Multi-realization seismic data processing with Deep Variational Preconditioners

Geophysical data processing is traditionally treated as a deterministic-centric discipline. Seismic data are usually processed through a chain of algorithms, where a given output becomes the input of a subsequent processing step. Geophysicists have recently started to recognize the importance of quantifying uncertainties within each processing step, such that they could be used as input to subsequent imaging and inversion processes. We present a two-steps approach where a Variational AutoEncoder (VAE) is first trained to generate realistic samples of the input seismic data at hand; parametric Variational Inference is then utilized to optimize the parameters of the VAE latent distribution for a given observed data and modelling operator of interest, and sample multiple realizations from the optimized parametric posterior distributions. Seismic deblending as well as joint interpolation and wavefield separation are used to showcase the proposed methodology.