Anisotropic Inversion of Seismic Data for Stressed Media - Theory and a Physical-Modeling Study on Berea Sandstone

Abstract

Nonhydrostatic stress, an often‐ignored source of seismic anisotropy, is universally present in the subsurface and may be as common as intrinsic or fracture‐induced anisotropy. Nonhydrostatic stress, applied to an initially transversely isotropic solid with vertical symmetry axis (VTI), results in an effective medium having almost orthorhombic symmetry (provided that one of the principal stresses is aligned with the symmetry axis). The symmetry planes observed in this orthorhombic medium are aligned with the orientations of the principal stresses, and anisotropic parameters (e(1,2), δ(1,2,3), and γ(1,2)) can reveal information about the stress magnitudes. Thus, time‐lapse monitoring of changes in anisotropy potentially can provide information on temporal variations in the stress field.We use nonlinear elasticity theory to relate the anisotropic parameters to the magnitudes of the principal stresses and verify these relationships in a physical modeling study. Under the assumption of weak background and str...