Parametrization of acoustic boundary absorption and dispersion properties in time-domain source/receiver reflection measurement

Abstract

Closed-form analytic time-domain expressions are obtained for the acoustic pressure associated with the reflection of a monopole point-source excited impulsive acoustic wave by a planar boundary with absorptive and dispersive properties. The acoustic properties of the boundary are modeled as a local admittance transfer function between the normal component of the particle velocity and the acoustic pressure. The transfer function is to meet the conditions for linear, time-invariant, causal, passive behavior. A parametrization of the admittance function is put forward that has the property of showing up explicitly, and in a relatively simple manner, in the expression for the reflected acoustic pressure. The partial fraction representation of the complex frequency domain admittance is shown to have such a property. The result opens the possibility of constructing inversion algorithms that enable the extraction of the relevant parameters from the measured time traces of the acoustic pressure at different offsets, parallel as well as normal to the boundary, between source and receiver. Illustrative theoretical numerical examples are presented.