Interaction of faults under slip‐dependent friction. Non‐linear eigenvalue analysis

Ionescu, Ioan R.; Wolf, Sylvie

doi:10.1002/mma.550

Cited by 22 publications

(22 citation statements)

References 22 publications

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“…This is true if and only if w ≡ 0 is a solution of (14). The first eigenvalue 0 for problem (2)-(3) can be related to the stability analysis near equilibrium: that was done in [12]. More precisely if…”

Section: Physical Motivationmentioning

confidence: 98%

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Earth surface effects on active faults: An eigenvalue asymptotic analysis

Ionescu

Volkov

2008

Journal of Computational and Applied Mathematics

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We study in this paper an eigenvalue problem (of Steklov type), modeling slow slip events (such as silent earthquakes, or earthquake nucleation phases) occurring on geological faults. We focus here on a half space formulation with traction free boundary condition: this simulates the earth surface where displacements take place and can be picked up by GPS measurements. We construct an appropriate functional framework attached to a formulation suitable for the half space setting. We perform an asymptotic analysis of the solution with respect to the depth of the fault. Starting from an integral representation for the displacement field, we prove that the differences between the eigenvalues and eigenfunctions attached to the half space problem and those attached to the free space problem, is of the order of d −2 , where d is a depth parameter: intuitively, this was expected as this is also the order of decay of the derivative of the Green's function for our problem. We actually prove faster decay in case of symmetric faults. For all faults, we rigorously obtain a very useful asymptotic formula for the surface displacement, whose dominant part involves a so called seismic moment. We also provide results pertaining to the analysis of the multiplicity of the first eigenvalue in the line segment fault case. Finally we explain how we derived our numerical method for solving for dislocations on faults in the half plane. It involves integral equations combining regular and Hadamard's hypersingular integration kernels.

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Section: Physical Motivationmentioning

confidence: 98%

“…and if w ∈ V is a local extremum for W, then w is a solution of (14) (see [10,12]). Moreover, there exists at least a global minimum for W on V. Let us now analyze the stability of the equilibrium w ≡ 0.…”

Section: Physical Motivationmentioning

confidence: 99%

Earth surface effects on active faults: An eigenvalue asymptotic analysis

Ionescu

Volkov

2008

Journal of Computational and Applied Mathematics

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“…In this subsection, we briefly describe the finite element numerical method used to solve the non‐linear spectral problem, which is detailed by Ionescu & Wolf (2005). Later, we will present the computation of the time‐dependent problem to test the spectral method.…”

Section: Numerical Resolution Of the Non‐linear Spectral Problemmentioning

confidence: 99%

“…This can be done by considering the successive iterates of the non‐linear operator, after choosing an initial guess. The detailed algorithm can be found in Ionescu & Wolf (2005). We only discuss here the properties of our spatial discretization.…”

Section: Numerical Resolution Of the Non‐linear Spectral Problemmentioning

confidence: 99%

Mechanics of normal fault networks subject to slip-weakening friction

Wolf

Manighetti

Campillo

et al. 2006

Geophysical Journal International

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International audienceWe seek to understand how the stress interactions and the slip-weakening process combine within a non-coplanar, normal fault network to allow a slip instability to develop, and shape the final slip distribution on the system. In a first part, we perform a non-linear spectral analysis to investigate the conditions of stability and the process of slip initiation in an antiplane non-coplanar fault system subject to a slip-dependent friction law. That numerical model allows determining the zones that are able to slip within a fault network, as well as the location of the stress singularities. The resulting slip profiles on the faults show only a few different shapes, some of them with long, linear sections. This leads to formulate a general classification of slip profiles that can be used to infer the degree of fault interaction within any non-coplanar system. In a second part of work, we use our modelling to try reproducing the cumulative slip profiles measured on three real normal interacting faults forming a large-scale en echelon system. For that, we assume that cumulative slip profiles can be compared to the first static modal solution of our conceptual model. We succeed reproducing the profiles quite well using a variable weakening along the faults. Overall, the weakening rate decreases in the direction of propagation of the fault system. Yet, modelling the slip along the propagating, isolated termination segment of the system requires an unlikely distribution of weakening. This suggests that factors not considered in our analysis may contribute to slip profile shaping on isolated, propagating faults

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“…The mathematical analysis of some models for antiplane frictional contact problems with elastic materials can be found in Refs. 1,13,14,17 and in the recent book Ref. 25.…”

Section: Introductionmentioning

confidence: 98%

Modeling and Analysis of an Antiplane Piezoelectric Contact Problem

Migórski

Ochał

Sofonea

2009

Math. Models Methods Appl. Sci.

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We study a mathematical model which describes the antiplane shear deformations of a piezoelectric cylinder in frictional contact with a foundation. The process is static, the material behavior is described with a linearly electro-elastic constitutive law, the contact is frictional and the foundation is assumed to be electrically conductive. Both the friction and the electrical conductivity condition on the contact surface are described with subdi®erential boundary conditions. We derive a variational formulation of the problem which is in the form of a system of two coupled hemivariational inequalities for the displacement and the electric potential¯elds, respectively. Then we prove the existence of a weak solution to the model and, under additional assumptions, its uniqueness. The proofs are based on an abstract result on operator inclusions in Banach spaces. Finally, we present concrete examples of friction laws and electrical conductivity conditions for which our results are valid.

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Interaction of faults under slip‐dependent friction. Non‐linear eigenvalue analysis

Cited by 22 publications

References 22 publications

Earth surface effects on active faults: An eigenvalue asymptotic analysis

Earth surface effects on active faults: An eigenvalue asymptotic analysis

Mechanics of normal fault networks subject to slip-weakening friction

Modeling and Analysis of an Antiplane Piezoelectric Contact Problem

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