Azimuth-dependent AVO in reservoirs containing non-orthogonal fracture sets

Azimuthal anisotropy in rocks can result from the presence of one or more sets of partially aligned fractures with orientations determined by the stress history of the rock. The symmetry of a rock with horizontal bedding that contains two or more non-orthogonal sets of vertical fractures may be approximated as monoclinic with a horizontal plane of mirror symmetry. For offsets that are small compared with the depth of the reflector, the azimuthal variation in P-wave AVO gradient for such a medium varies with azimuth as     where φ is the azimuth measured with respect to the fast polarization direction for a vertically polarized shear wave. φ ₂ depends on both the normal compliance B _N and the shear compliance B _T of the fractures and may differ from zero if B _N B _T varies significantly between fracture sets. If B _N B _T is the same for all fractures,     and the principal axes of the azimuthal variation in P-wave AVO for fixed offset are determined by the polarization directions of a vertically propagating shear wave. At larger offsets, terms in     and     are required to describe the azimuthal variation in AVO accurately. φ ₄ and φ ₆ also depend on B _N B _T. For gas-filled open fractures     but a lower value of B _N B _T may result from the presence of a fluid with non-zero bulk modulus.