easi

easi is a library for the Easy Initialization of model parameters in three (or less) dimensional domains. easi offers the possibility to parameterize the simulation without having to recompile SeisSol. Thanks to easi, all user can run their simulations with the same executable (no more hardcoded fortran initialization routines).

Writing easi models

easi uses configuration files written in Yet Another Markup Language (YAML). For example, a simple model with constant material parameters could be described in the following way:

!ConstantMap
map:
  lambda: 3.2044e+010
  mu:     3.2038e+010
  rho:    2670.
  Qp:     69.3
  Qs:     155.9

Complex models may be easily built, too. For example, built-in with easi come linear or polynomial models (e.g. to build depth-dependent models). Furthermore, one may sample parameters from large two- or three-dimensional uniform grids. Lastly, code may be supplied written in a C-like language, which is compiled at run-time.

Please refer to easi’s documentation and to easi’s examples for further details.

Invoking SeisSol

It is recommended to place easi models in the folder that also contains the parameter file. Within the parameter-file, add the parameter MaterialFileName to the equations block, e.g.

&equations
MaterialFileName = 'material.yaml'
/

When using Dynamic rupture, add the parameter ModelFileName to the DynamicRupture block, e.g.

&DynamicRupture
ModelFileName = 'fault.yaml'
/

Rheological model parameters

The following parameters need to be set by easi. The columms E, A, V, and P denote if the respective parameter is required when using an (isotropic) elastic, anisotropic (elastic), viscoelastic, and viscoplastic rheological model.

Parameter	Unit	E	A	V	P	Description
rho	\(\frac{kg}{m^3}\)	✓	✓	✓	✓	Density.
mu, lambda	Pa	✓		✓	✓	Lamé parameters.
c11, …, c66 [1]	Pa		✓			stiffness tensor.
Qp, Qs				✓		P-wave and S-wave quality factors.
bulkFriction					✓	Bulk friction coefficient.
plastCo	Pa				✓	Plastic cohesion.
s_xx, s_yy, s_zz, s_xy, s_yz, s_xz	Pa				✓	Initial stress tensor.

[1]

See Anisotropic for more details.

Fault parameters (dynamic rupture)

The following parameters need to be set by easi. The column FL denotes for which friction law the respective parameter is required. Please note that there are two ways to specify the initial stress on the fault: You may either specify a stress tensor (s_xx, s_yy, s_zz, s_xy, s_yz, s_xz), which has to be given for the same cartesian coordinate system as the mesh, or you may specify a traction vector (T_n, T_s, T_d), which has to be given in a fault local coordinate system. You must not specify both.

Parameter	Unit	FL	Description
s_xx, s_yy, s_zz, s_xy, s_yz, s_xz	Pa	all (excludes initial traction)	Initial stress tensor.
T_n, T_s, T_d	Pa	all (excludes initial stress)	Initial traction in n=normal, s=strike, d=dip direction.
cohesion	Pa	2, 6	Magnitude of cohesive force.
mu_s, mu_d		2, 6	Linear slip weakening: Static and dynamic friction coefficient.
d_c	m	2, 6	Linear slip weakening: Critical distance.
forced_rupture_time	s	16	Time of forced rupture.
rs_a, rs_srW, RS_sl0		101, 103	Rate-and-state friction parameter.
nuc_{xx, yy, zz, xy, yz, xz} or Tnuc_{n, s, d}	Pa	2, 3, 4, 103	Nucleation stress or tractions.

Debugging easi script

Most easi components return easy to track error, for example

test.yaml: yaml-cpp: error at line 6, column 9: illegal map value

Yet implajit function maps are more complex to debug. The following example:

27.1: syntax error, unexpected '}', expecting ;

indicates that an error occurred in the 27th line of the function, but does not indicate which file and which function.

Hopefully this will be improved in the future.

An example illustrating some subtleties of easi error logs

Let suppose that we try to retrieve s_zz located at (x,y,z)=(0,0,0) in group 1 from the following easi file:

[s_zz,s_yy,s_yz,s_xx,s_xz,s_xy,d_c,mu_s]: !AffineMap
  matrix:
    xf: [0.4054811 , -0.91410343,  0.   ]
    yf: [-0.62424723, -0.2769057 ,  0.73050574]
    zf: [-0.6677578 , -0.29620627, -0.68290656]
  translation:
    xf: 348441.377459
    yf: 4760209.93637
    zf: 0.0
  components: !ASAGI
          file: norciax_210fault_nncia.nc
          parameters: [s_zz,s_yy,s_yz,s_xx,s_xz,s_xy,d_c,mu_s]
          var: data
          interpolation: nearest

and get the following error log:

terminate called after throwing an instance of 'std::runtime_error'
  what():  fault2.yaml@2: Could not find model for point [ 348441 4.76021e+06 0 ] in group 1.

How to interpret this error log? The component at Line 2 is throwing the error (the AffineMap). The AffineMap component is complaining that its output point is not accepted by any of its child components. In this case, the point is outside the bounds of the ASAGI file.

Note that in the slightly different example below, without the AffineMap, easi will not verify that the point is outside the bounds of ASAGI file:

[s_zz,s_yy,s_yz,s_xx,s_xz,s_xy,d_c,mu_s]: !ASAGI
          file: norciax_210fault_nncia.nc
          parameters: [s_zz,s_yy,s_yz,s_xx,s_xz,s_xy,d_c,mu_s]
          var: data
          interpolation: nearest

In fact, in this case, ASAGI is directly queried and easi, therefore, does no verify that the point queried in inside the bounds of the ASAGI file. If the point is out of bounds, ASAGI will pick the value of the nearest grid point and issue a warning:

Thu Jan 09 14:32:22, Warn:  ASAGI: Coordinate in dimension 2  is out of range. Fixing.