Nonlinear inversion of seismic amplitude variation with offset for an effective stress parameter

Abstract

Effective stress estimates play important roles in reservoir characterization, for instance, in guiding the selection of fracturing areas in unconventional reservoirs. Based on Gassmann’s fluid substitution model, we have set up a workflow for nonlinear inversion of seismic data for dry rock moduli, fluid factors, and a stress-sensitive parameter. We first make an approximation within the fluid substitution equation, replacing the porosity term with a stress-sensitive parameter. We then derive a linearized reflection coefficient as a function of a stress-parameter reflectivity and reexpress it in terms of elastic impedance (EI). An amplitude-variation-with-offset (AVO) inversion workflow is set up, in which the seismic data are transformed to EI, after stacking within five incidence angle ranges; these are then inverted to determine the stress-sensitive parameter. The two-step process involves two inversions with significantly different properties. The first is a model-based least-squares inversion to estimate EI; the second is a more complex nonlinear inversion of the EI for a set of unknowns including the stress-sensitive parameter. Motivated by an interest in hybridizing AVO and full-waveform inversion (FWI), we set the latter step up to resemble some features of a published AVO-FWI formulation. The approach is subjected to synthetic validation, which permits us to analyze the response and test the stability of the workflow. We finally apply the workflow to real data acquired over a gas-bearing reservoir, which reveals that the approach generates potential indicators of fluid presence and stress prediction.