescent waves that can propagate within waveguides. Evanescent waves have complex wavenumbers and so their amplitudes can either grow or decay exponentially with propagation distance.…”

“…Growing evanescent waves are particularly problematic for numerical algorithms, as their amplitudes may overshadow the signals of interest. To correct this problem [58] modify the 'bilinear square-root' approximation (8) and extend this method to elastic waves. The bilinear approximation is modified by replacing the real coefficients with complex coefficients.…”