Efficient, Automatic, and Accurate Determination of Focal Depths for Local Earthquakes

Accurate determination of earthquake focal depths is a fundamental task in seismology. Precise source depths are critical to the understanding and interpretation of many seismological and tectonic processes. Therefore, developing a method that can systematically and efficiently estimate focal depths with high accuracy, especially for the vast number of small earthquakes that can only be observed at local distances, would make significant contributions to the geoscience research community. The traditional locating methods are all based on arrival times of P and/or S phases (e.g., HYPO71 or HYPOINVERSE). Although the P and S travel times can well constrain the origin time and epicenter of a seismic event, they are not sensitive to the variation of focal depth unless a dense seismic network is located close to the source. As a result, earthquake catalogs derived with traditional locating methods often have large depth uncertainties. Arrival times of depth phases, such as those reflected from the free surface or Moho discontinuity, can provide tight constraints on focal depth. However, the identification of depth phases is often done by visual inspection of seismograms that is time-consuming, labor-intensive, and requires considerable experiences. In this study, we develop a new automatic method to efficiently identify depth phases at local and regional distances. We first construct template waveforms of possible depth phases by applying various phase shifts to the original P and S waveforms to mimic the effect of reflection(s). We then systematically scan waveforms after the P and S phases for segments that match the depth-phase templates. The arrival times of those segments are compared to the theoretical arrival times of depth phases predicted with an assumed velocity model and focal depth. We repeat the above process for a range of focal depths, and the one with the most number of depth-phase matches and the minimal travel time residual is deemed the final solution. We conduct a series of synthetic experiments to verify the performance of our method. Accurate focal depths can be obtained with single or multiple stations located between 50 and 300 km away. Finally, we apply the new method to two induced earthquakes in Oklahoma to demonstrate its potential to solve challenging seismological problems.