Fault Heterogeneity and the Connection between Aftershocks and Afterslip

Abstract

Whether aftershocks originate directly from the mainshock and surrounding stress environment or from afterslip dynamics is crucial to the understanding of the nature of aftershocks. We build on a classical description of the fault and creeping regions as two blocks connected elastically, subject to different friction laws. We show analytically that, upon introduction of variability in the fault plane's static friction threshold, a non trivial stick-slip dynamics ensues. In particular we support the hypothesis [23] that the aftershock occurrence rate is proportional to the afterslip rate, up to a corrective factor that is also computed. Thus, the Omori law originates from the afterslip's logarithmic evolution in the velocity-strengthening region. We confirm these analytical results with numerical simulations, generating synthetic catalogs with statistical features in good agreement with instrumental catalogs. In particular we recover the Gutenberg-Richter law with a realistic b-value (b 1) when Coulomb stress thresholds obey a power law distribution.

The influence of the brittle-ductile transition zone on aftershock and foreshock occurrence

“…In ref. 11 , we have demonstrated this proportionality in a model with only two elastically coupled degrees of freedom. The first described the fault displacement, with an heterogeneous velocity-weakening friction, while the second corresponded to the ductile region displacement, with a velocity-strengthening friction.…”

“…1 from ref. 11 : each fault is modeled as a twodimensional layer (and no longer as a single block). The fault plane H is subject to velocity-weakening friction τ h , in the form of randomly placed pinning points (red disks) with varying pinning strength τ th i (disk radius).…”

“…In this article, we show that friction heterogeneities and the slow deformation of a velocity-strengthening layer are sufficient ingredients to explain the whole ensemble of instrumental findings regarding the organization in time, space, and magnitude of both aftershocks and foreshocks. To this extent, we combine the model of two blocks of Lippiello et al 11 with the description of the fault plane originally proposed by Burridge and Knopoff (BK) 33 : a twodimensional elastic interface with many degrees of freedom, each being subject to a velocity-weakening friction law. Therefore our model of the fault consists in a collection of sliding blocks connected to a more ductile region, itself treated as an extended interface subject to velocity-strengthening rheology.…”

The influence of the brittle-ductile transition zone on aftershock and foreshock occurrence

“…At the same time, the stress redistributed by the mainshock in velocity strengthening regions induces some slow deformations, commonly defined as afterslip In ref. [4], we have demonstrated this proportionality in a model with only two elastically coupled degrees of freedom. The first described the fault displacement, with an heterogeneous velocity weakening friction, while the second corresponded to the ductile region displacement, with a velocity strengthening friction.…”

“…To this extent we combine the model of two blocks of ref. [4] with the description of the fault plane originally proposed by Burridge & Knopoff (BK) [26]: a two-dimensional elastic interface with many degrees of freedom, each being subject to a velocity weakening friction law. Therefore our model of the fault consists in a collection of sliding blocks connected to a more ductile region, itself treated as an extended interface subject to velocity strengthening rheology.…”