Depth-Scanning Algorithm: Accurate, Automatic, and Efficient Determination of Focal Depths for Local and Regional Earthquakes

Precise source depths are critical to the understanding and interpretation of many seismological and tectonic processes. However, conventional earthquake location methods based on the arrival times of direct P and S phases have far less constraint on focal depths than on epicenters. 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 and regional distances, would make significant contributions to the geoscience research community. In this study, we develop a new method, named "Depth-Scanning Algorithm," 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 assumed focal depths, and the one most consistent with the theoretical prediction is deemed the final solution. Synthetic tests and applications to real data demonstrate the merits of our method compared to conventional location methods.