LAUSR

Earthquake location is one of the oldest problems in seismology, yet remains an active research topic. With dense seismic monitoring networks, it is possible to obtain reliable locations for microearthquakes; however, in many cases dense networks are lacking, limiting the location accuracy, or preventing location when there are too few observations. For small events in all settings, recording may be sparse and location may be difficult due to low signal-to-noise ratio. In this work, we introduce a new, distance-geometry-based method to locate seismicity clusters using only one or two seismic stations. A distance geometry problem consists in determining the location of sets of points based only on the distances between member pairs. Applied to seismology, our approach allows earthquake location using the interevent distance between earthquake pairs, which can be estimated using only one or two seismic stations. We first validate the method with synthetic data that resemble common cluster shapes, and then test the method with two seismic sequences in California: the August 2014   Mw 6.0 Napa earthquake and the July 2019 Mw 6.4 Ridgecrest earthquake sequence. We demonstrate that our approach provides robust and reliable results even for a single station. When using two seismic stations, the results capture the same structures recovered with high-resolution double-difference locations based on multiple stations. The proposed method is particularly useful for poorly monitored areas, where only a limited number of stations are available.