Azimuthal Seismic Difference Inversion for Tilted Fracture Weaknesses

Tilted transverse isotropy (TTI) provides a useful model for analyzing how tilted fractures affect seismic wave propagation in subsurface layers. To determine the TTI properties of a medium, we propose an approach of employing azimuthal differencing of seismic amplitude data to estimate tilted fracture weaknesses. We first derive a linearized P-to-P reflection coefficient expression in terms of tilted fracture weaknesses, and then we formulate a Bayesian inversion approach in which amplitude differences between seismic data along two azimuths are used to determine tilted fracture weaknesses. Tests with simulated data confirm that the unknown parameter vector involving tilted fracture weaknesses is stably estimated from seismic data containing a moderate degree of additive Gaussian noise. Applying the inversion approach to real data, we obtain interpretable tilted fracture weaknesses, which are consistent with expected reservoir geology.