Uncertainty estimation for full waveform inversion with a prior information from depth migration

We use Bayesian inference framework to estimate model uncertainties associated with full waveform inversion. A prior covariance operator is built based on the estimated slopes of migrated images and plane-wave construction. Frequencydomain full waveform inversion is used to search for the maximum a posterior model. Evaluation of posterior covariance requires knowledge on the prior-preconditioned Hessian. In this study, we apply a randomized SVD approach to analyze the spectrum of the preconditioned Hessian. Strong decay of its eigenvalues indicates that data are most informative to low dimensional subspaces of model parameters. 2D Marmousi model is used as a numerical example to validate the proposed framework. Comparing random samples from the prior and posterior distributions allows us to estimate model uncertainties associated with full waveform inversion.