Multiazimuthal modeling and inversion of qP reflection coefficients in fractured media

We present a method for the exact modeling and inversion of multiazimuthal qP-wave reflection coefficients at an interface separating two anisotropic media. This procedure can be used for media with at least one of its planes of symmetry parallel to the interface (i.e., monoclinic or higher symmetri es). To illustrate the method, we compute qP-wave reflection coefficients a t an interface separating an isotropic medium (representing a seal rock) fr om a transversely isotropic medium (representing a reservoir rock with vert ical aligned fractures). Forward modeling shows that the difference in the offset of the critical angles for different azimuths is proportional to the fracture density: the higher the fracture density, the larger the differen ce. In the second part of the paper, we use a global optimization technique (genetic algorithm) to invert wide-angle amplitude variation with offset ( AVO) synthetic data. The model space consists of mass density and five elas tic parameters of a transversely isotropic medium with a horizontal symmetr y axis (HTI medium), which, to the first order, represents the fractured re servoir rock. For this model, we find that the configuration of three azimu ths of data acquisition is the minimum number of acquisition planes needed to invert amplitude variation with offset/amplitude variation with azimuth (AVO/AVA) data. Further, there is a need fbr incidence angles up to 40 degr ees; a more narrow range of angles can lead to models that fit the data per fectly only up to the "maximum" incidence angle. We assume that the velocit ies and density of the isotropic rock are known, but use no prior informati on on the values of the model space parameters of the fractured rock except for reasonable velocity values in crystal rocks and constraints of elastic stability of solid media. After inversion for the model space parameters, we compute statistics of the 30 best models and likelihood functions, which provide information on the nonuniqueness and quality of the AVO/AVA invers e problem.