Deep generative models in inversion: The impact of the generator's nonlinearity and development of a new approach based on a variational autoencoder

When solving inverse problems in geophysical imaging, deep generative models (DGMs) may be used to enforce the solution display highly structured spatial patterns which are supported by independent information (e.g. geological setting) of subsurface. In such case, inversion formulated a latent space where low-dimensional parameterization is defined and Markov chain Monte Carlo or gradient-based methods applied. However, mapping between original (pixel) representations usually nonlinear cause some difficulties for inversion, especially methods. this contribution we review conceptual framework with DGMs propose that nonlinearity caused mainly changes topology curvature induced function. As result, identify conflict two goals: accuracy generated feasibility inversion. addition, show how training parameters variational autoencoder, particular instance DGM, chosen so tradeoff these goals achieved acceptable results obtained stochastic gradient-descent scheme. A series test cases using synthetic channel different complexity cross-borehole traveltime tomographic data involving both linear forward operator proposed method provides useful performs better compared previous approaches