Bayesian-Deep-Learning Estimation of Earthquake Location from Single-Station Observations

We present a deep learning method for single-station earthquake location, which we approach as a regression problem using two separate Bayesian neural networks. We use a multi-task temporal-convolutional neural network to learn epicentral distance and P travel time from 1-minute seismograms. The network estimates epicentral distance and P travel time with absolute mean errors of 0.23 km and 0.03 s respectively, along with their epistemic and aleatory uncertainties. We design a separate multi-input network using standard convolutional layers to estimate the back-azimuth angle, and its epistemic uncertainty. This network estimates the direction from which seismic waves arrive to the station with a mean error of 1 degree. Using this information, we estimate the epicenter, origin time, and depth along with their confidence intervals. We use a global dataset of earthquake signals recorded within 1 degree (~112 km) from the event to build the model and to demonstrate its performance. Our model can predict epicenter, origin time, and depth with mean errors of 7.3 km, 0.4 second, and 6.7 km respectively, at different locations around the world. Our approach can be used for fast earthquake source characterization with a limited number of observations, and also for estimating location of earthquakes that are sparsely recorded -- either because they are small or because stations are widely separated.