Complex wavelet transform: an application to retrieve shear wave splitting time behavior at Mt. Vesuvius

Shear wave splitting is the elastic equivalent of the well-known phenomenon of optical birefringence. A shear wave, propagating through an anisotropic volume, splits into two S waves (qS1 and qS2) that travel with different velocities and different polarization directions. This process generates two observables: Td that is the time delay between the two split S-waves, and the polarization direction of the faster one, qS1. Interpretations indicate that in the upper crust this phenomenon occurs in zones of fluid-filled cracks, microcracks or preferentially oriented pore spaces. The time evolution of the anisotropic distribution of the microcracks due to differential stress according to the nonlinear anisotropic poroelasticity model, is explained by the migration of the fluid along pressure gradients between neighbouring microcracks and pores. In this framework, the shear wave splitting parameters are indicators of the state of stress in the upper crust. We obtained shear wave splitting measurements for local earthquakes occurring before the largest earthquake (M=3.6 occurred on October 9, 1999) recorded at Mt. Vesuvius after the last eruption (March 1944). The arrival times of split shear waves and the polarization directions were detected by using the wavelet transform of a three-component signal. In order to avoid any spatial effects on the time behaviour of the parameters, we performed the analysis for a selected data set of doublets. A short term (of the order of tens of days) variation of both Td and qS1 parameters are retrieved before the occurrence of the M=3.6 event.