Self similar slip distributions on irregular shaped faults

We propose a strategy to place a self similar slip distribution on a complex fault surface that is represented by an unstructured mesh. This is possible by applying a strategy based on the composite source model where a hierarchical set of asperities, each with its own slip function which is dependent on the distance from the asperity centre. Central to this technique is the efficient, accurate computation of distance between two points on the fault surface. This is known as the geodetic distance problem. We propose a method to compute the distance across complex non-planar surfaces based on a corollary of the Huygens’ principle. The difference between this method compared to others sample-based algorithms which precede it, is the use of a curved front at a local level to calculate the distance. This technique produces a highly accurate computation of the distance as the curvature of the front is linked to the distance from the source. Our local scheme is based on a sequence of two trilaterations, producing a robust algorithm which is highly precise. We test the strategy on a planar surface in order to assess its ability to keep the self similarity properties of a slip distribution. We also present a synthetic self-similar slip distribution on a real slab topography for a M8.5 event. This method for computing distance may be extended to the estimation of first arrival times in both complex 3D surfaces or 3D volumes.