Sensitivity Kernels for Coda Wave Interferometry: Theory and Numerical Evaluation in 2-D Anisotropically Scattering Media

Abstract:

Coda wave interferometry is a technique which exploits tiny waveform changes in the coda to detect temporal variations of seismic properties in evolving media. Observed waveform changes are of two kinds: travel-time perturbations and distortion of seismograms. In the last ten years, various theories have been published to relate either background velocity changes to travel-time perturbations, or changes in the scattering properties of the medium to waveform decorrelation. These theories have been limited by assumptions pertaining to the scattering process itself -in particular isotropic scattering-, or to the propagation regime -single-scattering and/or diffusion-. In this work, we unify and extend previous results from the literature using a radiative transfer approach. This theory allows us to incorporate the effect of anisotropic scattering and to cover a broad range of propagation regimes, including the contribution of coherent, singly-scattered and multiply-scattered waves. Using basic physical reasoning, we show that two different sensitivity kernels are required to describe travel-time perturbations and waveform decorrelation, respectively, a distinction which has not been well appreciated so far. Previous results from the literature are recovered as limiting cases of our general approach. To illustrate the theory, we consider a series of scattering media displaying increasing levels of scattering anisotropy and discuss the impact on the travel-time and decorrelation kernels. The role of anisotropy is particularly pronounced for the decorrelation sensitivity kernel, which probes temporal changes in the scattering properties of the medium. Compared to the isotropic case, scattering anisotropy strongly increases the sensitivity of coda waves in the vicinity of the single-scattering ellipse, which may have important implications for imaging applications. This point is illustrated in the Figure where travel-time and decorrelation kernels are plotted for both isotropic and strongly anisotropic scattering. In addition to demonstrating the impact of non-isotropic scattering on the sensitivity kernels of coda waves, our work offers a practical solution to model this process accurately.