Sensitivity analysis of fracture scattering

Abstract

The understanding of seismic scattering of a finite fracture is very important in reservoir fracture characterizations, but the analytical solution of this problem is not available. Thus, in this paper, we present an approach for numerical study of the seismic response of a finite fracture. The way fractures affect seismic waves depends on fracture mechanical parameters, such as compliance and saturating fluid, and on their geometric properties, such as dimensions and spacing. When fractures are small relative to the seismic wavelength, waves will be weakly affected by fractures, and in effective medium theory, a zone comprised of many small fractures is equivalent to a homogeneous anisotropic zone without fractures (Hudson, 1991; Coates and Schoenberg, 1995; Schoenberg and Sayers, 1995; Grechka and Kachanov, 2006; Grechka, 2007; Sayers, 2009). When fractures are much larger than the seismic wavelength, then we can take fracture interfaces as infinite planes and apply plane wave theory to calculate their reflection and transmission coefficients and interface waves (Schoenberg, 1980; Pyrak‐ Nolte and Cook, 1987; Gu et al., 1996). In field reservoirs, fractures always have finite length, and fractures with characteristic lengths on the order of seismic wavelength are the scattering sources that generate seismic codas. Sanchez‐ Sesma and Iturraran‐ Viveros (2001) derived an approximate analytical solution of scattering and diffraction of SH waves by a finite fracture, and Chen (submitted 2010 SEG abstract) derived an analytical solution for scattering from a 2D elliptical crack in an isotropic acoustic medium. However, so far it is still difficult to derive the analytical elastic solution of a finite fracture with a linear‐ slip boundary and characteristic length on the order of the seismic wavelength. Although fractures are usually present as fracture networks in reservoirs, and the interaction between fracture networks and seismic waves is very complicated, scattering from a single fracture can be considered as the 1st order effect on the scattered wave field. Therefore, to study the general elastic response of single finite fracture is essential to reservoir fracture characterization, and this has been done numerically. Here, we adopt Schoenberg's (1980) linear‐ slip fracture model and use the effective medium method (Coates and Schoenberg, 1995) for finite‐ difference modeling of fractures. In this model, a fracture is modeled as an interface across which the traction is taken to be continuous, yet displacement is allowed to be discontinuous. And the displacement discontinuity vector and the traction vector are linearly related by the fracture compliance matrix Zij. For a rotationally symmetric fracture, the fracture compliance matrix only has two independent components: the normal compliance ZN and the tangential compliance ZT.