Low-frequency slow-wave dispersion computations by compound-matrix propagation

Abstract

Slow P-SV modes whose horizontal slowness tends to infinity while the horizontal wave number tends to zero, as the frequency tends to zero, exist in certain laterally homogeneous fluid-solid media. These modes can be characterized by an asymptotic analysis of the dispersion function. Only certain powers of frequency are possible for the asymptotic increase of the horizontal slowness as the frequency tends to zero: −1/3, −1/2, −3/5, and −2/3. In order to investigate the accuracy of the asymptotic predictions, dispersion-curve computations by propagator techniques are attempted for media composed of homogeneous fluid and solid layers. However, numerical precision is lost by cancellation effects for the elements of the solid-layer compound-matrix propagators that are involved. Guided by the asymptotic growth of these compound-matrix elements, cancellation-free expressions are derived for applications to the slow modes at very low frequencies. The harmful contributions causing loss of numerical precision are eliminated analytically. To demonstrate the success, a numerical case study is performed leading to conjectures about the next-to-leading terms in low-frequency asymptotic expansions of the slow-mode modal slownesses.