Seismic inversion aims to reconstruct subsurface medium parameters from recorded seismic data. It is solved as a large-scale constrained optimization problem in the deterministic approach. Different objective functions have been proposed to tackle the nonconvexity and high degree of nonlinearity. For this infinite-dimensional problem, Bayesian inversion aims to recover a field rather than a single state as in the deterministic approach, but sampling the full posterior is not feasible, which requires millions of wave modeling. The analogy between objective functions in the deterministic inversion and likelihood functions in Bayesian inversion motivates us to analyze the noise model each objective function accounts for under the Bayesian inference setting. A combination of both approaches achieve the optimal results.
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