3D rupture dynamics of earthquakes simulations for branching fault systems.

P. Galvez(1), J.P Ampuero(3), T. Nissen-Meyer(2) and L. Dalguer(1). 1.  Swiss Seismological Service (ETH-Zurich) , 2. Institute of Geophysics (ETH-Zurich) 3. California Institute of Technology (Caltech)

Introduction

An important goal of computational seismology is to simulate earthquake dynamics and strong ground motion in realistic models that include crustal heterogeneities and complicated fault geometries. The goal of this work are the integration of dynamic earthquake rupture in an unstructured spectral element (SEM) solver to provide high flexibility in meshing complex.

The 3D open source spectral element (SEM) code SPECFEM3D-SESAME, the latest version of SPECFEM3D current version of this code provides the possibility of modeling dynamic rupture for multiple faults with non--planar geometries governing by slip weakening friction laws. Our implementation follows the principles introduced by Ampuero (2002) and Kaneko et al. (2008). Unstructured meshes of hexahedral elements are generated by CUBIT, a general purpose state-of-the-art mesh generation software. Meshing with progressive coarsening away from the fault pushes the absorbing boundaries away to allow an accurate resolution of the static field. The modularity of the code allows fast implementation of different friction laws and non--linear constitutive laws (damage and plasticity) in the fault zone or other physical processes related to dynamic rupture. Due to its capability to handle unstructured meshing, dynamic rupture in complex fault systems can be readily simulated. The current code has been successfully validated in the several SCEC benchmarks, including a 3D problem with branched faults.

Complex fault geometries systems.

A section of megathrust dipping fault (Went. et. al. 2009)

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M˙ ̇ u + ku = B−+τ,

Finite faults in SPECFEM3D

1. Motivation

2. Formulation

Meshing faults with “CUBIT” for planar faults : [(SPECFEM3D+CUBIT= “SESAME”) +( “Finite-Fault”) ]=“GOAL”

The discretization of the weak form of the equation of motion leads to the matrix equation:

3.1. Branching faults of strike slip events .

5. Conclusions

Figure 3. Meshing branching faults systems with coarsening using CUBIT .

Figure 4. Sketch of splay faults in subduction zones .

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Bij,ije+ = ±wiw jJe

ij ,

3. SIMULATIONS. 4. Results

3.3 Splay fault system in subduction zones.

SCEC  (Southern  California  Earthquake  Center)  .  (Rupture  Dynamics  Code  Valida>on  Workshop  ,  February  25th  2011).  

Sequence of slip rate snapshots simulations at t = 2.5s , 3.5 and 5s.

Figure 1. Plot (a) the entire California and the zooms of the boxed areas for (b) northern and (c) southern California. ( R. Ando et. al. 2009 )

3.2. Meshing faults with CUBIT.

TPV  15.   Asperity   Main  fault   Branch  fault  

Shear  Stress  (Mpa)   -­‐81.6   -­‐70   -­‐78  STRIKE SLIP LEFT LATERAL FAULTING.

4.1. Validation (2011 SCEC Benchmark)

where “M” and “K” are the mass stifffness matrix respectively given by Komatish et al. (2005). is traction vector on the fault The “B” faut boundary matrix is sparse rectangular matrix given by Kaneko et. al. (2008) Appendix A

This code has been compared with other programs in the 2011 SCEC validation benchmark . Figure bellow show the comparison of Rupture front , slip rate of different codes.

4.2. Splay faults in subduction zones.

Rupture Front (Main fault) Rupture Front (Branch fault) Slip of fault station: Strike 5.0 km dip 7.5km

Displacement at surface station: Strike 5.0 km dip 7.5km

Figure 2.. 2011 SCEC dynamic rupture validation workshop.

6. FUTURE WORK

1.  We have successfully implemented in the latest unstructured spectral element SPECFEM3D-SESAME the dynamic rupture formulation governed by slip weakening friction law.

2.  This formulation provides high flexibility in meshing complex faults such as fault with branches, dipping fault with splay faults.

3.  The code has been validated with SCEC benchmark problem TPV15.

4.  We have reproduced the rupture dynamic simulation of a dipping fault with splay fault activation studied by Went. et. al. (2009).

We will apply this dynamic rupture model to study the 2011 Mw9.0 Tohoku Japan earthquake . Implementation   of   a   hybrid   SEM-Discontinuous  Galerkin  formulation  on  the  fault   boundary   to   efficiently   dissipate  spurious  high--frequency  artifacts.    

where denote the weights associated with the GLL integration quadrature and is the Jacobian on the fault.

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wk

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Jeij

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τ

Barrier model Homogeneous model

Present work

Went et. al. (2009) Went et. al. (2009)

Present work

Slip (m)

Vertical displacement (m) Vertical displacement (m)

Slip (m)