Operator Learning for Earthquake Location: Methodology and Application to Out-of-Network Events in the Mendocino Triple Junction

ABSTRACT Accurate location of earthquakes outside the boundaries of seismic networks is a well-known challenge due to limited azimuthal coverage. Offshore earthquakes, particularly along the Mendocino Transform fault, pose considerable risks to nearby communities. However, the lack of permanent stations in marine environments hinders accurate earthquake location. This study investigates the feasibility of locating offshore earthquakes around the Mendocino Triple Junction (MTJ) using advanced deep learning techniques. We propose the location neural operator (LocNO), an innovative operator learning framework that directly estimates earthquake locations from full-waveform data, even under sparse and nonideal network conditions. The approach integrates the Fourier neural operator and graph neural operator to capture the intricate spatiotemporal dependencies of seismic wavefields across stations and to estimate a spatial pseudoprobability density function over earthquake source coordinates (easting, northing, and depth). Trained on historical seismicity and simulated sparse network scenarios, LocNO generalizes across varying network geometries and provides robust estimates for out-of-network events, with the mean absolute errors on the order of 10 km horizontally and 4 km in depth. A case study of the 2017 Mw 5.7 earthquake sequence, 218 km west of Ferndale, California, demonstrates that LocNO yields robust locations for out-of-network earthquakes newly detected by the phase neural operator, even when recorded by only a few stations with large azimuthal gaps. These results open a new avenue for investigating MTJ seismotectonics using deep-learning-enhanced earthquake catalogs.