Recovery of the main fracturing direction of oil reservoirs from seismic and AVO data

Abstract

In the present work, we formulate and solve an inverse problem to recover the main fracturing direction of petroleum reservoirs from seismic and AVO data. Equivalent media theory provides a starting point for modeling an equivalent anisotropic medium starting from an isotropic background with fractures. We then represent the equivalent medium in a new coordinate system whose x-axis is parallel to the reservoir's top. Using the classical theory of wave propagation and the Invariant Embedding technique (specially to deal with anisotropic media), we solve exactly the elastodynamic equations of motion to compute the reflection of P, SV, SH waves at the reservoir's top, without the need of using the so-called Zoeppritz approximation. In the inverse problem formulation, we assume that we know a priori the reservoir isotropic background elastic constants as well as the fracture system behavior, by means of its effective compliance. We then apply a metaheuristic to recover the main fracturing direction whose input data are the amplitudes of the reflected waves recorded by the geophones and the output are two Euler-angles representing the fracturing direction. We validate the methodology using noiseless synthetic data and further test its robustness using incomplete and noisy synthetic data.