Using a global search inversion to constrain earthquake kinematic rupture history and to assess model uncertainty

Abstract

We use a two-stage nonlinear technique to invert strong motions records and geodetic data to retrieve the rupture history of an earthquake on a finite fault. The unknown model parameters, spatially variable peak slip velocity, slip direction, rupture time and rise time, are given at the vertices of subfaults, whereas the parameters within a subfault can vary through a bilinear interpolation of the vertex values. The forward modeling is performed with a discrete wavenumber technique, whose Green's functions include the complete response of the vertically varying non-attenuating Earth structure. The GPS coseismic data are compared with the synthetic displacements using a L2 norm, while the recorded and modeled waveforms are compared in the frequency domain, using a cost function that is a hybrid representation between L1 and L2 norms. During the first stage (search), an algorithm based on heat-bath simulated annealing generates an ensemble of models that efficiently sample the good data-fitting regions of the parameter space. During this stage multiple Earth structures can be used to allow for uncertainty in the true structure. In the second stage (appraisal), the algorithm performs a statistical analysis of the model ensemble and computes a weighted mean model and its standard deviation by weighting all models by the inverse of the cost function values. We do not use any smoothing operator. This technique, rather than simply looking at the best model, extracts the most stable features of the earthquake rupture that are consistent with the data and gives an estimate of the variability of each model parameter. We present some applications to recent earthquakes such as the 2000 western Tottori (Mw 6.7) and the 2007 Niigata (Mw 6.6) (Japan) earthquakes in order to test and show the effectiveness of the method. Our methodology allows the use of different slip velocity time functions and we emphasize the relevance of adopting source time functions in kinematic inversions compatible with earthquake dynamics. We have verified that the choice of source time function affects ground motion time histories within the frequency band commonly used in waveform inversions and has a clear impact on the inferred peak slip velocity and rise time and, consequently, on the dynamic traction evolution inferred from kinematic models. Furthermore, the assessment of model uncertainty could be useful to predict ground motion time histories for seismic hazard assessment.