There are many different ways to setup the initial fault tractions and friction parameters in dynamic spontaneous rupture simulations. There are many factors that influence the choices for parameters, including:
- Bulk constitutive model (the behavior of a purely linear elastic medium is controlled by the changes in stress, not the absolute stress, whereas the behavior of an elastoplastic medium depends on the absolute level of stress);
- Accounting for depth dependent overburden pressure (hydrostatic pore pressure corresponds to pressure that increases with depth due to gravitational body forces);
- Importance of initial and final conditions (some choices of parameters lead to a more homogeneous stress field whereas others maintain or increase the amount of spatial heterogeneity)
Some choices are more consistent with some sets of observations than others. Depending on which types of observations are being matched, one may emphasize different choices or approaches to selecting the initial fault tractions and fault constitutive parameters.
For a background stress field, one usually selects a stress tensor consistent with the tectonic setting. See for example, Simpson (1997).
References (also see references therein) discussing various issues:
Uenishi and Rice, 2003 (classic paper on parameters controlling nucleation)
Background stress field
Aagaard et al., 2004 (example of effect of background stress field in 3-D dynamic spontaneous rupture simulations)
I also suggest reading papers by members of the SCEC dynamic rupture technical activity group. Harris, Ruth A.; Barall, Michael; Aagaard, Brad T.; Ma, Shuo; Roten, Daniel; Olsen, Kim B.; Duan, Benchun; Liu, Dunyu; Luo, Bin; Bai, Kangchen; Ampuero, Jean-Paul; Kaneko, Yoshihiro; Gabriel, Alice-Agnes; Duru, Kenneth; Ulrich, Thomas; Wollherr, Stephanie; Shi, Zheqiang; Dunham, Eric; Bydlon, Sam; Zhang, Zhenguo; Chen, Xiaofei; Somala, Surendra N.; Pelties, Christian; Tago, Josue; Cruz-Atienza, Victor Manuel; Kozdon, Jeremy; Daub, Eric; Aslam, Khurram; Kase, Yuko; Withers, Kyle; Dalguer, Luis. A good place to start is the most recent paper by Harris et al, 2018.