Quasi‐dynamic modeling of seismicity on a fault with depth‐variable rate‐ and state‐dependent friction

Abstract

[1] Neither the Omori type of clustering prior to and following large earthquakes nor the Gutenberg-Richter distribution are reproducible by present continuous models. Discrete models, on the other hand, give rise to more complex and closer to realistic earthquake clustering. The objective of this study is twofold: to explore the consequences of spatial discreteness on the distribution in time and space of earthquake activity on a fault governed by rate-and-state friction and to examine the effect of interaction between seismic slip and aseismic creep on aftershock sequences. To that end we model a long, vertical, two-dimensional strike-slip fault that is governed by rate-and state-dependent friction and is embedded in a three-dimensional elastic half-space. Quasi-dynamic motion on the fault is driven by steady displacement applied below the fault and at distance W/2 on either side of the fault plane. The model is said to be spatially discrete in that the computational cells are oversized with respect to the critical length scale that is implied by the friction law. The model reproduces some of the characteristics of natural seismicity, including the nonperiodic recurrence times and the Omori type of clustering prior to and following large earthquakes. It also produces a wide range of earthquake magnitudes but with a ratio of small to large earthquakes that is in excess with respect to what is inferred form natural catalogs. We examined the effect of a stress step applied on the creeping portions of the model and confirmed that aftershock sequences resulting from stress relaxation on creeping segments decay asymptotically to 1/time. Finally, we discuss fundamental differences between seismicity models employing rate-and-state friction and those employing static/kinetic friction.Citation: Ziv, A., and A. Cochard (2006), Quasi-dynamic modeling of seismicity on a fault with depth-variable rate-and statedependent friction,

Interactions and triggering in a 3‐D rate‐and‐state asperity model

“…Motivated by friction experimental results, more mechanical models have nevertheless been proposed to produce a realistic seismicity. That is, for instance, the case of discrete models of faults that include rate‐and‐state friction as well as realistic stress interaction kernels [ Dieterich , ; Ziv and Rubin , ; Ziv and Cochard , ]. Although these models are able to produce satisfying statistics, including Omori decay and Gutenberg‐Richter distribution, they are limited by the impossibility to obtain realistic nucleation because of over‐sized computational cells compared to the critical length for nucleation predicted by rate‐and‐state theory [ Rice and Ruina , ; Ruina , ], or to group computational cells in order to define asperities since all the cells are independent.…”

Three‐dimensional boundary integral modeling of spontaneous earthquake sequences and aseismic slip

“…The quasi-dynamic formulation has been widely used in earthquake studies [e.g., Rice, 1993;Ben-Zion and Rice, 1995;Rice and Ben-Zion, 1996;Hori et al, 2004;Kato, 2004;Hillers et al, 2006;Ziv and Cochard, 2006]. It ignores wave-mediated stress transfers expressed through convolutions integrals in equation (5) by setting During the first event, dynamic rupture interacts with the stronger patch and produces a supershear burst.…”

“…[7] Section 6 compares the fully dynamic formulation developed in this work with quasi-dynamic approaches [e.g., Rice, 1993], which have been widely used in earthquake studies [e.g., Rice, 1993;Ben-Zion and Rice, 1995;Rice and Ben-Zion, 1996;Hori et al, 2004;Kato, 2004;Hillers et al, 2006;Ziv and Cochard, 2006]. Quasi-dynamic approaches significantly simplify the treatment of inertial effects during simulated earthquakes by ignoring wavemediated stress transfers.…”

“…[3] Several approaches to modeling long-term histories of fault slip have been proposed [e.g., Shibazaki and Mastsu'ura, 1992;Cochard and Madariaga, 1996;Kato, 2004;Duan and Oglesby, 2005;Liu and Rice, 2005;Hillers et al, 2006;Ziv and Cochard, 2006] but all of them adopted simplified treatments of either slow tectonic loading and hence aseismic slip, or inertial effects during dynamic rupture, or transition between interseismic periods and dynamic rupture. Lapusta et al [2000], on the basis of prior studies [Tse and Rice, 1986;Rice and Ben-Zion, 1996; Ben-Zion and Rice, 1997], developed a methodology capable of capturing both seismic and aseismic slip and the gradual process of earthquake nucleation.…”

Character of slip and stress due to interaction between fault segments along the dip direction of a subduction zone

“…Those numerical simulations show that events with smaller rupture areas generally also have smaller seismic slips and the ensuing relation between frequency and magnitude obeys the Gutenberg-Richter distribution (e.g., Hirose and Hirahara, 2004;Ziv and Cochard, 2006). If a large earthquake is treated as a coalescence of small earthquakes, those simulation results support the constant stress-drop model (e.g., Liu-Zeng et al, 2005;Kanamori and Anderson, 1975), which is different from our results in which seismic rupture propagation is stopped by a large aseismic segment.…”