Low-frequency dispersion computations by compound-matrix propagation

Abstract

The basic propagating waveguide modes in underwater acoustics have lower cutoff frequencies. As the frequency is decreased below the cutoff frequency, the modal horizontal slowness typically becomes complex and tends to infinity while the modal wave number tends to a nonvanishing complex number. In certain laterally homogeneous fluid–solid media, there also exist slow P−SV modes for which the horizontal slowness tends to infinity along the real axis while the horizontal wave number tends to zero as the frequency tends to zero. The flexural wave for an ice sheet on top of the ocean is a particular example. To investigate the low-frequency behavior of the modal horizontal slowness for these kinds of modes, computations of dispersion curves by propagator techniques are attempted for media composed of homogeneous fluid and solid layers. However, loss of numerical precision by cancellation effects appears for the needed elements of the solid-layer compound-matrix propagators. Guided by theoretical results for the asymptotic growth of these elements, cancellation-free expressions are derived. The harmful contributions causing loss of numerical precision at low frequencies are eliminated analytically. As an application of the new expressions, a numerical case study is performed. Improved results on low-frequency asymptotic expansions of the modal slownesses are obtained.