Elastic full waveform inversion results uncertainty analysis: a comparison between the model uncertainty given by machine learning methods and conventional FWI
Tianze Zhang, Scott Keating, Kristopher A. Innanen
Uncertainty analysis is an important aspect of quantifying the results of the inversion problem. In this report, we compare the uncertainty analysis given by two methods for full waveform inversion. The first method is by using the approximation of the inverse Hessian to perform the uncertainty analysis, as the approximation of the inverse Hessian is closely related to the posterior model covariance matrix. The second method is based on a machine learning-based method, which uses the Bayesian neural network (BNN) to generate elastic models and then performs the inversion. In the BNN, each trainable weight is represented as a Gaussian distributed probability distribution function (pdf). When BNN is well trained, we can forward calculate the BNN several times and perform the statistic analysis for the prediction results and give the uncertainty analysis for the generated models. Our numerical results suggested that both methods can generate promising inversion results and reasonable uncertainty quantification when compared with the true model errors.