Variational Bayesian Multiparameter Seismic Inversion with Structural Similarity Constraints

Summary This work addresses the nonlinear multiparameter seismic imaging problem, which is inherently high-dimensional, ill-posed and susceptible to interparameter trade-offs (crosstalk). To mitigate crosstalk and enhance reconstruction quality, we enforce structural similarity among target parameters by jointly penalizing their spatial gradients. Specifically, the inversion is formulated within a Bayesian framework, where gradient penalization is modeled using Laplace distributions, equivalent to an anisotropic total variation approach. Expressing further these Laplace priors in hierarchical form enables the derivation of efficient inversion algorithms. The hyperparameters introduced in the hierarchical models for each target parameter, which serve as weights on the spatial gradients, are constrained to be identical at every spatial location, thereby enforcing structural similarity among the parameters. By further employing a Variational Bayesian approach, we efficiently infer these hyperparameters jointly with the target parameters, resulting in robust estimation at a reduced computational cost. We also discuss the computational complexity of the approach and propose a more efficient implementation that can be well-suited for large-scale problems while maintaining comparable reconstruction quality. The proposed method will be then evaluated by reconstructing subsurface velocity and density in a seismic imaging problem, demonstrating its effectiveness in mitigating crosstalk compared to traditional inversion techniques.