Bayesian amplitude variation with angle and azimuth inversion for direct estimates of a new brittleness indicator and fracture density

Abstract

Estimates of natural fractures or fracture-prone brittleness sweet spots are of great importance for the seismic characterization of fracability and successful commercial production of a shale play. Young’s modulus is commonly considered as a measure of brittleness. However, Young’s modulus may be unsuitable to characterize the brittleness of the organic-rich shale gas reservoirs because it exhibits an inverse relationship to porosity, total organic carbon, and gas saturation. The [Formula: see text] attribute (the ratio of Young’s modulus E to the first Lamé constant [Formula: see text]) is more sensitive than the commonly used Young’s modulus to the organic-rich shale gas reservoirs, making it a sensitive brittleness indicator. We have proposed a novel inversion technique of amplitude variation with angle and azimuth (AVAZ) for direct estimates of the new brittleness indicator [Formula: see text] and fracture density in shale gas reservoirs. Considering a horizontally transverse isotropic model formed by a system of rotationally invariant vertical fractures embedded in an isotropic background, we first derive a linearized PP-wave reflection coefficient as a function of Young’s modulus, new brittleness indicator, density, and fracture density. The new linearized approximation allows us to estimate the brittleness and fracture properties of the reservoir in a more direct manner. Next, we present a Bayesian AVAZ inversion incorporating Cauchy-sparse and smoothing-model constraint regularization to directly estimate these model parameters from azimuthal seismic data. Finally, we apply the proposed inversion approach to a synthetic example and a real data set of a shale gas reservoir from the southern Sichuan Basin to illustrate its potential in the seismic characterization of brittleness and natural fractures.