Coupled body and surface wave sensitivity kernels for coda-wave interferometry in a three-dimensional scalar scattering medium

Abstract

Analysis of long recordings of ambient seismic noise has shown to be effective for estimation of seismic responses between points located on the surface. This includes both the ballistic and the coda part of the waveforms. Passive image interferometry is used to analyse perturbations in the reconstructed coda, to detect and locate changes in the medium. This method has been shown to be effective in monitoring variations in seismic velocity produced by a wide range of phenomena. However, localization of the sources of these changes is still an open problem for a 3-D half-space, given the difficulties of integrating body and surface waves within the same framework. In this study, we approach this problem by developing the sensitivity kernels of a scalar model that integrates the body and surface scalar waves. First, we establish a parallel between the penetration depth of the surface waves for the elastic and scalar cases, which equips the latter with a natural scaling with frequency that is otherwise not included in the model. Next, using a variational approach, we quantify how a velocity perturbation in the medium affects the propagation velocity of the surface waves. Based on these results, we extend the sensitivity theory to include the body and surface waves as modes of propagation and detection, as restricted to a 1-D depth-dependent perturbation description, for simplicity. The obtained kernel can be expressed as the sum of a surface and a body waves sensitivity kernels, which are inter-dependent through a set of traveltime distributions. These distributions are estimated with Monte Carlo simulations based on the radiative transfer equations of the system, with the source and the receiver located in the same position at the surface. The sensitivity at depth is in good agreement with previous results based on full wavefield elastic simulations in 3-D inhomogeneous half-space. The temporal evolution of the body and surface waves sensitivity is quantified, as well as the contribution of all the possible modes of propagation and detection to each of these sensitivities. We show how the position of the source affects the sensitivity between the two types of waves. We find that the efficacy of energy conversion from surface to body waves is controlled by the ratio between the surface wave penetration depth and the mean free path, a feature that has not been reported in previous studies. This means that configurations that share this ratio have the same sensitivity as long as all the spatial and temporal variables (e.g. elapsed time, depth) are non-dimensionalized with the mean free path and the mean free time, respectively.