Source complexity inference by trans-dimensional inversion and application to the 2004 M6.0 Parkfield earthquake .

Abstract:

Co-seismic surface displacements are in general related with a spatial slip distribution on a fault surface by linear integral equations which parametric expansion of fault slip distribution by a finite number of known basis functions yields a set of observation equations expressed in a simple vector form. Generally in the geodetic inversion the source is parameterized with some fixed number of unknowns. This parametrization yield non-uniqueness of the results. The Bayesian procedure lets us to include a priori to abandon this problem. Nevertheless this fixed number of unknowns is not mostly considered as a parameter, which can be limited by data. Then the number of parameters can give us an idea about the complexity of the source. In order to do such an inversion we need to apply a trans-dimensional procedure in which the number of parameters is a parameter of the problem. Here we are going to apply the trans-dimensional approach in a Bayesian framework to invert the 2004 M6.0 Parkfield earthquake co-seismic offsets. The trans-dimensional approach has a upper limit for the number of parameters, which is limited by the number of observations. In other words after we cross this limit, regardless of the complexity of source we can not have bigger number of parameters in our inversion. In the case of geodetic static data which decays as 1/r² , where r is the distance between the source and the observation point, one can apply a priori in order to have a tessellation which represent this resolution power. This means if the source is a complex one we can have more finer patches close to GPS sites in order to get a better resolved slip distribution. The results of synthetic tests and the 2004 M6.0 Parkfield earthquake show that the the data limits the number of parameters. The results of the 2004 M6.0 Parkfield earthquake indicates that this event has a homogeneous slip distribution. In our results, the hypocenter slip which is present in the inversions with fixed number of parameters and a global smoothness as a priori, does not exist.