Estimating rock and fluid properties in the subsurface from geophysical measurements is a computationally and memory-intensive inverse problem. For nonlinear problems with non-Gaussian variables, analytical solutions are generally not available. and the solutions of those inverse problems must be approximated using sampling and optimization methods. To reduce the computational cost, model and data can be reparameterized into low-dimensional spaces where the solution of the inverse problem can be computed more efficiently. Among the potential dimensionality reduction methods, deep-learning algorithms based on deep generative models provide an efficient approach to reduce the dimension of the model and data vectors. However, such dimension reduction might lead to information loss in the reconstructed model and data, reduction of the accuracy and resolution of the inverted models. and under- or overestimation of the uncertainty of the predicted models. To comprehensively investigate the impact of model and data dimension reduction with deep generative models on uncertainty quantification, we compare the prediction uncertainty in nonlinear inverse problem solutions obtained from Markov chain Monte Carlo and ensemble-based data assimilation methods implemented in lower dimensional data and model spaces using a deep variational autoencoder. Our workflow is applied to two geophysical inverse problems for the prediction of reservoir properties: prestack seismic inversion and seismic history matching. The inversion results consist of the most likely model and a set of realizations of the variables of interest. The application of dimensionality reduction methods makes the stochastic inversion more efficient.
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