Modeling the 1992 Landers Earthquake with a Rate and State Friction Model.

We study rupture propagation in realistic earthquake models under rate and state dependent friction and we apply it to the modeling of the 28 June 1992, Landers earthquake. In our simulations we use a modified version of rate and state proposed by Perrin, Rice and Zheng, the so called PRZ law. Full inversion with PRZ is not yet possible because of the much higher numerical cost of modeling a fault under rate and state than with slip weakening friction laws (SW). Also PRZ has a larger number of independent parameters than slip weakening. We obtain reasonable initial models through the use of the ratio κ between available strain energy and energy relase rate. Because in PRZ friction there are more parameters than in SW we have not yet been able to identify all relevant non-dimensional numbers that control rupture in this model, but a very important one is a logarithmic map that controls whether instable slip may occur or not. This map has the form log ˙ D/v₀ = λ ˙ D/v₀, where λ is a nondimensional number akin to κ . It includes the parameters of the friction law and the characteristic length of the initial stress, velocity or state fields. ˙ D is slip velocity and v₀ a reference speed that defines the initial stress field. Using the results of dynamic inversion from Peyrat et al, we find reasonable rupture models for the initiation of the Landers earthquake. The slip weakening distance in rate and state D_c, as defined by Bizarri and Cocco, is of the order of a few tens of cm. D_c is determined from L, the relaxation length in rate and state, as a subproduct of the logarithmic map cited above.