DeepISMNet: three-dimensional implicit structural modeling with convolutional neural network

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, using various mathematical methods to solve for a scalar field that optimally fits all the inputs under an assumption of smooth regularization. However, these approaches may not reasonably represent complex geometries and relationships of structures and may fail to fit a global structural trend when the known data are too sparse or unevenly distributed. Additionally, solving a large system of mathematical equations with iterative optimization solvers could be computationally expensive in 3-D. To deal with these issues, we propose an efficient deep learning method using a convolution neural network to create a full structural model from the sparse interpretations of stratigraphic interfaces and faults. The network is beneficial for the flexible incorporation of geological empirical knowledge when trained by numerous synthetic models with realistic structures that are automatically generated from a data simulation workflow. It also presents an impressive characteristic of integrating various types of geological constraints by optimally minimizing a hybrid loss function in training, thus opening new opportunities for further improving the structural modeling performance. Moreover, the deep neural network, after training, is highly efficient for the generation of structural models in many geological applications. The capacity of our approach for modeling complexly deformed structures is demonstrated by using both synthetic and field datasets in which the produced models can be geologically reasonable and structurally consistent with the inputs.