Exact solution of reflection coefficient in reservoirs with tilted fractures

Huaizhen Chen, Kristopher Innanen

ABSTRACT

We first present detailed expressions of polarization vectors of P- and SV-waves for a transversely isotropic medium with a tilted symmetry axis (TTI) as a function of stiffness parameters of a transversely isotropic medium with a vertical symmetry axis (VTI), and then we propose the equation to calculate the exact solution of PP-wave reflection coefficient in TTI media. In order to relate the stiffness matrix of TTI media to fracture properties (e.g. fracture density and fillings moduli), we use the stiffness matrix of HTI media given by the linear slip theory to obtain the stiffness matrix of VTI media using the Bond rotation, which provides us to calculate stiffness parameters for TTI media given different fracture properties and tilted angles. We also study how to compute the transmission angle in TTI media using the extended Snell's law. We finally model PP-wave reflection coefficient vari-ations with the incidence angle and the azimuthal angle given different values of fracture density and tilted angle. We conclude that in the case of TI media with a high tilted an-gle, the tilted angle mainly affects the value of the reflection coefficient, while the fracture density affects the variation of reflection coefficient with the azimuthal angle.

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