Local time in diffusive media and applications to imaging

Seismic Coda-Waves Imaging Based on Sensitivity Kernels Calculated Using an Heuristic Approach

In this paper we review and discuss the seismic method based on the analysis of seismic coda waves used in the last 10 years by the present authors and/or their co-workers, to produce separate images of intrinsic- and scattering attenuation in zones of peculiar geological interest (mainly volcanoes). Such separate attenuation images are considered by the scientific community as complementary to those from ordinary velocity-tomography and useful to improve the geological interpretation in volcanoes and in tectonically active zones. In this review we only list but do not discuss the most significative papers showing the images obtained, as we are focused to review the method and not the interpretation of data analysis. For sake of completeness, we anyway show also a new analysis applied to data from Stromboli volcano. We thus first introduce the physical model describing the seismogram Energy Envelope (derived from the solution of the Energy Transport integral Equation) and discuss its asymptotic approximations (Diffusion- and Single-scattering model). Then, we describe a numerical method to heuristically calculate the Sensitivity Kernels for the propagation of the scattered waves in the assumption of isotropic scattering. We attribute to these Sensitivity Kernels the physical meaning of probability that for a single source-receiver couple the measured attenuation parameters can be associated with the space coordinates. Based on this definition, the attenuation image can be obtained mapping the estimated attenuation parameters onto the zone under study weighting with the Sensitivity Kernels. We further discuss how to estimate the uncertainties associated with the results and report the list of the papers describing the (separated) scattering- and intrinsic-attenuation structures investigated using this approach.

A Bayesian approach for high resolution imaging of small changes in multiple scattering media

This paper introduces a Bayesian approach to achieve high-resolution imaging of sub-wavelength changes in the presence of multiple scattering. The approach is based on the minimization of a cost function defined by the decorrelations induced in the measured waveforms by the apparition of a local changes. Minimization is achieved via a Monte Carlo Markov Chain (MCMC) algorithm combined to an analytical model that computes the sensitivity kernel of the medium. In the inversion procedure, the parameters to infer represent the physics of the problem, such as the diffusivity in the medium and/or the geometrical features of the reflector (position and scattering cross-section). The method is successfully compared to the linear inversion approach initially proposed for the so-called Locadiff imaging method through several examples, both numerical and experimental.