A New Focal Mechanism Calculation Algorithm (REFOC) Using Inter‐Event Relative Radiation Patterns: Application to the Earthquakes in the Parkfield Area

Abstract

Accurate earthquake focal mechanisms are essential for solving fault zone structure, estimating stress variations, and assessing seismic hazards. Small earthquakes' focal mechanisms are usually solved using P‐wave first‐motion polarities and/or S‐/P‐wave amplitude ratios, which are limited due to the low signal‐to‐noise ratio of small‐earthquake waveforms and a limited number of three‐component seismograms. To increase the number of high‐quality focal mechanisms, we develop a method that utilizes the inter‐event relative radiation patterns to perform a joint focal mechanism inversion of numerous clustered events (called REFOC). The method first uses P‐wave polarities and S‐/P‐wave amplitude ratios to constrain the initial solutions and then combines these solutions and the inter‐event P‐/P‐wave and S‐/S‐wave amplitude ratios to refine solutions. For example, we apply the method to 38,413 earthquakes in the Parkfield region, California. The REFOC outperforms traditional methods with 57% more solutions with <55° uncertainties (>70% of the catalog events) and 126% more solutions with <25° uncertainties (>40% of the catalog events), illuminating unprecedented fine‐scale rupture processes. Instead of rupturing along the main fault, many M < 2 focal mechanisms show >45° angular differences from the 2004 Mw 6.0 Parkfield earthquake. The variation of focal mechanism properties is spatially related to the variation of fault strength and geometry, and temporally correlated with the shear stress variations before, during, and after the 2004 Mw 6.0 earthquake. The observations highlight the potential of applying REFOC to monitor unprecedented details of fault zone structure and stress field, providing new insights into fault rupture physics, seismotectonic processes, and seismic hazards.

3D architecture and complex behavior along the simple central San Andreas fault

“…The variation of fault geometry and surface roughness 58 can also significantly affect the fault strength. One possible way to estimate the strength of the CSAF might be the direct estimation of absolute stress levels before moderate earthquake ruptures along the CSAF based on changes of small earthquake focal mechanisms 29 . For example, we can search over possible absolute stress levels, model the stress rotation in the fault zone before and after the 2004 Parkfield earthquake using finite source slip models 59,60 , and compare the results with the focal mechanism observations 61 .…”

“…In this study, we calculate the focal mechanisms along the CSAF using the REFOC algorithm 29 , which uses first-motion polarities, S-/P-wave amplitude ratios to obtain the initial earthquake focal mechanisms and further constrain them using the P-wave amplitude ratios and S-wave amplitude ratios of closely located earthquakes within 3 km hypocentral distance. We utilize the polarities, P-and Swave phases manually picked by data analysts, and the relocated earthquake catalog archived by the Northern California Earthquake Data Center (NCEDC).…”

“…We utilize the polarities, P-and Swave phases manually picked by data analysts, and the relocated earthquake catalog archived by the Northern California Earthquake Data Center (NCEDC). We use the same P-wave velocity models 29 and the S-wave velocity models are derived from P-wave velocity models by assuming that the P-/S-wave velocity ratio equals 1.732. We apply a 1-10 Hz band-pass-filter to earthquake waveform data from NCEDC, choose 0.5s before to 1.5s after P-and S-wave arrivals as the signal windows and 2.5s to 0.5s before P-wave arrivals as noise windows, and take the difference between maximum and minimum amplitude values in each time window to be the estimated signal and noise amplitudes.…”

“…1922, 1934, 1966, and 2004 𝑀6.0 Parkfield earthquake), abundant small earthquakes 24 , and repeating earthquakes whose recurrence rate is proportional to the fault creep rate at depth 25,26,27,28 . In order to obtain focal mechanisms of the above-mentioned small earthquakes, we use a recently developed relative focal mechanism calculation algorithm 29 and obtained high-quality focal mechanisms (uncertainty < 35 degree) of ~80% of the 𝑀 " ≥ 1 catalog events 24 . The diverse fault deformation patterns, abundant earthquakes, and their focal mechanisms provide a great opportunity to comprehensively characterize and understand multiscale fault zone deformation processes along the CSAF and their connections (Figs.…”

CANVAS: An Adjoint Waveform Tomography Model of California and Nevada

“…Understanding the seismic risk to the populations of California and Nevada requires accurate seismic wavespeed modeling to provide more accurate estimations of shaking during large earthquakes (e.g., Rodgers et al., 2020). Accurate velocity models are also necessary for calculating stress variation using moment tensors (e.g., Cheng et al., 2023), which is also vital for understanding seismic hazard.…”