Automatic determination of focal depth with the optimal period of Rayleigh wave amplitude spectra and uncertainty assessment in 3D velocity model

Focal depth of earthquakes is essential for studies of seismogenic processes and seismic hazards. Surface waves are usually the strongest seismic phases at local and regional distances, and its excitation is sensitive to source depth. We observe that the optimal period (the period corresponding to the maximum amplitude) of Rayleigh waves at local distances shows an almost linear correlation with focal depth, based on which we propose a method for resolving the focal depth of local earthquakes. We propose an automated data processing workflow, and applications to earthquakes in diverse tectonic settings demonstrate that reliable focal depth with uncertainty of 1~2 km can be determined even with one or a few seismic stations. Then, we use the Longmenshan region as a case study to systematically assess the impact of the 3D velocity model on the results through forward simulation. A total of 191 events at depths ranging from 5 to 20 km are simulated. The standard deviation between the focal depths determined by this method and the input values is approximately 1.5 km, with 95% events having errors within 2 times the standard deviation. This indicates that the method exhibits good applicability even in regions with complex velocity structures, and highlights the applicability of the method in scenarios characterized by sparse network coverage or historical events.