  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.
