Nonlinear rock physics model for estimation of 3D subsurface stress in anisotropic formations: Theory and laboratory verification

Abstract

We develop a rock physics model based on nonlinear elasticity that describes the dependence of the effective stiffness tensor as a function of a 3D stress field in intrinsically anisotropic formations. This model predicts the seismic velocity of both P-and S-waves in any direction for an arbitrary 3D stress state. Therefore, the model overcomes the limitations of existing empirical velocity-stress models that link P-wave velocity in isotropic rocks to uniaxial or hydrostatic stress.To validate this model, we analyze ultrasonic velocity measurements on stressed anisotropic samples of shale and sandstone. With only three nonlinear constants, we are able to predict the stress dependence of all five elastic medium parameters comprising the transversely isotropic stiffness tensor. We also show that the horizontal stress affects vertical S-wave velocity with the same order of magnitude as vertical stress does. We develop a weakanisotropy approximation that directly links commonly measured anisotropic Thomsen parameters to the principal stresses. Each Thomsen parameter is simply a sum of corresponding background intrinsic anisotropy and stressinduced contribution. The stress-induced part is controlled by the difference between horizontal and vertical stresses and coefficients depending on nonlinear constants. Thus, isotropic rock stays isotropic under varying but hydrostatic load, whereas transversely isotropic rock retains the same values of dimensionless Thomsen parameters. Only unequal horizontal and vertical stresses alter anisotropy. Since Thomsen parameters conveniently describe seismic signatures, such as normal-moveout velocities and amplitudevariation-with-offset gradients, this approximation is suitable for designing new methods for the estimation of 3D subsurface stress from multicomponent seismic data.

Exploring Trends in Microcrack Properties of Sedimentary Rocks: An Audit of Dry and Water Saturated Sandstone Core Velocity–Stress Measurements

“…For instance, [11] present a 1D empirical formulation to describe vertical travel time perturbation due to changes in vertical strain and vertical velocity from 4D seismic data. Authors [12][13][14] use third-order elasticity theory to characterize 3D stress dependence elasticity and anisotropy. Authors [15][16][17] introduce nonlinear models consistent with empirically derived phenomenological equations [18].…”

Overburden geomechanical effects on 4D seismic response – influences of stiffness contrast, anisotropy, and geometry

“…Resulting effective stress changes will alter the seismic properties of the rocks involved (Hornby, 1998;Sayers, 2002;Prioul et al, 2004;Ciz & Shapiro, 2009). This makes time lapse seismic an important tool to monitor subsurface alterations (e.g., Landrø 2001) and thereby improving recovery or storage capacity by optimal placement of new wells.…”

Reservoir stress path and induced seismic anisotropy: results from linking coupled fluid-flow/geomechanical simulation with seismic modelling

“…Coupled fluid-flow and geomechanical numerical simulation algorithms integrate the influence of multi-phase fluid-flow as well as deviatoric stress and strain to provide more accurate models of the spatial and temporal behaviour of various rock properties within and outside the reservoir (e.g., Herwanger et al 2010). Linking changes in reservoir physical properties, such as porosity, permeability and bulk modulus, to changes in seismic attributes is accomplished via rock physics models (e.g., Prioul et al 2004) to generate socalled dynamic (high strain rate and low strain magnitude suitable for seismic frequencies) elastic models.…”