Propagation and attenuation of sound in a canonical model of shallow water with a thermocline and with a Biot sediment in the bottom

Abstract

Objective is benchmark solution, analytic in internal detail, for testing geoacoustic inversion methods. The water column has two isovelocity layers separated by a narrow thermocline. The bottom is a porous (Biot model) sediment, with an elastic matrix coexisting with a fluid filling the pores; coefficients are frequency independent, slowly varying with depth, and analogous to those in works by Stoll, Badiey, and Chotiros. Source and receiver are in the middle region of the water column. Constant frequency problem formulation has field expressed as a Fourier integral over horizontal coordinates, with a z-dependent kernel having discontinuous slope at source depth. Equations for the bottom region yield ratio of derivative to kernel amplitude at bottom interface, this being a complex function of wave number and frequency. Singularities in kernel at discrete complex values of k correspond to the natural modes, imaginary parts of k are attenuation constants. Simplifying approximations, especially those of perturbation theory, are guided by order of magnitude estimates of dimensionless groups, with the suppositions that the orders of magnitude of propagation frequency, water depth, and propagation distance are 100 Hz, 100 m, and from 2 to 100 km, and that Biot model parameter magnitudes are comparable to known measured values.