Reflection coefficient frequency-dependent inversion of a planar interface with spherical waves: Using critical and post-critical angles

Abstract

As a zero-order approximation of spherical wave theory, plane wave theory based on the Zoepprtizs equations and various linear approximations has been widely used in seismic exploration, such as prestack inversion, deconvolution and Q compensation. Since localized sources excited in field acquisition usually produce spherical wavefronts, the plane wave approximation fails to correctly utilize post-critical information and frequency-dependent characteristics have been completely neglected. Unlike conventional prestack inversion using multiple angles, the existence of frequency dependency makes the inversion using reflected record of a single angle possible. Therefore, the feasibility of frequency-dependent inversion of a planar interface using one angle is analyzed and investigated. A strategy of choosing frequency-band in frequency-domain inversion is given by fitting the geometric distribution of reflection coefficients on a complex plane. The sensitivity, resolution matrix and objective function are adopted to analyze the coupled relationship between different parameters and to determine the parameters to be inverted. Combining a global optimal algorithm, the effectiveness of frequency-dependent inversion is verified using synthetic data and cross-well seismic data. The velocity and density parameters are well-inverted, especially when the data of critical offset is included. Moreover, the inversion uniting frequency-dependency with multiple angles offers more accurate estimations for both density and velocity parameters.