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Rupture Directivity Characteristics of the 2003 Big Bear Sequence

Ying Tan, & Donald V. Helmberger

Published 2010, SCEC Contribution #1603

We have developed a forward modeling technique to retrieve rupture characteristics of
small earthquakes (3<M<5), including rupture propagation direction, fault dimension, and rupture speed. The technique is based on an empirical Green’s function (EGF) approach, where we use data from collocated smaller events as Green’s functions to study the bigger events. We tend to choose smaller events with similar focal mechanisms for EGFs, however, we show that the events with different focal mechanisms can work equally well when corrected for radiation pattern effect. Compared to deconvolution, this forward modeling approach allows full use of both the shape and amplitude information produced by rupture propagation. Assuming a simple 1D source model, we parameterize the source time function of a target event as the convolution of two boxcars, featuring the rise time τr and the rupture time τc, and we solve for τr and τc in a grid search manner by minimizing the waveform misfit between the three-component data and the “synthetics” constructed from the EGFs. The rupture propagation direction, fault length and rupture speed can then be estimated by fitting the observed azimuthal pattern of τc from P and S waves. We apply the approach to the twelve largest events (Mw ≥ 3.3) of the 2003 Big Bear sequence (excluding the main shock) in southern California. Among them, seven events are found to exhibit robust rupture directivity. The fact that the rupture of these events propagates in all directions suggests great complexity in the compact fault zone. Our results show large variations in stress drop, Δσ, which appears inversely correlated with rupture speed Vr. In particular, events with larger Δσ tend to propagate at smaller Vr, whereas events with smaller Δσ popagate faster.

Tan, Y., & Helmberger, D. V. (2010). Rupture Directivity Characteristics of the 2003 Big Bear Sequence. Bulletin of the Seismological Society of America, 100.