An improved method for determining the regional stress tensor using earthquake focal mechanism data: Application to the San Fernando Earthquake Sequence

Abstract

The orientations of fault planes and slip directions indicated by a population of earthquake focal mechanisms can be used to determine best fit regional principal stress directions and R = (σ 2–σ 1)/(σ 3–σ 1), a measure of relative stress magnitudes, under the assumption of uniform stress in the source region. This analysis allows for the possibility that failure occurs on preexisting zones of weakness of any orientation. In the inversion we perform a grid search of stress models to find the one which requires the smallest total rotation of all the fault planes that is needed to match the observed and predicted slip directions; the method allows for errors in orientations of both the fault planes and slip directions. We have an objective means for identifying the more likely of the two possible fault planes from each focal mechanism relative to a given stress model; thus we do not face the problem of ambiguity of nodal planes which plagues other analyses of this kind. By using a grid search of stress models rather than a linearization scheme, we are able to perform a realistic error analysis and thus establish confidence limits for the preferred regional stresses. The method can be used to investigate possible stress inhomogeneities during earthquake sequences by analyzing subsets of the data population. The technique has been applied to 76 events from the San Fernando earthquake sequence for which we have found best fit stresses (plunge and azimuth): σ 1, = 7,187; σ 2 = 27,281; σ 3 = 62,84; and R = 0.65. The average misfit between this stress model and all the data is about 8°, and all but eight of the aftershocks have misfits of less than 20°. These values are considerably less than the uncertainty of the focal mechanism determinations; therefore significant stress inhomogeneities are not required by the data. Our analysis does not support the suggestion of a change in stresses during the aftershock sequence, as proposed by others on the basis of an apparent change in focal mechanisms.