Seismo Lab Brown Bag Seminar

The boundary element method (BEM) holds a lot of promise for solving various linear partial differential equations inexpensively. In the tectonics and earthquake physics communities, BEM are used for a variety of problems ranging from kinematic imaging of fault slip over the earthquake cycle to mechanical simulations of sequences of earthquakes and aseismic slip (SEAS). Modern implementations of BEM have mostly focused on the high-performance computing aspect of the problem, while attempting to work around a major shortcoming of the basis of BEM solutions - hypersingular kernels. These kernels contain functions that have characteristic decays in space of the form 1/rn where n>1, meaning that not only do quantities such as stress (gradients of the solution) grow to infinity as r approaches 0 but strain energy is not conserved. To address these shortcomings, we derive higher order displacement discontinuity solutions (quadratic source Greens functions) in two dimensions and implement continuity and differentiability of the sources over the meshed boundary guaranteeing non-singular stresses everywhere in the medium. In the talk, I will show an example of implementing smooth slip functions to evaluate strain energy budgets for the Himalayas over the earthquake cycle. I will also discuss future improvements we are pursuing to account for internal sources, which will allow us to tackle various pore-fluid and thermomechanical couplings.