Deep learning seismic substructure detection using the Frozen Gaussian approximation

Abstract

We propose a deep learning algorithm for seismic interface and pocket detection with neural networks trained by synthetic high-frequency displacement data efficiently generated by the frozen Gaussian approximation (FGA). In seismic imaging high-frequency data is advantageous since it can provide high resolution of substructures. However, generation of sufficient synthetic high-frequency data sets for training neural networks is computationally challenging. This bottleneck is overcome by a highly scalable computational platform built upon the FGA, which comes from the semiclassical theory and approximates the wavefields by a sum of fixed-width (frozen) Gaussian wave packets.Training data for deep neural networks is generated from a forward simulation of the elastic wave equation using the FGA. This data contains accurate traveltime information (from the ray path) but not exact amplitude information (with asymptotic errors not shrinking to zero even at extremely fine numerical resolution). Using this data we build convolutional neural network models using an open source API, GeoSeg, developed using Keras and Tensorflow. On a simple model, networks, despite only being trained on data generated by the FGA, can detect an interface with a high success rate from displacement data generated by the spectral element method. Benchmark tests are done for P-waves (acoustic) and P- and S-waves (elastic) generated using the FGA and a spectral element method. Further, results with a high accuracy are shown for more complicated geometries including a three-layered model, a sine interface, and a 2D-pocket model where the neural networks are trained by both clean and noisy data.