Strain waves, earthquakes, slow earthquakes, and afterslip in the framework of the Frenkel-Kontorova model

Abstract

The one-dimensional Frenkel-Kontorova ͑FK͒ model, well known from the theory of dislocations in crystal materials, is applied to the simulation of the process of nonelastic stress propagation along transform faults. Dynamic parameters of plate boundary earthquakes as well as slow earthquakes and afterslip are quantitatively described, including propagation velocity along the strike, plate boundary velocity during and after the strike, stress drop, displacement, extent of the rupture zone, and spatiotemporal distribution of stress and strain. The three fundamental speeds of plate movement, earthquake migration, and seismic waves are shown to be connected in framework of the continuum FK model. The magnitude of the strain wave velocity is a strong ͑almost exponential͒ function of accumulated stress or strain. It changes from a few km/s during earthquakes to a few dozen km per day, month, or year during afterslip and interearthquake periods. Results of the earthquake parameter calculation based on real data are in reasonable agreement with measured values. The distributions of aftershocks in this model are consistent with the Omori law for temporal distribution and a 1 / r for the spatial distributions.

Nonlinear waves and solitons in models of fault block geological media

“…In a study of Gershenzon et al (2009), the SG solution as slow cnoidal waves was used to model the strain dynamics at plate boundaries in the transform fault zones and related effects. The model describes quantitatively the evolution of the seismic process and slow earthquakes.…”

“…The mathematical models of fault dynamics, rotation, and sliding of blocks, which fit the SG equation, include as variables either the rotation angle (Garagash, 1996;Nikolaevskiy, 1995Nikolaevskiy, , 1996 or fault-parallel displacement of crust blocks (Bykov, 2000a;Gershenzon et al, 2009Gershenzon et al, , 2011.…”

“…Faulting, rotation, and slippage of crust blocks that induce strain waves have been modeled in recent two decades using the sine-Gordon (SG) equation, applied also to interpret the related tectonic effects (Bykov, 2001a(Bykov, , 2006(Bykov, , 2008Garagash, 1996;Gershenzon et al, 2009Gershenzon et al, , 2011Majewski, 2006a,b;Mikhailov and Nikolaevskiy, 2000;Nikolaevskiy, 1995Nikolaevskiy, , 1996Vikulin, 2008). The classical SG equation has several qualitatively different analytical solutions in the form of kinks, breathers, solitons, and slow and fast cnoidal waves, each referring to a certain evolution pattern of blocks and faults (Bykov, 2000a).…”

Slow strain waves in blocky geological media from GPS and seismological observations on the Amurian plate

“…The sine-Gordon equation solution in the shape of a breather has previously been applied for modeling the wave dynamics of faults and strain waves (Mikhailov and Nikolaevskiy, 2000;Gershenzon et al, 2009;Erickson et al, 2011). Mikhailov and Nikolaevskiy (2000) considered a scenario when collision of two tectonic waves (kink-antikink collision) resulted in the occurrence of a large earthquake.…”

“…Mikhailov and Nikolaevskiy (2000) considered a scenario when collision of two tectonic waves (kink-antikink collision) resulted in the occurrence of a large earthquake. The solution in the shape of a breather has also been applied for the interpretation of the features of fault dynamics observed after the 1989 Loma Prieta earthquake (Gershenzon et al, 2009). Based on a modified Burridge-Knopoff model, a solution has been obtained that corresponds to a localized failure -a breather that propagates along a fault and is damping in the fault segment of the final length (Erickson et al, 2011).…”