Parameters Setting

Table parameters setting

The simulation parameters are implemented by modifying the parameter.txt file, rather than by changing the source code. The input variable list is in Table 1. If InputHetoparamter in Table 1 is True, heterogeneous stress and friction parameters are imported from external files. The external filename is defined in parameter.txt and must remain in the same directory as parameter.txt. In this case, you don’t need to set the parameters of Table 4 and Table 5. Otherwise, you need to appropriately set the parameters of stress and frictional initial conditions shown in Table 4 and Table 5. Table 2 and Table 3 must be set up if fluid-induced dilatancy and thermal pressurization are considered.

Table 1 General Parameters Settings

Parameter	Default	Description
Corefunc directory		The storage path for the kernel function matrix composed of stress Green’s functions.
Node_order	False	If True, the node order of the triangular element is clockwise.
save Corefunc	False	If True, save the kernel function so that it does not need to be recalculated next time.
Scale_km	True	If True, coordinates are scaled up by 1000 (modeled in km, suitable for natural earthquakes); otherwise remain in meters (suitable for laboratory earthquakes).
Hmatrix_mpi_plot	False	Draw H-matrix structure diagram; different colors represent sub-matrices calculated by different processes.
Lattice Matrice	False	Using Lattice H-Matrice
Lattice Partitioning depth	2	The initial Lattice partitioning depth.
Using C++ green function	True	If True, use C++ to calculate stress Green’s functions; otherwise use Python.
GPU	False (GPU only)	If True, enable GPU parallel acceleration (using pytorch).
GPU_cores	2 (GPU only)	Number of GPUs for parallel acceleration (using pytorch).
Max thread workers	50 (single CPU/GPU version only and not updated any more)	Number of processors in ProcessPoolExecutor to parallelize Green’s function calculations.
Batch_size	1000 (single CPU/GPU version only and not updated any more)	Number of batches in ProcessPoolExecutor to parallelize Green’s function calculations.
Input Hetoparamter	False	If True, import heterogeneous stress and friction parameters from external files.
Inputparamter file		File name of imported heterogeneous stress and friction parameters.
Lame constants	0.32 × 10¹¹ Pa	First Lamé constant.
Shear modulus	0.32 × 10¹¹ Pa	Shear modulus.
Rock density	2670 kg/m³	Rock mass density.
Reference slip rate	1 × 10⁻⁶ m/s	Reference slip rate.
Reference friction coefficient	0.6	Reference friction coefficient.
Plate loading rate	1 × 10⁻⁹ m/s	Plate loading rate.

Note

The initial Lattice partitioning depth, typically 2 corresponds to 4*4 grids, and 3 corresponds to 8*8 grids.A larger depth indicates a greater degree of parallelism, but also a greater memory cost. Please ensure that the number of cpus used is an integer multiple of pow(2, depth). For example, if Lattice Partitioning depth=2, then the number of cpus used must be 4, 8, 12, 16, etc.; if Lattice Partitioning depth=3, then the number of cpus used must be 8, 16, 24, 32, etc.

Table 2 Fluid Parameters Settings

Parameter	Default	Description
If Dilatancy	False	If True, implement shear-induced dilatation.
If Coupledthermal	True	If True, coupled implement shear-induced dilatation and thermal pressurization in earthquake cycle.
Dilatancy coefficient	3 × 10⁻⁴	Quantifies the volume change (dilation or contraction) in a porous medium due to shear deformation.
Hydraulic diffusivity	1 × 10⁻⁵ m²/s	The rate at which pore fluid diffuses across the fault.
Shear zone width	2 × 10⁻³ m	The thickness of the actively shearing zone represents the width of the region undergoing significant shear deformation.
Effective compressibility	8 × 10⁻¹¹ Pa⁻¹	The volumetric strain response of the porous medium to changes in pore pressure.
Constant background porepressure	2 MPa	Constant pore pressure.
Initial porepressure	2 MPa	Initial pore pressure.

Table 3 Thermal Pressurization Parameter Settings

Parameter	Default	Description
If thermal	False	If True, implement thermal pressurization.
Thermal diffusivity	1 × 10⁻⁶ m²/s	Material property that describes how quickly heat spreads through a material.
Shear zone width	2 × 10⁻³ m	The thickness of the actively shearing zone represents the width of the region undergoing significant shear deformation.
Ratio of thermal expansivity to compressibility	1 × 10⁻⁵	Ratio of thermal expansivity to compressibility.
Heat capacity	3 × 10⁻⁶ J/K	A measure of how much heat energy is required to raise the temperature of a system.
Background temperature	0 Celsius degree	Background temperature.
Initial temperature	0 Celsius degree	Initial temperature.

Note

The implementation of dilatation and thermal pressurization is controlled by the following parameters:

• No dilatation or thermal pressurization

  • Dilatancy = False

  • Coupledthermal = True or False

  • thermal = False

• Dilatation only

  • Dilatancy = True

  • Coupledthermal = True or False

  • thermal = False

• Thermal pressurization only

  • Dilatancy = True

  • Coupledthermal = False

  • thermal = True

• Coupled dilatation and thermal pressurization

  • Dilatancy = True

  • Coupledthermal = True

  • thermal = True

• Limitation

  • The GPU version does not currently include thermal pressurization.

