Analysis of earthquake body wave spectra for potency and magnitude values: implications for magnitude scaling relations

Abstract

We develop a simple methodology for reliable automated estimation of the low-frequency asymptote in seismic body wave spectra of small to moderate local earthquakes. The procedure corrects individual P- and S-wave spectra for propagation and site effects and estimates the seismic potency from a stacked spectrum. The method is applied to >11 000 earthquakes with local magnitudes 0 < M_L < 4 that occurred in the Southern California plate-boundary region around the San Jacinto fault zone during 2013. Moment magnitude M_w values, derived from the spectra and the scaling relation of Hanks & Kanamori, follow a Gutenberg–Richter distribution with a larger b-value (1.22) from that associated with the M_L values (0.93) for the same earthquakes. The completeness magnitude for the M_w values is 1.6 while for M_L it is 1.0. The quantity (M_w – M_L) linearly increases in the analysed magnitude range as M_L decreases. An average earthquake with M_L = 0 in the study area has an M_w of about 0.9. The developed methodology and results have important implications for earthquake source studies and statistical seismology.