Extended Finite Element Methods for Repeated Rupture

Ethan Coon, Columbia University

Modeling earthquakes and geologically short time-scale events on fault networks is a rich problem with important implications for human safety and design. In order to quantitatively model earthquakes, scientists must understand the role of the complex geometries inherent to fault networks. Computationally, this provides a stern challenge for modelers — static and dynamic equations must be solved on domains with discontinuities using frictional boundary conditions on these discontinuities. This is difficult using most mesh-based methods, but is naturally handled by meshless methods such as the extended finite element method, which introduces discontinuous basis functions to the approximaton space.

In this work, we examine the application of the extended finite element method to problems of repeated earthquake rupture, including stick-slip friction and non-trivial geometries. Weak stick-slip frictional laws are derived, and methods for driving repeated earthquakes are implemented. Statistics of populations of many events are studied to compare physical and numerical choices in the equations solved.

Abstract Author(s): Ethan T. Coon, Bruce Shaw, and Marc Spiegelman