Probabilistic waveform inversion for focal parameters of local earthquakes

Abstract

For a given earth model and hypocenter location, short-period local waveforms are inverted for the six unknown moment tensor rate functions (MTRFs) by a linear procedure. Subsequently, the MTRFs are decomposed into the source time function (STF) and the time independent moment tensor, fully describing the focal mechanism of the event. In case of short epicentral distances, routinely determined hypocenters are usually not accurate enough to be used in focal mechanism inversion. However, introducing hypocenter co-ordinates as unknown parameters leads to a nonlinear inversion problem. In order to solve this nonlinear problem, a probabilistic approach is applied in this study. The a priori probability density function (PDF) for the hypocenter location is given by a routinely used location algorithm. Assuming that all uncertainties can be described by Gaussian PDFs, measurement errors and theoretical errors are estimated. Then the results of the Bayesian approach are the posterior PDFs for both the hypocenter co-ordinates and the MTRFs. Decomposing the MTRFs, the PDFs for the STF and the moment tensor are also deduced. The estimated uncertainties in the moment tensor components are plotted on the focal sphere in such a way, that the significance of the double-couple, the CLVD, and the volumetric parts of the source can be assessed. The method is illustrated through the waveform inversion of a local event that occurred in the central part of the Pannonian Basin. The moment tensor solution for the selected event has negligible volumetric part, implying the tectonic nature of the event. The retrieved mechanism is in agreement with the available clear readings of first-arrival P-wave polarities. The principal axes of the resulting source mechanism also agrees well with the main stress pattern published for the epicentral region.