The goal of seismic inversion is to obtain subsurface properties from surface measurements. Seismic images have proven valuable, even crucial, for a variety of applications, including subsurface energy exploration, earthquake early warning, carbon capture and sequestration, estimating pathways of sub-surface contaminant transport, etc. These subsurface properties (such as wave speed, density, and elastic velocities) influence the transmission of seismic waves through the subsurface media, and well-understood physics models (so-called “forward models”) can be used to predict what surface measurements would be made, for any given subsurface configuration. Seismic inversion is the inverse problem: given actual surface measurements, infer what subsurface configuration would give rise to those measurements. Like most inverse problems, seismic imaging is ill-posed, meaning many different subsurface configurations can give rise to the same surface measurements. Iterative optimization algorithms for the inverse problem are typically very computationally expensive because they require many evaluations of the forward model, which is itself computationally expensive. A further challenge is the different sensitivity of subsurface properties to the seismic data; density for example is more difficult to accurately infer than is P-wave velocity. But recent advances in algorithms and computing provide an opportunity for remarkable progress in seismic inversion, and efficient solutions to previously infeasible problems have been obtained using data-driven approaches (such as the deep learning methods that were developed primarily for problems in computer vision). The excellent performance of learning-based methods arises from its ability to exploit large amounts of high-quality training data, without the need for hand-designed features. Unlike computer vision, however, seismic inversion is not a data-rich domain. There is a relatively small amount of field data in existence due to the high cost of acquisition, and as a result of its commercial value, a very limited amount is publicly available. To alleviate the data scarcity issue and improve model generalization, there has been growing interest in combining physics knowledge with machine learning for solving seismic inversion problems. This review will survey methods for incorporating physics knowledge with machine learning (primarily deep neural networks) to solve computational seismic inversion problems. We will provide a structured framework of the existing research in the seismic inversion community, and will identify technical challenges, insights, and trends.

Accurate earthquake location and magnitude estimation play critical roles in seismology. Recent deep learning frameworks have produced encouraging results on various seismological tasks (e.g., earthquake detection, phase picking, seismic classification, and earthquake early warning). Most existing machine learning earthquake location methods utilize waveform information from a single station. However, multiple stations contain more complete information for earthquake source characterization. Inspired by recent successes in applying graph neural networks in graph-structured data, we develop a Spatio-Temporal Graph Convolutional Neural Network (STGCN) for estimating earthquake locations and magnitudes. Our graph neural network leverages geographical and waveform information from multiple stations to construct graphs automatically and dynamically by an adaptive feature integration process. Given input waveforms collected from multiple stations, the neural network constructs different graphs and fuses spatial-temporal consistency effectively from various stations based on graphs’ edges. Using a recent graph neural network and a fully convolutional neural network as baselines, we apply STGCN to earthquakes cataloged by Southern California Seismic Network from 2000 to 2019 and induced earthquakes collected in Oklahoma from 2014 to 2015. STGCN yields more accurate earthquake locations than those obtained by the baseline models and performs comparably in terms of depth and magnitude prediction, though the ability to predict depth and magnitude remains weak for all tested models. Our work demonstrates the potential of using graph neural networks and multiple stations for better automatic estimation of earthquake epicenters.