Modeling groundwater levels in California's Central Valley by hierarchical Gaussian process and neural network regression

Modeling groundwater levels continuously across California's Central Valley (CV) hydrological system is challenging due to low-quality well data which is sparsely and noisily sampled across time and space. A novel machine learning method is proposed for modeling groundwater levels by learning from a 3D lithological texture model of the CV aquifer. The proposed formulation performs multivariate regression by combining Gaussian processes (GP) and deep neural networks (DNN). Proposed hierarchical modeling approach constitutes training the DNN to learn a lithologically informed latent space where non-parametric regression with GP is performed. The methodology is applied for modeling groundwater levels across the CV during 2015 - 2020. We demonstrate the efficacy of GP-DNN regression for modeling non-stationary features in the well data with fast and reliable uncertainty quantification. Our results indicate that the 2017 and 2019 wet years in California were largely ineffective in replenishing the groundwater loss caused during previous drought years.

Seismic Bayesian evidential learning: Estimation and uncertainty quantification of sub-resolution reservoir properties

We present a framework that enables estimation of low-dimensional sub-resolution reservoir properties directly from seismic data, without requiring the solution of a high dimensional seismic inverse problem. Our workflow is based on the Bayesian evidential learning approach and exploits learning the direct relation between seismic data and reservoir properties to efficiently estimate reservoir properties. The theoretical framework we develop allows incorporation of non-linear statistical models for seismic estimation problems. Uncertainty quantification is performed with Approximate Bayesian Computation. With the help of a synthetic example of estimation of reservoir net-to-gross and average fluid saturations in sub-resolution thin-sand reservoir, several nuances are foregrounded regarding the applicability of unsupervised and supervised learning methods for seismic estimation problems. Finally, we demonstrate the efficacy of our approach by estimating posterior uncertainty of reservoir net-to-gross in sub-resolution thin-sand reservoir from an offshore delta dataset using 3D pre-stack seismic data.