DeepISMNet: Three-Dimensional Implicit Structural Modeling with Convolutional Neural Network

Abstract

Abstract. Implicit structural modeling using sparse and unevenly distributed data is essential for various scientific and societal purposes ranging from natural source exploration to geological hazard forecasts. Most advanced implicit approaches formulate structural modeling as least-squares minimization or spatial interpolation problem and solve partial differential equations (PDEs) for a scalar field that optimally fits all the input data under smooth regularization assumption. However, the PDEs in these methods might be insufficient to model highly complex structures in practice and may fail to reasonably fit a global structure trend when the known data are too sparse. In addition, solving the PDEs with iterative optimization solvers could be computationally expensive in 3-D. In this study, we propose an efficient deep learning method using a convolution neural network to predict a scalar field from sparse structural data associated with multiple distinct stratigraphic layers and faults. Our deep learning architecture is beneficial for the flexible incorporation of empirical geological knowledge by training with numerous and realistic structural models that are automatically generated from a data simulation workflow. It also presents an impressive characteristic of integrating various types of structural constraints by optimally minimizing a hybrid loss function to compare predicted and reference structural models, opening new opportunities for further improving geological modeling. Moreover, the deep neural network, after training, is highly efficient to predict implicit structural models in practical applications. The capacity of our approach for modeling highly deformed geological structures is verified by using both synthetic and real-world datasets, where the produced models are geologically reasonable and structurally consistent with the inputs.