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 ((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 stress-induced anisotropy, each effective anisotropic parameter reduces to the sum of the corresponding Thomsen parameter for the unstressed VTI background and the corresponding parameter associated with the nonhydrostatic stress. The stress-related anisotropic parameters depend only on the differences between the magnitudes of principal stresses; therefore, principal stresses can influence anisotropic parameters only if their magnitudes differ in the symmetry plane in which the anisotropic parameters are defined. We test these predictions on a physical modeling data set acquired on a block of Berea Sandstone exhibiting intrinsic VTI anisotropy. Uniaxial stress, applied normal to the VTI symmetry axis, i.e., horizontally, produces an effective medium that is close to orthorhombic. We use two different methods to estimate the anisotropic parameters and study their variation as a function of stress. The first method utilizes conventional measurements of transmission velocities along the principal axes of the sample. The second method uses PP and PS reflection data acquired along seven different azimuths on the surface of the block. In accordance with theoretical predictions, the anisotropic parameters in the vertical plane normal to the stress are almost insensitive to the magnitude of the stress. In contrast, anisotropic parameters in the vertical plane of the applied stress increase approximately in a linear fashion with increasing stress. Except for the parameter δ (1) , comparison of the measured values of anisotropic parameters with theoretical predictions shows satisfactory agreement. Despite some documented discrepancies, we believe that nonlinear elasticity may provide a suitable framework for estimating pore pressure and 3D stresses from seismic data.

Comparison of geomechanical deformation induced by megatonne-scale CO 2 storage at Sleipner, Weyburn, and In Salah

“…Extension or compaction of the overburden can be imaged by travel time shifts through these areas. Additionally, changes in seismic anisotropy, measured via azimuthal variations in seismic attributes, can be particularly revealing in terms of rotations of stress tensors during deformation (33,34).…”

Estimating fluid-induced stress change from observed deformation

“…An alternative approach, one that provides estimates away from boreholes, relies on stress-induced anisotropy and associated velocity changes (Crampin 1978;Bakulin & Protosenya 1982;Leary et al 1990;Mavko et al 1995;Sinha & Kostek 1996;Johnson & Rasolofosaon 1996;Sarkar et al 2003;Prioul et al 2004;Shapiro & Kaselow 2005;Gurevich et al 2011). This indirect technique relies on an inversion of seismic observations.…”

“…This work is written by (a) US Government employee(s) and is in the public domain in the US. 1 2 D.W. Vasco et al has only been applied in the laboratory (Thurston & Brugger 1964;Johnson & Rasolofosaon 1996;Sarkar et al 2003;Prioul et al 2004;Shapiro & Kaselow 2005;Gurevich et al 2011) and has never been attempted in the field.…”

Uncovering Seismic HTI Anisotropy of the Cooper Basin

“…Many authors have discussed how information about stress and fractures can be extracted from azimuthal anisotropy observed in 3D seismic data (Perez and Gibson Jr 1996, Sarkar, et al 2003, Sayers and Rickett 1997. However, it is very difficult to define if anisotropy, in any case, is associated with stress or fractures.…”