Frequency-dependent anisotropy due to two orthogonal sets of mesoscale fractures in porous media

Seismic anisotropy can occur in rocks that have complicated internal structures and thin layering. Wave-induced fluid flow (WIFF) is one of the major causes of elastic wave dispersion and anisotropy. The principle goal of this paper is to combine the effects of WIFF and layer-induced anisotropy in orthorhombic (OTR) models that are often used in the seismic industry nowadays to describe azimuthal and polar anisotropy. We derive the effective frequency-dependent anisotropy parameters based on the Chapman model that accounts for the WIFF mechanism. First, we summarize two major problems to establish the link between the frequency-dependent seismic anisotropy and the multiple sets of fractures with different scales and orientations. Then we specify the multiple mesoscale fractures to be vertical and orthogonal so as to simplify the rock physics model to be an ORT medium. We also give the explicit expressions for the effective stiffness and the Thomsen-style parameters (v(P0), v(S0), epsilon(1), epsilon(2), gamma(1), gamma(2), delta(1), delta(2), delta(3)). Finally, we derive the effective frequency-dependent anisotropy parameters for ORT multiple layers using the Backus averaging under the approximation of weak contrast between layers. We also investigate the influence of frequency, fracture parameters (density and scale), effective porosity and volume fraction on the Thomsen-style parameters.