SCEC TPV34
The TPV34 benchmark features a rightlateral, planar, vertical, strikeslip fault set in a halfspace. The velocity structure is the actual 3D velocity structure surrounding the Imperial Fault, as given by the SCEC Community Velocity Model CVMH.
Geometry
The model volume is a halfspace. The fault is a vertical, planar, strikeslip fault. The fault reaches the Earth’s surface. Rupture is allowed within a rectangular area measuring 30000 m alongstrike and 15000 m downdip.
There is a circular nucleation zone on the fault surface. The hypocenter is located 15 km from the left edge of the fault, at a depth of 7.5 km.
The geometry is generated with Gmsh. All the files that are needed for the simulation are provided at https://github.com/SeisSol/Examples/tree/master/tpv34.
Material
To obtain the velocity structure for TPV34, we need to install and run the SCEC Community Velocity Model software distribution CVMH. For TPV34, we are using CVMH version 15.1.0 and we use ASAGI to map the material properties variations onto the mesh. Detailed explanations are provided at https://github.com/SeisSol/Examples/blob/master/tpv34/generate_ASAGI_file.sh. We generate 2 netcdf files of different spatial resolution to map more finely the 3D material properties close to the fault. The domain of validity of each netcdf files read by ASAGI is defined by the yaml tpv34_material.yaml file:
[rho, mu, lambda]: !IdentityMap
components:
# apply a finer CVMH data inside the refinement zone
 !AxisAlignedCuboidalDomainFilter
limits:
x: [25000.0, 25000.0]
y: [25000.0, 25000.0]
z: [15000.0, 0.0]
components: !ASAGI
file: tpv34_rhomulambdainner.nc
parameters: [rho, mu, lambda]
var: data
# apply a coarser CVMH data outside the refinement zone
 !ASAGI
file: tpv34_rhomulambdaouter.nc
parameters: [rho, mu, lambda]
var: data
Parameters
TPV34 uses a linear slip weakening law on the fault. The parameters are listed in Table below.
Parameter 
inside the nucleation zone 
Value 
Unit 

mu_s 
static friction coefficient 
0.58 

mu_d 
dynamic friction coefficient 
0.45 

d_c 
critical distance 
0.18 
m 
The cohesion is 1.02 MPa at the earth’s surface. It is 0 MPa at depths greater than 2400 m, and is linearly tapered in the uppermost 2400 m. The spatial dependence of the cohesion is straightforwardly mapped using Easi.
[mu_d, mu_s, d_c]: !ConstantMap
map:
mu_d: 0.45
mu_s: 0.58
d_c: 0.18
[cohesion]: !FunctionMap
map:
cohesion: 
return 425.0*max(z+2400.0,0.0);
Initial stress
The initial shear stress on the fault is pure rightlateral.
The initial shear stress is \(\tau_0\) = (30 MPa)(\(\mu_x\))
The initial normal stress on the fault is \(\sigma_0\) = (60 MPa)(\(\mu_x\)).
In above formulas, we define \(\mu_x = \mu / \mu_0\), where \(\mu\) is shear modulus and \(\mu_0\) = 32.03812032 GPa.
[s_xx, s_yy, s_zz, s_xy, s_yz, s_xz]: !EvalModel
parameters: [radius,mux]
model: !Switch
[mux]: !AffineMap
matrix:
x: [1.0,0.0,0.0]
z: [0.0,0.0,1.0]
translation:
x: 0.0
z: 0.0
components: !ASAGI
file: tpv34_muxfault.nc
parameters: [mux]
var: data
[radius]: !FunctionMap
map:
radius: 
xHypo = 0.0;
zHypo = 7500.0;
return sqrt(((x+xHypo)*(x+xHypo))+((zzHypo)*(zzHypo)));
components: !FunctionMap
map:
s_xx: return 60000000.0*mux;
s_yy: return 60000000.0*mux;
s_zz: return 0.0;
s_xy: 
pi = 4.0 * atan (1.0);
s_xy0 = 30000000.0*mux;
s_xy1 = 0.0;
if (radius<=1400.0) {
s_xy1 = 4950000.0*mux;
} else {
if (radius<=2000.0) {
s_xy1 = 2475000.0*(1.0+cos(pi*(radius1400.0)/600.0))*mux;
}
}
return s_xy0 + s_xy1;
s_yz: return 0.0;
s_xz: return 0.0;
Results
All examples here can be visualized in Paraview. The output folder contains a series of files for fault dynamic rupture (hdf5 and .xdmf), wavefield (hdf5 and .xdmf), onfault receiver (.dat) and offfault receivers (.dat). The fault dynamic rupture and wavefield files can be loaded in Paraview. For example, open Paraview and then go through File > import > ‘prefix’fault.xdmf.