Probabilistic physics-informed neural network for seismic petrophysical inversion#xD;

The main challenge in the inversion of seismic data to predict the petrophysical properties of hydrocarbon-saturated rocks is that the physical relations that link the data to the model properties are often non-linear and the solution of the inverse problem is generally not unique. As a possible alternative to traditional stochastic optimization methods, we propose to adopt machine learning algorithms by estimating relations between data and unknown variables from a training dataset with limited computational cost and without prior assumptions. We present a probabilistic approach for seismic petrophysical inversion based on physics-informed neural network with a reparameterization network. The novelty of the proposed approach includes the definition of a physics-informed neural network algorithm in a probabilistic setting, the use of an additional neural network for rock physics model hyperparameters estimation, and the implementation of Approximate Bayesian Computation to quantify the model uncertainty. The reparameterization network allows including unknown model parameters, such as rock physics model hyperparameters. The proposed method predicts the most likely model of petrophysical variables based on the input seismic dataset and the training dataset and provides a quantification of the uncertainty of the model. The method is scalable and can be adapted to various geophysical inverse problems. We test the inversion on a North Sea dataset with post-stack and pre-stack data to obtain the prediction of petrophysical properties. Compared to regular neural networks, the predictions of the proposed method show higher accuracy in the predicted results and allow quantifying the posterior uncertainty.