A workflow to model anisotropy in a vertical transverse isotropic medium

Abstract

Velocity anisotropy, which is known as the directional dependency of velocities, is becoming increasingly important in subsurface imaging and characterization. Most elasticity theories consider an isotropic medium to describe the phenomena in the field of reservoir geophysics. This assumption is challenged by the reality of the subsurface which is subject to a complex geological history such as tectonic movements and changes in the differential stress that can typically introduce fractures. In some cases, these factors can make the subsurface highly anisotropic. In general, four classes of anisotropy can be defined, ranging between the two extremes of a completely isotropic medium (with two elastic constants) and a completely anisotropic medium (with 21 elastic constants). The four classes refer to specific conditions where we can reduce the number of elements of the elastic stiffness tensor. These are known as Cubic (with three independent elastic constants), Transverse Isotropic or TI (five independent elastic constants), Orthorhombic (nine independent elastic constants) and Monoclinic (13 independent elastic constants). TI is the most often used to describe sedimentary rock. Anisotropy as an extension to isotropic approaches is usually dealt with using Thomsen (1986) parameters as approximations. Thomsen (1986) suggested three parameters to correct for anisotropy effects in weakly anisotropic media. These parameters, ε, δ and γ, are regularly used in all reservoir geophysics disciplines to address anisotropy effects. However, determining these three parameters is not straightforward and requires information such as laboratory data or well logs acquired in boreholes in different directions with respect to the symmetry axis of the anisotropy. The purpose of this paper is to review anisotropy in vertically isotropic media and use existing theory to model changes in the elastic stiffness tensor based on conventional well logs. Furthermore, this elastic stiffness tensor can be used to calculate the Thomsen parameters or even to model anisotropic velocities directly.