In inverting populations of focal mechanisms to estimate stress, misfits may arise owing to (1) errors in determining the fault plane solutions and (2) real variations in the state of stress. Among a number of techniques that invert for stress, most effectively regard only the latter and only indirectly describe the former through statistical means so make it difficult to differentiate real stress variations from noisy data. Ambiguity arises because realistic methods for determining focal mechanisms for small earthquakes depend on P wave first motions in a highly nonlinear manner, which is difficult to propagate into stress inversions. To address these issues, we present a new method for constraining stress tensors, in which first-motion observations are directly inverted for stress without assuming that focal mechanisms are known. The technique produces estimates of four stress parameters, a suite of focal mechanisms consistent with both the stress tensor and the first motions, and estimates of the uncertainty in stress. It also provides a natural test of the stress homogeneity hypothesis and a means to identify those earthquakes whose first motions are not consistent with a homogeneous stress tensor. When tested against artificial data, the method correctly recovers input stresses and yields uncertainties that depend upon both data distribution and reliability of first motion picks, as expected. Utilizing first motions from the southern California catalog, the method is applied to several clusters and aftershock sets, from 1981 to 1992. Typical uncertainties in stress orientation exceed 20-30 degrees at the 95% confidence level, resulting from similar to5% mispick rates typical of even the cleanest data. These uncertainties exceed some previous estimates for similar populations, presumably because they account for focal mechanism uncertainties, and perhaps indicating that some previously reported stress variations are not statistically significant. Most populations are found to be internally consistent with a homogeneous stress field, the most significant exceptions being aftershock sequences of some major earthquakes. In at least one case, the 1992 Landers sequence, aftershocks at the north end of the rupture zone appear to reflect exceedingly heterogeneous stresses. Overall, the method provides a useful and robust approach for evaluating stress constraints provided by P wave first motions.
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