SCEC TPV29

TPV 29 contains a vertical, right-lateral fault with rough fault interface (Figure [fig:tpv29]). The fault surface has 3D stochastic geometrical roughness (blue and red colors). In TPV 29, the surrounding rocks respond elastically.

Diagram of TPV 29.

Diagram of TPV 29. The fault is 40 km long along the strike. There is a circular nucleation zone on the right-lateral fault surface. The fault surface has 3D stochastic geometrical roughness (blue and red colors). The hypocenter is located 15 km from the left edge of the fault, at a depth of 10 km.

Geometry

The roughed fault interface model is generated with Gmsh is complicated than planar faults in previous sections. There are 5 steps to generate the model.

1.Download fault topography data from SCEC. There are 2001 nodes
along the strike and 1201 nodes along the downdip. The node files should contain:
Line 1: nx, ny
Line 2 to nx: positions of nodes along the strike (in meters)
Line nx+3 to ny+nx+3: positions of nodes along the downdip (in meters)
Line to the end: fault topography of each nodes (nx\*ny, in meters)

Save this file as mytopo_tpv29.

2.Make a model with plane fault as Figure [fig:tpv29geo]. The Gmsh tpv29.geo file can be found at

Diagram showing the geometry of TPV 29.

Diagram showing the geometry of TPV 29. The center of nucleation is at (-8, 0, -10) km on the main fault.

3.Use gmsh_plane2topo.f90 and interpol_topo.in* to shift the planar fault according to positions given in mytopo_tpv29.

$ ./gmsh_plane2topo interpol_topo.in
This will generate a step1_modified.msh file which containing rough
fault surface.

4.Make a new step2.geo file that contains the new rough fault and mesh following general Gmsh process.

Diagram showing the geometry of TPV 29.

Diagram showing the geometry of TPV 29. The center of nucleation is at (-8, 0, -10) km on the main fault.

5. Generate MSH mesh with the command line:

& gmsh tpv29_step2.geo -3 -optimize_netgen -o tpv29_step2.msh

option optimize_netgen is necessary for optimizing meshing with good quality.

Material parameters

In TPV29, the entire model volume is a linear elastic material, with the following parameters listed in Table [table:tpv29material].

Parameter Description Value Unit
\(\rho\) density 2670 \(kg/m^{3}\)
\(\lambda\) Lame’s first parameter 3.2044e10 Pa
\(\mu\) shear module 3.2038e10 Pa
\(h_{edge}\) element edge length 200 m
\(V_p\) P wave velocity 6000 m/s
\(V_s\) S wave velocity 3464 m/s

[table:tpv29material]

Initial stress

The initial stress are listed in Table [table:tpv29fault].

Parameter Description Value Unit
mu_s static friction coefficient 0.12  
mu_d dynamic friction coefficient 0.18  
d_c critical distance 0.30 m
s_zz \(\sigma_{zz}\) -2670*9.8*depth Pa
Pf fluid pressure 1000*9.8*depth Pa
s_xz,s_yz \(\sigma_{xz}, \sigma_{yz}\) 0 Pa
s_yy   \(\Omega * b33*(\sigma_{zz} + P_f) - P_f\) Pa
s_xx   \(\Omega * b11*(\sigma_{zz} + P_f) - P_f\) Pa
s_xy   \(\Omega * b13*(\sigma_{zz} + P_f)\) Pa

Table: Table of initial stress in TPV 29. \(b11, b33,b13\) are 1.025837, 0.974162, −0.158649, respectively.

Note that the effective stress tensor is :

\[\begin{split}\bar{\sigma}_{effective}= \begin{bmatrix} &\sigma_{xx} + P_f , & \sigma_{xy} ,& \sigma_{xz} \\ &\sigma_{xy}, &\sigma_{yy} +P_f , &\sigma_{yz} \\ &\sigma_{xz} ,&\sigma_{yz} , &\sigma_{zz} +P_f \end{bmatrix}\end{split}\]

where \(\Omega\) is defined as:

\[\begin{split}\Omega = \left\{ \begin{array}{lr} &1, depth \leq 17000 m \\ & (22000 - depth)/5000 m, 17000 < depth < 22000 m \\ & 0, depth \geq 22000 m\\ \end{array} \right.\end{split}\]

Nucleation parameters

TPV29 uses a similar strategy for dynamic rupture nucleation.

\[\begin{split}T = \left\{ \begin{array}{lr} & \frac{r}{0.7Vr} + \frac{0.081*r_{crit} }{0.7Vr} (\frac{1}{1-(r/r_{crit})^2} - 1), r \leq r_{crit} \\ & 1E+09, r > r_{crit}\\ \end{array} \right.\end{split}\]

The cohesion zone is defined as :

\[\begin{split}C_0 = \left\{ \begin{array}{lr} & 0.4 MPa + 0.000675 MPa * (4000- depth), depth < 4000 m \\ & 0.4 MPa, depth \geq 4000 m\\ \end{array} \right.\end{split}\]

The friction parameters on the fault are listed in Table [table:tpv29fric].

Parameter Description Value Unit
mu_s static friction coefficient 0.12  
mu_d dynamic friction coefficient 0.18  
d_c critical distance 0.30 m
t_0 forced rupture delay time 0.5 s

Table: Table of friction parameters in TPV 29.

Results

The earthquake rupture is artificially nucleated in a circular zone on the fault surface.

Snapshot of slip rate along the strike

Snapshot of slip rate along the strike at T=3 s in TPV 29. The fault has a rough surface.