Locating clustered seismicity using Distance Geometry Solvers: applications for sparse and single-borehole DAS networks

SUMMARY The determination of seismic event locations with sparse networks or single-borehole systems remains a significant challenge in observational seismology. Leveraging the advantages of the location approach HADES (eartHquake locAtion via Distance gEometry Solvers), which was initially developed for locating clustered seismicity recorded at two stations, through the solution of a Distance Geometry Problem, we present here an improved version of the methodology: HADES-R (HADES-Relative). Where HADES previously needed a minimum of four absolutely located master events, HADES-R solves a least-squares problem to find the relative inter-event distances in the cluster, and uses only a single master event to find the locations of all events and subsequently applies rotational optimizer to find the cluster orientation. It can leverage iterative station combinations if multiple receivers are available, to describe the cluster shape and orientation uncertainty with a bootstrap approach. The improved method requires P- and S-phase arrival picks, a homogeneous velocity model, a single master event with a known location, and an estimate of the cluster width. The approach is benchmarked on the 2019 Ridgecrest sequence recorded at two stations, and applied to two seismic clusters at the FORGE geothermal test site in Utah, USA, with a microseismic monitoring scenario with a Distributed Acoustic Sensing in a vertical borehole. Traditional procedures struggle in these settings due to the ill-posed network configuration. The azimuthal ambiguity in such a scenario is partially overcome by the assumption that all events belong to the same cluster around the master event and a cluster width estimate. We are able to find the cluster shape in both cases, although the orientation remains uncertain. HADES-R contributes to an efficient way to locate multiple events simultaneously with minimal prior information. The method’s ability to constrain the cluster shape and location with only one well-located event offers promising implications, especially for environments where limited or specialized instrumentation is in use.