Seismic moment tensor resolution by waveform inversion of a few local noisy records—I. Synthetic tests

A theory is described that takes into account the effects of the random noise contained in seismic records, the mislocation of the hypocentre and the inaccurate knowledge of the velocity structure, while estimating the error affecting the mechanism and the source time function determined by waveform inversion of noisy records. Assuming Gaussian errors, the variance of the forward model error is defined and then transformed into confidence regions of eigenvalues and eigenvectors of the moment tensor and into error bars of the source time function. The method allows us to treat point sources, composed of a few subevents, either acting simultaneously or delayed in time. Therefore, in a series of synthetic tests, we investigate separately the effects of the noise level, the mislocation of the hypocentre and the inaccurate knowledge of the medium on the resolution of the two parts of a focus, composed of a double‐couple (DC) and a volumetric (V) source, a general case that we find in volcanic areas. The crucial effect of the recording network geometry on the mechanism resolution is confirmed and quantitatively estimated for both the vertical component and the three‐component configuration of the network. Our goal is to apply this method to the investigation of the reliability of the retrieval of the focal mechanism and the time function associated with events of low magnitude ( M d <4) recorded by local stations, both in tectonic and in volcanic areas. Special attention is devoted to volcanic areas, where the non‐double‐couple components of the source may reveal the existence of complex fracture processes, which are due to fluid movements in the crust