Bayesian linearized seismic inversion with locally varying spatial anisotropy

Abstract Inversion of seismic data is commonly used in the quantitative estimation of acoustic properties of reservoirs. Locally varying anisotropy (LVA) is incorporated in the Bayesian formulation of the inverse problem to impose spatial constraints in the lateral continuity of the acoustic properties. Unlike elastic anisotropy used to define the directional dependence of elastic properties, locally varying anisotropy in this context describes the heterogeneity of elastic properties using scale lengths associated to the directions of maximum and minimum temporal/spatial continuity. This approach favors a multiple trace-based inversion to provide geologically consistent estimates of the model parameters at the seismic scale especially in geological formations that display complex nonlinear features such as channels or folds. The proposed method uses covariances obtained through quantitative modeling of the spatial statistics of the elastic parameters. The computation of spatial correlation uses anisotropic distances between locations within the geological formation. A synthetic validation of the method using a least squares approach shows an improvement in the inference of acoustic impedances from seismic data when nonlinear geological features are present.