Inversion of Apparent Attenuation and Phase Velocity to Determine Scattering Parameters

Abstract

Summary We invert apparent attenuation in order to determine the scattering power spectrum. Examples are given illustrating this general inversion procedure including Wu's (1982) single-scattering theory for acoustic waves, and Lerche & Petroy's (1987) mean-field scattering model of both compressive and shear-waves by fluid-filled fractures. Frequency dependent phase velocity and attenuation factors for both compressive and shear-waves provide improvements in the inverse methods for separating intrinsic and apparent attenuation factors. In the cases where only total attenuation factors (phase velocities) are available, phase velocities (attenuation factors) can be determined by using causality considerations. For a small degree of attenuation per unit wavelength travelled approximate solutions provide relatively simple expressions connecting phase velocity and attenuation. If both phase velocity and apparent attenuation factors are measured for compressive and/or shear-waves, then the Kramers-Kronig causality relations provide consistency requirements which must be met. the non-linear nature of these causal requirements is used to explore an inverse method for separating intrinsic and apparent attenuation factors. the non-linear connections of (1) total attenuation to wave phase speeds, and (2) apparent attenuation to intrinsic attenuation, can be used to determine intrinsic properties of the propagation characteristic of the medium.