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Amplitude signatures in fractured media

Most of existing rocks are typically fractured that effectively result in anisotropic model of different complexity (Tsvankin and Grechka, 2011). The anisotropy signatures can be defined by traveltime and reflection&transmission amplitudes at plane interface between the rocks of different properties. Here, we focus on reflection amplitude by introducing the uniform approach to embed the fracture sets of different orientation. We utilize the linear slip theory (Schoenberg and Helbig, 1997) to add the fractures of arbitrary weakness parameters. The anisotropic model sequence consists of isotropic model (later used as a background), transversely isotropic model with a vertical symmetry axis (due to horizontal fracture set), orthorhombic model (due to horizontal and vertical fracture sets), monoclinic model with a horizontal symmetry plane (due to horizontal and two non-orthogonal vertical fracture sets) and triclinic model (due to horizontal, two nonorthogonal vertical and one inclined fracture sets). The general equation for the matrix of stiffness coefficients is given by the inverse sum of the fracture weakness matrices multiplied with density. The isotropic background stiffness coefficient matrix is defined by inverse of background weakness matrix. Each fracture weakness matrix generally has three independent parameters that are normal, tangential and horizontal weaknesses. In addition to these parameters, the fracture orientation angles in 3D space are also taken into account, and the rotation matrix is defined for each set of fractures. The uniform non-rotated weakness matrix can be chosen for brevity’s sake, however, all fracture sets might have their own weaknesses. We analyze the plane P wave reflection coefficient computed at plane interface between isotropic background and fractured background half-spaces. It is convenient to show reflection coefficient versus horizontal slowness projections. To compute reflection coefficients, we use the method developed by Jin and Stovas (2020).