Estimating source time function and moment tensor from moment tensor rate functions by constrainedL1norm minimization

Abstract

Linear inversion of three-component waveform data for the time-varying moment tensor rate functions (MTRFs) is a powerful method for studying seismic sources. After finding the MTRFs, however, we should try to represent an earthquake by just one moment tensor and one source time function (STF), if possible. This approach is particularly justified when dealing with weak local events. Unfortunately, extraction of a moment tensor and STF from the MTRFs is essentially a non-linear inverse problem. In this paper, we introduce an iterative Lp norm minimization technique to retrieve the best moment tensor and STF from the MTRFs obtained by waveform inversion. To allow only forward slip during the rupture process, we impose a positivity constraint on the STF. The error analysis, carried out by using Monte Carlo simulation, allows us to estimate and display the uncertainties of the retrieved source parameters. On the basis of the resulting moment tensor uncertainties, the statistical significance of the double-couple, compensated linear vector dipole and volumetric parts of the solution can be readily assessed. Tests on synthetic data indicate that the proposed algorithm gives good results for both simple and complex sources. Confidence zones for the retrieved STFs are usually fairly large. The mechanisms, on the other hand, are mostly well resolved. The scalar seismic moments are also determined with acceptable accuracy. If the MTRFs cannot resolve the complex nature of a source, the method yields the average source mechanism. If the subevents are well separated in time, their mechanisms can be estimated by appropriately splitting the MTRFs into subintervals. The method has also been applied to two local earthquakes that occurred in Hungary. The isotropic component of the moment tensor solutions is insignificant, implying the tectonic nature of the investigated events. The principal axes of the source mechanisms agree well with the main stress pattern published for the epicentral region.