HR: 16:15h
AN: NG12C-02 INVITED     [PDF]
TI: A generalized law for aftershock rates in a damage rheology model
AU: * Ben Zion, Y
EM: benzion@earth.usc.edu
AF: Department of Earth Sciences, University of Southern California, Los Angeles, CA 90089-0740 United States
AU: Lyakhovsky, V
EM: vladi@geos.gsi.gov.il
AF: The Geological Survey of Israel, Malkhei Israel 30, Jerusalem, 95501 Israel
AB: Aftershocks are the response of a damaged rock surrounding large earthquake ruptures to the stress perturbations produced by the large events. Lyakhovsky et al. [JGR, 1997] developed a damage rheology model that provides a quantitative treatment for macroscopic effects of evolving distributed cracking with local density represented by a state variable a. The equation for damage evolution, based on the balance equations of energy and entropy and generalization of linear elasticity, accounts for both degradation and healing as a function of the existing strain tensor and material properties that may be constrained by lab data (rate coefficients and ratio of strain invariants separating states of degradation and healing). Analyses of stress-strain and acoustic emission laboratory data during deformation leading to brittle failure indicate further [Liu et al., AGU, F01; Hamiel et al., this meeting] that the fit between model predictions and observations improves if we also incorporate gradual accumulation of a non-reversible deformation with a rate proportional to the rate of damage increase. For analysis of aftershocks, we consider the relaxation process of a material following the application of a strain step associated with the occurrence of a mainshock. The coupled differential equations governing the damage evolution and stress relaxation can be written in non-dimensional form by scaling the elastic stress to its initial value and the time to characteristic time of damage evolution td. With this, the system behavior is controlled by a single non-dimensional ratio R = td/tM representing the ratio between the damage time scale to the Maxwell relaxation time tM. For very small R there is no relaxation and the response consists of constant rate of damage increase until failure. For very large R there is rapid relaxation without significant change to the level of damage. For intermediate cases the equations are strongly coupled and nonlinear. The analytical solution for the damage evolution contains error functions and is richer than a simple power law relation. However, the results associated with the analytical expression can be fitted well for various values of R with a power law similar to the modified Omori law for aftershocks. This also holds for 3D numerical simulations of aftershock sequences with our damage rheology model. Initial results based on 3D simulations indicate that high values of R corresponding to low viscosity material produce diffuse (swarm-like) aftershock sequences, while low values of R corresponding to more brittle material produce clear (Omori-like) aftershock sequences.
DE: 3210 Modeling
DE: 7209 Earthquake dynamics and mechanics
DE: 7260 Theory and modeling
SC: Nonlinear Geophysics [NG]
MN: 2003 Fall Meeting