A first principles approach to understand the physics of precursory accelerating seismicity

Taxiarchis Papakostas Taxiarchis Papakostas,Filippos Vallianatos Filippos Vallianatos,Dimitrios Pliakis Dimitrios Pliakis

doi:10.4401/ag-5363

Taxiarchis Papakostas Taxiarchis Papakostas, Filippos Vallianatos Filippos Vallianatos + Show 1 more

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https://doi.org/10.4401/ag-5363

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Abstract

Observational studies from rock fractures to earthquakes indicate that fractures and many large earthquakes are preceded by accelerating seismic release rates (accelerated seismic deformation). This is characterized by cumulative Benioff strain that follows a power law time-to-failure relation of the form C(t) = K + A(Tf – t)m, where Tf is the failure time of the large event, and m is of the order of 0.2-0.4. More recent theoretical studies have been related to the behavior of seismicity prior to large earthquakes, to the excitation in proximity of a spinodal instability. These have show that the power-law activation associated with the spinodal instability is essentially identical to the power-law acceleration of Benioff strain observed prior to earthquakes with m = 0.25-0.3. In the present study, we provide an estimate of the generic local distribution of cracks, following the Wackentrapp-Hergarten-Neugebauer model for mode I propagation and concentration of microcracks in brittle solids due to remote stress. This is a coupled system that combines the equilibrium equation for the stress tensor with an evolution equation for the crack density integral. This inverse type result is obtained through the equilibrium equations for a solid body. We test models for the local distribution of cracks, with estimation of the stress tensor in terms of the crack density integral, through the Nash-Moser iterative method. Here, via the evolution equation, these estimates imply that the crack density integral grows according to a (Tf – t)0.3-law, in agreement with observations.

Highlights

It is well accepted that there is a wide range of problems in geophysics where it is necessary to understand how rock deforms, from earthquake prediction to the driving forces of plate tectonics [Main 1999]
The rock physics approach to understanding these geophysical processes is based on the premise that the macroscale behavior of rock is governed by microscale interactions
We extend in three dimensional space the studies of Wackertapp et al [2000] that derived a system of an ordinary differential equation coupled to the elliptic system of elasticity, introducing the crack density integral: I^jh = # ct^l, jhldl

Summary

Introduction

The failure of a solid due to microcrack concentration and propagation has been studied in various disciplines, including material sciences [Scherbakov and Turcotte 2003], rock mechanics [Turcotte et al 2003], solid earth geophysics [Main 1999], and seismology.It is well accepted that there is a wide range of problems in geophysics where it is necessary to understand how rock deforms, from earthquake prediction to the driving forces of plate tectonics [Main 1999]. To study the physics of seismicity in a similar way to the fracture of a solid, numerous approaches have appeared that have dealt with the propagation of cracks, and with static [Taguchi 1989] and dynamic [Wackertapp et al 2000, Mignan et al 2007] distributions of microcrack concentration. They derive the equations for the time evolution of an integral quantity related to the crack density.

Results

Conclusion