A probabilistic full waveform inversion of surface waves

Over the past decades, surface wave methods have been routinely employed to retrieve the physical characteristics of the first tens of meters of the subsurface, particularly the shear wave velocity profiles. Traditional methods rely on the application of the multichannel analysis of surface waves to invert the fundamental and higher modes of Rayleigh waves. However, the limitations affecting this approach, such as the 1D model assumption and the high degree of subjectivity when extracting the dispersion curve, motivate us to apply the elastic full-waveform inversion, which, despite its higher computational cost, enables leveraging the complete information embedded in the recorded seismograms. Standard approaches solve the full-waveform inversion using gradient-based algorithms minimizing an error function, commonly measuring the misfit between observed and predicted waveforms. However, these deterministic approaches lack proper uncertainty quantification and are susceptible to get trapped in some local minima of the error function. An alternative lies in a probabilistic framework, but, in this case, we need to deal with the huge computational effort characterizing the Bayesian approach when applied to non-linear problems associated with expensive forward modelling and large model spaces. In this work, we present a gradient-based Markov chain Monte Carlo full-waveform inversion where we accelerate the sampling of the posterior distribution by compressing data and model spaces through the discrete cosine transform. Additionally, a proposal is defined as a local, Gaussian approximation of the target density, constructed using the local Hessian and gradient information of the log posterior. We first validate our method through a synthetic test where the velocity model features lateral and vertical velocity variations. Then we invert a real dataset from the InterPACIFIC project. The obtained results prove the efficiency of our proposed algorithm, which demonstrates to be robust against cycle-skipping issues and able to provide reasonable uncertainty evaluations with an affordable computational cost.