Annual Report, 1997

Management of LARSE II (UCLA) Stress Modeling and Data Analysis

Paul Davis and Steve Persh

Inversions of strong motion seismic records in California have indicated that earthquakes preferentially nucleate towards the base of the brittle crust (~15 km), and evidence is accumulating that post-seismic creep on a fault (Shen et al., 1994; Jackson et al., 1997) can account for a sign)ficant fraction of the total moment release. A common model for earthquakes consists of brittle rupture of an elastic crust overlying a viscoelastic half-space. We are performing dynamic earthquake calculations in the context of this model to investigate the earthquake cycle. In the dynamical calculation, the final displacement on the fault and maximum depth of penetration of the crack are governed by the form of the stress drop, which is the difference between the applied stress just prior to nucleation and the dynamic friction.

We follow Burridge and Halliday's calculation in which a cohesionless crack is brought to rest by increasing friction at depth (due to overburden pressure). We assume that on short time scales associated with rupture, the viscoelastic effects are negligible and dynamic friction in the half-space increases with depth as in the brittle region. Thus, during the earthquake, the crack penetrates into the viscoelastic region. Because the dynamic friction is assumed to increase with depth, the stress drop eventually changes sign. In this model, the limiting depth of earthquake rupture is determined by the depth at which this occurs.

On longer time scales, however, this region undergoes ductile flow so that over time the static stress increase in the substrate resulting from the halting of the earthquake is relaxed by viscous dissipation. This relaxation imposes stress on the locked overlying region, with the greatest amount concentrated at its base, near the brittle-ductile transition. The applied stress state is therefore the sum ofthree stresses: those remaining from the previous earthquake; those due to tectonic motion; and the loading from the relaxation of the underlying region. Because the latter's distribution peaks towards the locked zone's base, we expect that with time the overall stress in the lower few km of the brittle crust will increase faster with depth than elsewhere. Nucleation, which occurs when the applied stress exceeds the rock strength, will therefore be more likely at these depths.

Figure ( 1 ) shows various stages of the earthquake cycle after several cycles have been run: (1) pre-stress before the earthquake (2) stress immediately after rupture (3) Superposition of stress changes from viscous relaxation of the substrate showing that the stress peak moves upwards into the brittle zone (4) build-up of tectonic stress to give a
stress distribution similar to (1) and (5) the cycle recommences showing stress immediately after the next earthquake. The high stress at stage (4) favors nucleation at depth. We propose to match this non-dimensional model with seismic and geodetic observations in our next cycle.

Burridge, R. and G.S. Halliday, Dynamic shear cracks with friction as models for shallow focus earthquakes, Geophys. J. R. astr. Soc., 261-283, 1971.