Scaling, self-similarity and slip-complexity in earthquake rupture models.
A spectacular feature of earthquakes is the wide range of scales over which they occur. The observed distribution of sizes is a power-law ranging over 10 orders of magnitude. The origin of the Gutenberg-Richter power law remains an outstanding question in earthquake sciences. This project will investigate which nonlinear physical mechanisms may be responsible for generating the spatio-temporal complexity observed in natural seismicity patterns.An analogy can be drawn between earthquake mechanics and fluid dynamics. Whereas fluid motion is very complicated on the microscopic scale, a simple law, the Navier-Stokes equation can describe most fluids on long time and size scales. Physics works because simple laws emerge on large scales. In fluids, these microscopic fluctuations and complexities disappear on large scales. Can we derive such a law for earthquake dynamics?
In any theoretical approach there is the question of spatial and temporal resolution of the model space. A well-documented problem which arises in numerical simulations of both mechanical failure and earthquakes is where they become extremely sensitive to the spatial discretisation due to nonlinearities in the physics. This project will examine the physical basis and interpretation of mesh dependency in theoretical models of earthquake rupture [Rice, JGR, 1993]. We show that mesh sensitivity may provide hidden clues in discovering a physical law capable of generating earthquake complexity. This is a first step towards finding a simple law which can describe the scale-invariant behaviour in earthquake sizes and reconcile continuum and discrete models of earthquake rupture. Applications of this work extend far beyond earthquake rupture models and can be used to improve the numerical efficiency and stability of any general nonlinear partial differential equation.
Advisor: Dr Louise Olsen-Kettle
Level of Project: Honours/MSc/PhD