The influence of relative source-receiver positions on the recovery of P- and S-waves and energy contributions by GFSNC-binary-operator

Abstract

Recently, the possibility of gathering relevant information from correlations of movements due to seismic noise has been demonstrated. Such is the case of the Green's function that is widely known as one mathematical solution of the wave equation and commonly used to represent particle displacements given an excitation source. That is the reason of its importance in the field of geophysics and seismology. From seismic noise correlations, it is also possible to obtain not only the Green's function, but the energy contributions of the wave types that are propagating in an elastic medium. For instance, in a two-dimensional (2D) medium, only the movement of compressional (P-) and shear (S-) waves takes place, each one providing fixed amounts of energy. A formulation that allows both, recovering of the Green's function from seismic noise correlations also called GFSNC binary-operator and, the gathering of related energy contributions of P- and S-waves for several representations of materials and models, is applied in this paper. As consequence of this study, it has been shown that the number of sources and their relative distribution with respect the observation points, are essential parameters for an accurate recovery of the exact Green's function. It is also proved that in all cases, P-waves have less energy in proportion to S-waves and even more, the P-wave energy contribution vanishes for Poisson's ratios close to 0.5. Having Poisson's ratios of ν={0.1,0.2,0.3,0.4}, P-waves contribute with approximately 30, 27, 22 and 14% of the total energy, while S-waves with 69, 72, 77 and 85%, respectively. These results agree with theoretical data and might be of much help to understand the origin of wave amplifications, seismic acquisition designs with artificial sources and modeling of the seismic response by potential earthquakes.