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 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 M _w 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.

Plain Language Summary

Earthquakes and other tectonic activities are largely controlled by the stress field and structures within the Earth's crust, which are difficult to measure because of the lack of direct observations in depth. Earthquake focal mechanisms, containing fault plane and slip motion information, are the key to monitoring crustal state in seismogenic crust. However, solving the focal mechanisms of M < 3 earthquakes is very challenging due to the limited number of high‐quality records. In this study, we utilize the relative amplitudes of closely located earthquakes as additional observational parameters to constrain small‐earthquake focal mechanisms. The new method was applied to earthquakes in the Parkfield segment of the San Andreas fault and provided a twofold increase in the number of the focal mechanism solutions. Our results show that many small‐earthquake focal mechanisms are not consistent with the main fault slip. We suggest that the variation of focal mechanism properties is spatially related to fault strength and geometry, and temporally correlated with the shear stress variations before and after 2004 M _w 6.0 earthquake. The observations suggest that the large number of focal mechanisms solved using our new algorithm have the potential to monitor unprecedented small‐scale stress perturbations and fault structures and help better understand crustal dynamics.

Key Points

• We present a new focal mechanism calculation method using polarities, S/P amplitude ratios and inter‐event P/P and S/S amplitude ratios

• The application to the Parkfield area shows 43% of the events have high‐quality focal mechanisms (∼2 times the traditional catalog)

• Focal mechanism variations are spatially related to fault strength and geometry, and temporally correlated with the 2004 M _w 6.0 earthquake