Deep learning techniques applied to 3-D probabilistic inversion of controlled-source electromagnetic data in a marine environment

We designed an computer efficient, probabilistis 3-D inversion algorithm for CSEM data. It is commonly known that multiple physical descriptions of the subsurface fit the geophysical data equally well, due to incomplete measurement coverage, incomplete physical description of the problem, and model overparameterization. A probabilistic inversion approach allows us to explicitly account for data and model uncertainty. Probabilistic inversion is a demanding process in terms of the number of forward model computations required to sample the posterior probability density function of model parameters. Therefore, we use an efficient sampling algorithm (DREAM(ZS)) combined with strategies to optimize the forward model by approximations and error estimation with deep learning techniques. Regarding the latter, we propose an alternative (approximate) approach to our forward model for simulating the electromagnetic (EM) response which reduces the computing time, and we quantify the modeling error committed directly in the inversion process. Thus, we create a statistical error-model related to the approximate EM response by training a Spatial Generative Adversarial Network (SGAN). In contrast to other neural networks, the SGAN training process has the particularity of being a competition between a Generator, which creates fake samples of the training set, and a Critic, which scores the quality of both true or fakesamples. After training the Generator results in a parametric model of the probability density function of the training set (modeling errors). This parametric error-model is incorporated into the inversion process as a complement to correct and quantify the error in our approximate forward model. To test our methodology we first proposed a synthetic experiment of a marine exploration environment. The implementation and subsequent training of the network allowed us to show that SGAN is useful to generate a statistical error-model. The comparison between a set of samples created with the Generator and the training set shows similarities in the statistical properties of both. Thus, we obtain a parameter-reduced error-model capable of representing the different components of the EM response at a considerable number of receivers and frequencies. In addition, the inversion process is significantly accelerated by introducing the forward model approximations, and the incorporation of the statistical error-model improved the determination of the true parameters in our synthetic test case. We then applied our methodology to the inversion of CSEM data acquired in a marine environment.