Constraining friction, dilatancy and effective stress with earthquake rates in the deep crust

Abstract:

Similar to their behavior on the deep extent of some subduction zones, families of recurring low-frequency earthquakes (LFE) within zones of non-volcanic tremor on the San Andreas fault in central California show strong sensitivity to stresses induced by the tides. Taking all of the LFE families collectively, LFEs occur at all levels of the daily tidal stress, and are in phase with the very small, ~200 Pa, shear stress amplitudes while being uncorrelated with the ~2 kPa tidal normal stresses.

Following previous work we assume LFE sources are small, persistent regions that repeatedly fail during shear within a much larger scale, otherwise aseismically creeping fault zone and that the correlation of LFE occurrence reflects modulation of the fault creep rate by the tidal stresses. We examine the predictions of laboratory-observed rate-dependent dilatancy associated with frictional slip. The effect of dilatancy hardening is to damp the slip rate, so high dilatancy under undrained pore pressure reduces modulation of slip rate by the tides. The undrained end-member model produces: 1) no sensitivity to the tidal normal stress, as first suggested in this context by Hawthorne and Rubin [2010], and 2) fault creep rate in phase with the tidal shear stress. Room temperature laboratory-observed values of the dilatancy and friction coefficients for talc, an extremely weak and weakly dilatant material, under-predict the observed San Andreas modulation at least by an order of magnitude owing to too much dilatancy. This may reflect a temperature dependence of the dilatancy and friction coefficients, both of which are expected to be zero at the brittle-ductile transition. The observed tidal modulation constrains the product of the friction and dilatancy coefficients to be at most 5 x 10^-7 in the LFE source region, an order of magnitude smaller than observed at room temperature for talc. Alternatively, considering the predictions of a purely rate-dependent talc friction would constrain the ambient effective normal stress to be no more than 40 kPa. In summary, for friction models that have both rate-dependent strength and dilatancy, the observations require intrinsic weakness, low dilatancy, and lithostatic pore fluid pressures.