Table 4 Stress and Friction Settings

Parameter	Default	Description
Half space	False	If True, calculating half-space Green’s functions.
Fix_Tn	True	If True, fixed the normal stress.
Vertical principal stress (ssv)	1.0	The vertical principal stress scale: the real vertical principal stress is obtained by multiplying the scale and the value.
Maximum horizontal principal stress (ssh1)	1.6	Maximum horizontal principal stress scale.
Minimum horizontal principal stress (ssh2)	0.6	Minimum horizontal principal stress scale.
Angle between ssh1 and X-axis	30°	The angle by which the principal stress orientation rotates counterclockwise with the X-axis.
Vertical principal stress value	50 MPa	Vertical principal stress value when Shear traction solved from stress tensor is True, or normal stress when it is False.
Vertical principal stress value varies with depth	True	If True, vertical principal stress value varies with depth, and the horizontal principal stress value also changes with depth simultaneously.
Turning depth	5000 m	If Vertical principal stress value varies with depth is True, starting at this depth, the stress no longer changes with depth.
Shear traction solved from stress tensor	False	If True, the non-uniform shear stress is projected onto the non-planar fault surface by the stress tensor.
Rake solved from stress tensor	False	If True, the non-uniform rakes are solved from the stress tensor.
Fix_rake	30°	If True, set fixed rakes when Rake solved from stress tensor is False.
Widths of VS region	5000 m	The width of the velocity-strengthening (VS) region near boundary.
Widths of surface VS region	2000 m	Widths of velocity-strengthening (VS) region near free surface.
Transition region from VS to VW region	3000 m	Transition region width from velocity-strengthening (VS) to velocity-weakening (VW) region.

Table 5 Nucleation Settings

Parameter	Default	Description
Set_nucleation	False	If True, sets a patch whose shear stress and sliding rate are significantly greater than the surrounding area to meet the nucleation requirements.
Radius of nucleation	8000 m	The radius of the nucleation region.
Nuclea_posx	34000 m	X-coordinate of the nucleation center.
Nuclea_posy	15000 m	Y-coordinate of the nucleation center.
Nuclea_posz	-15000 m	Z-coordinate of the nucleation center.
Rate-and-state parameters a in VS region	0.04	Rate-and-state friction parameter a in velocity-strengthening (VS) region.
Rate-and-state parameters b in VS region	0.03	Rate-and-state friction parameter b in velocity-strengthening (VS) region.
Characteristic slip distance in VS region	0.13 m	Characteristic slip distance (L) in velocity-strengthening (VS) region.
Rate-and-state parameters a in VW region	0.004	Rate-and-state friction parameter a in velocity-weakening (VW) region.
Rate-and-state parameters b in VW region	0.03	Rate-and-state friction parameter b in velocity-weakening (VW) region.
Characteristic slip distance in VW region	0.13 m	Characteristic slip distance (L) in velocity-weakening (VW) region.
Rate-and-state parameters a in nucleation region	0.004	Rate-and-state friction parameter a in nucleation region.
Rate-and-state parameters b in nucleation region	0.03	Rate-and-state friction parameter b in nucleation region.
Characteristic slip distance in nucleation region	0.14 m	Characteristic slip distance (L) in nucleation region.
Initial slip rate in nucleation region	3e-2 m/s	Initial slip rate imposed in the nucleation region.
ChangefriA	False	If True, the parameter a changes gradually while b remains unchanged (and vice versa if False).
Initlab	True	If True, apply random non-uniform normal stress distribution.

Table 6 Output Settings

Parameter	Default	Description
totaloutputsteps	2000	The total number of calculation time steps.
outsteps	50	The time step interval for outputting VTU files.
outputSLIPV	False	If True, output slip rate data for each recorded step.
outputstu	True	If True, VTU files will be saved in the outvtk directory.

External file format

In addition to parameter.txt, the program requires an external .msh file for the geometry, as well as input parameter files if Input Hetoparamter is set to True. The filename(s) for these input parameter files are defined within parameter.txt.

The .msh file contains the necessary mesh data (node coordinates, element connectivity, etc.) and must be exported from Gmsh software. Please ensure that you select the Version 2 / ASCII format, as this is the only format compatible with the current reader in the code.

When Input Hetoparamter == True, heterogeneous initial conditions and friction/stress parameters can be imported from external file(s). The format of each row in the input parameter file is:

rake(0) a(0) b(0) dc(0) f0(0) tau(0) sigma(0) vel(0) taudot(0) sigdot(0) InitP(0) hs(0)
rake(1) a(1) b(1) dc(1) f0(1) tau(1) sigma(1) vel(1) taudot(1) sigdot(1) InitP(1) hs(0)
…

The total number of rows equals the number of triangular elements (cells) in the mesh.

• Column 1: rake angle (in degrees). This value can vary during the simulation.

• Columns 2-5: rate-and-state friction law parameters - Column 2: a - Column 3: b - Column 4: characteristic slip distance dc (or L) - Column 5: reference friction coefficient f0

• Columns 6-7: initial traction - Column 6: initial shear traction tau - Column 7: initial normal traction sigma (positive for compression)

• Column 8: initial slip rate vel

• Columns 9-10: additional loading rates (beyond the tectonic plate loading) - Column 9: shear traction loading rate taudot - Column 10: normal traction loading rate sigdot (usually 0)

• Column 11-12 (optional): initial pore pressure InitP and shearing zone width hs. If fluid flow is not enabled or these two columns are omitted, a uniform initial setting defined elsewhere will be used.