Slip-rate imposed on a DR boundary
This “pseudo” friction law allows imposing slip-rate of a kinematic source model as a boundary condition on a fault plane. This implentation is equivalent to the approach used e.g. in Tinti et al. (2005, https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2005JB003644) and Causse et al. (2014, https://academic.oup.com/gji/article/196/3/1754/583512#9427920).
The advantage of this approach is that the displacement discontinuity can be accurately represented in SeisSol’s discontinuous finite element space. A multi point-source representation, in comparison, may give rise to spurious waves due the continuity of the basis functions within a finite element (smearing), and to the discrete spatial sampling between point sources (aliasing).
The current implementation allows either imposing kinematic models parameterized by regularized Yoffe functions (FL=33, see Tinti et al., 2005, https://doi.org/10.1785/0120040177) or by Gaussian source time functions (FL=34).
The Yoffe functions are parametrized by
rupture_onset is the onset time of the rupture,
tau_S is a parameter closely related (see hereafter) with
T_acc, the duration of the positive slip acceleration (time to the peak slip-rate),
tau_R is a parameter that, in combination with
tau_S, allow defining the effective duration of slip
tau_S/tau_R ratio, we can assume
T_acc = 1.27 tau_S. Yet, the factor can range from about 1.15 (for
tau_S/tau_R close to 0) to about 1.4 (for
tau_S/tau_R close to 0.4).
In addition, we can typically assume
tau^eff_R = tau_R + 2 tau_S.
Note that in the code, we apply
tau_R = max(tau_R, tau_S) to ensure that
tau_S (the contrary could occur after interpolation from ASAGI).
The Gaussian source time functions are parametrized by
The slip distribution is defined by the
All these parameters are read by easi from the dynamic rupture yaml file.
Warning: the direction of positive
dip_slip is based on the convention of Seissol (e.g. positive strike_slip for right-lateral faulting).
A fully working example based on Northridge is given at https://github.com/SeisSol/Examples/tree/master/Northridge_FL33.
Note that the yaml and netcdf files describing the kinematic model parameters, and the ts file describing the fault geometry are automatically generated by this script.
Misfits information printed by this script can help choosing the best threshold value (see option
--PSRthreshold) and which of the Yoffe or Gaussian source time function to use.