Fractal models of roughness & earthquake statistics

A widely used model in the statistical study of earthquakes is the Burridge–Knopoff model (1967). It is a mechanical model in earthquake physics used to simulate and understand the dynamics of fault slip and earthquake generation. Carlson & Langer (1989) performed the first study of the statistical properties of the B–K model, paying attention to the magnitude distribution of earthquake events and its dependence on friction parameters. They used velocity-weakening friction and were able to produce a frequency–magnitude plot with a b-value around 1. In this project, the student is expected to: (1) review the derivation of the Burridge–Knopoff model (1967), (2) reproduce the results for the frequency–magnitude relation in Carlson & Langer (1989), and (3) explore ways to include fractal models of roughness.

Web/Literature References:

Alghannam, M., Nordbotten, J. M., & Juanes, R. (2025). Stick–slip from heterogeneous Coulomb friction. Physical Review E, 111(5), 055505.

Bak, P. (2013). How nature works: The science of self-organized criticality. Springer Science & Business Media.

Burridge, R., & Knopoff, L. (1967). Model and theoretical seismicity. Bulletin of the Seismological Society of America, 57(3), 341–371.

Carlson, J. M., & Langer, J. S. (1989). Properties of earthquakes generated by fault dynamics. Physical Review Letters, 62(22), 2632–2635.

Main, I. (1988). Prediction of failure times in the Earth for a time-varying stress. Geophysical Journal International, 92(3), 455–464.

Power, W., & Tullis, T. (1995). Review of the fractal character of natural fault surfaces with implications for friction and the evolution of fault zones. In Fractals in the earth sciences (pp. 89–105). Springer.