SCEC TPV24¶
TPV24 is designed to illustrate dynamic rupture in a fault branching system. TPV24 contains two vertical, planar strikeslip faults; the main fault and a branch fault intersecting at an angle of 30 degrees (Figure [fig:tpv24]). The earthquake rupture is artificially nucleated in a circular zone on the main fault surface and then spontaneously propagates to the branching fault.
Geometry¶
There are two faults, called the main fault and the branch fault (Figure [fig:tpv24]). The two faults are vertical, planar, strikeslip faults. The faults reach the earth’s surface.
The main fault is a rectangle measuring 28 000 m alongstrike and 15 000 m deep. The branch fault is a rectangle measuring 12 000 m alongstrike and 15 000 m deep. There is a junction point. It is located 12 000 m from the right edge of the main fault, and the main fault passes through it.
The branch fault makes an angle of 30 degrees to the main fault. The branch fault ends at the junction point.
The hypocenter is centered alongstrike at a depth of 10 km on the left side of the main fault. That is, the hypocenter is 8000 m from the junction point, and 10 000 m deep.
Figure [fig:tpv24mesh] shows the fault model generated in Gmsh. The mesh file can be found at. The mesh can be generated following the detailed process in Section [sec:tpv5].
Initial stress¶
The initial stress condition is depthdependent at the depth above 15600 m. Table [table:tpv24] summarizes the initial stress conditions in TPV24.
Parameter  Description  Value  Unit 

s_zz  \(\sigma_{zz}\)  2670*9.8*depth  Pa  
s_xz  \(\sigma_{xz}\)  0  Pa 
P_f  fluid pressure  1000*9.8*depth  Pa  
s_yz  \(\sigma_{yz}\)  0.0  Pa 
inside the nucleation zone  
s_yy  \(b33*(\sigma_{zz} + P_f)  P_f\)

Pa  
s_xx  \(b22*(\sigma_{zz} + P_f)  P_f\)

Pa  
s_xy  \(b23*(\sigma_{zz} + P_f)\)

Pa  
outside the nucleation zone  
s_yy  \(\sigma_{zz}\)

Pa  
s_xx  \(\sigma_{zz}\)

Pa  
s_xy  0

Pa 
Note that the effective stress tensor is :
\[\begin{split}\bar{\sigma}_{effective}= \begin{bmatrix} &\sigma_{xx} + P_f , & \sigma_{xy} ,& \sigma_{xz} \\ &\sigma_{xy}, &\sigma_{yy} +P_f , &\sigma_{yz} \\ &\sigma_{xz} ,&\sigma_{yz} , &\sigma_{zz} +P_f \end{bmatrix}\end{split}\]
Nucleation parameters¶
Nucleation is performed by forcing the fault to rupture, within a circular zone surrounding the hypocenter. Forced rupture is achieved by artificially reducing the friction coefficient, beginning at a specified time. The parameter specifies how long it takes for the friction coefficient to be artificially reduced from its static value to its dynamic value. So, the friction coefficient reaches its dynamic value at time. We reduce the friction coefficient gradually, over an interval of time, in order to smooth the nucleation process and reduce unwanted oscillations.
The cohesion zone is defined as :
Note that the frictional cohesion is 3.00 MPa at the earth’s surface. It is 0.30 MPa at depths greater than 4000 m, and its value is linearly tapered in the uppermost 4000 m.
The friction parameters are listed in Table [table:tpv24fric].
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 
C_0  fault cohesion  Pa  
T  forced rupture time  s  
t_0  forced rupture delay time  0.5  s 
Table: Table of LSR parameters on the fault in TPV24.
Results¶
The model is run for 12.0 seconds after nucleation. The earthquake rupture is artificially nucleated in a circular zone on the main fault surface. The rupture then spontaneously propagates on the main fault and encounters a branching fault. The branching fault continues to rupture as well as the rest main fault. The fault slip rate is shown in Figure [fig:tpv24result1].