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

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 degrees uncertainties (> 70% of the catalog events) and 126% more solutions with < 25 degrees 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 degrees angular differences from the 2004 M-w 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.