Abstract

We have developed procedures for inverting broadband waveforms for the finite-moment tensors (fmts) of regional earthquakes. The fmt is defined in terms of second-order polynomial moments of the source space–time function; it removes the fault-plane ambiguity of the centroid moment tensor (cmt) and yields several additional parameters of seismological interest: the characteristic length Lc, width Wc, and duration Tc of the faulting, as well as the directivity vector vd of the fault slip. Following McGuire et al. (2001), we represent the observed waveform relative to the synthetic in terms of two frequency-dependent differential times, a phase delay δτp(ω) and an amplitude-reduction time δτq(ω), which we measure using the generalized seismological data functional (gsdf) method (Gee and Jordan, 1992). We numerically calculate the fmt partial derivatives, which allows us to use synthetics computed by using any forward-modeling tools. We have tested our methodology on Southern California Seismic Network (scsn) recordings of the 03 September 2002 Yorba Linda earthquake (MW 4.3). Using 1D synthetic Green’s functions, we determined the cmt and resolved fault-plane ambiguity. To resolve the details of source finiteness, we employed a joint-inversion technique that recovers the cmt parameters of the aftershocks and the cmt and fmt parameters of the mainshock. The joint system of equations relating the data to the source parameters of the mainshock–aftershock cluster is denuisanced for path anomalies in both observables; this projection operation effectively corrects the mainshock data for path-related anomalies in a way similar to, but more flexible than, empirical Green’s function (egf) techniques. Our results indicate that the Yorba Linda rupture occurred as left-lateral slip on a fault-patch conjugate to the nearby, right-lateral Whittier fault. We obtained source dimensions of Lc = 0.7 ± 0.1 km, Wc = 0.4 ± 0.1 km, and Tc = 0.2 ± 0.05 sec, implying a stress drop of about 3.2 MPa, and we found a directivity of 0.8 ± 0.2, oriented up and to the northeast. The inferred fault plane is consistent with the mainshock–aftershock distribution relocated by Hauksson et al. (2002).

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