# 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`, `tau_S` and `tau_R`, where `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), and `tau_R` is a parameter that, in combination with `tau_S`, allow defining the effective duration of slip `tau^eff_R`.

For typical `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_R` >= `tau_S` (the contrary could occur after interpolation from ASAGI).

The Gaussian source time functions are parametrized by `rupture_onset` and `rupture_rise_time`.

The slip distribution is defined by the `strike_slip` and `dip_slip` variables. All these parameters are read by easi from the dynamic rupture yaml file.

Warning:
• the direction of positive `strike_slip` and `dip_slip` is based on the convention of Seissol (e.g. positive strike_slip for right-lateral faulting).

• Select SlipRateOutputType=0 in the parameter file to calculate slip-rate output properly.

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.