| Popis: |
SUMMARY We model azimuthal amplitude variations of seismic P-wave reflections at the top of a layer with a fracture set with arbitrary orientation, embedded in a homogeneous isotropic background medium. We remove the isotropic constituents of the reflection coefficients and derive linearized expressions for the residual, based on scattering theory. The azimuthal variation of the AVO gradient and curvature can be approximated as a superposition of the normal and tangential fracture weakness, with coefficients depending on the fracture orientation with respect to the azimuth of observation. An inversion method is presented to estimate the fluid indicator, a quantitative measure for the fluid saturation, from AVO gradient variations with azimuth, assuming that the orientation and tangential weakness are known a priori. The tangential weakness can be related to the fracture density, which can be estimated from shear wave splitting, whereas the fracture strike can be determined from peaks and troughs of azimuthal AVO variations. We compute AVO gradient variations with azimuth for a fracture set with horizontal axis of symmetry (HTI) and a dipping fracture set and compare our results with those of an exact algorithm. The inversion method is successfully tested on a synthetic example of a dipping fracture set, where the input variables and the synthetic AVO gradient variations are corrupted with up to 10 % random noise. |
