Sensitivity Kernels for Static and Dynamic Tomography of Scattering and Absorbing Media with Elastic Waves: A Probabilistic Approach

Abstract:

Scattered seismic coda waves are frequently used to characterize small scale medium heterogeneities, intrinsic attenuation or temporal changes of wave propagation properties. Spatial variability of the scattering and attenuation properties raises questions about the spatial sensitivity of scattered seismic waves. Especially the continuous monitoring of medium perturbations using ambient seismic noise led to a demand for approaches to image perturbations observed with coda waves. An efficient approach to localize the property variations in the medium is to invert the observations from different source-receiver combinations and different lapse times in the coda for the location of the perturbations. The key of such an inversion is the calculation the coda-wave sensitivity kernels which describe the connection between observations and the perturbation. Most discussions of sensitivity kernels use the acoustic approximation in a spatially uniform medium and often assume wave propagation in the diffusion regime.

We model 2-D elastic multiple nonisotropic scattering in a random medium with spatially variable heterogeneity and attenuation. The Monte Carlo method is used to numerically solve the radiative transfer equation that describes the wave scattering process. Recording of the specific energy density of the P and S components of the elastic wavefield E(r,n,t) allows us to calculate sensitivity kernels according to rigorous theoretical derivations. We derived the reciprocity relation for the energy density of scattered elastic waves which is the key for employing the adjoint equations to calculate the sensitivity kernels. We illustrate the numerical calculation results of the traveltime sensitivity kernels in media with a uniform distribution of heterogeneity as well as in media which contain spatially variable heterogeneity. These sensitivity kernels reflect the effect of the spatial variations of medium properties on the wavefield and constitute the first step in the development of a tomographic inversion approach for different types of medium properties based on scattered waves.