Traveltime tomography and efficient physics-informed Bayesian inversion

Abstract

Bayesian inversion provides the same information as regularized inversion of seismic data, except it also supplies a probability estimate of the solution throughout model space. The cost, however, is that Bayesian inversion is orders-of-magnitude more expensive than regularized inversion by a gradient optimization method. To mitigate this cost, we present an efficient physics-informed Bayesian inversion method that combines regularized inversion to get both the optimal solution and the posterior probability functions in model space. A gradient optimization method is used to efficiently estimate the maximum a posterior (MAP) solution, and so function evaluations are only needed around the MAP point in model space. This efficiently provides the posterior probability in that neighbourhood, and therefore avoids the tremendous expense of sampling points throughout the high-dimensional model space. We apply this physics-informed Bayesian inversion to VSP traveltime data. The tomogram is computed with the assistance of an analytic inverse, and the posterior probability estimate is computed with an order-of-magnitude less cost than standard Bayesian analysis. This procedure can also be adapted to refraction traveltime tomography for near-surface imaging.