A computationally efficient probabilistic full waveform inversion: application to the BP model

Abstract

Summary Traditional methods solve the full-waveform inversion making use of gradient-based algorithms that minimize an error function, which commonly measures the distance between observed and predicted waveforms. This deterministic approach only provides a “best-fitting” model and cannot account for the uncertainties affecting the predicted solution. On the other hand, casting this inverse problem into a probabilistic framework must deal with the formidable computational effort of the Bayesian approach when applied to high dimensional non-linear problems. We present a gradient-based Markov Chain Monte Carlo full-waveform inversion in which the posterior sampling is accelerated by compressing the data and model spaces through the discrete cosine transform, and by also defining a proposal that is a local, Gaussian approximation of the target posterior probability density. We demonstrate the applicability of the approach by performing a synthetic inversion test on the initial portion of the BP acoustic model. The results obtained by the implemented method are also validated against those obtained using a classic deterministic approach. The outcomes of the proposed probabilistic inversion can also play the role of starting models for a subsequent local inversion step aimed at improving the spatial resolution of the probabilistic result, which was limited by the model compression.