ALBERT

Description: 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: traveltime perturbations and distortion of seismograms. In the last 10 yr, various theories have been published to relate either background velocity changes to traveltime 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 manuscript, 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 traveltime 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 evaluate numerically the sensitivity functions, we introduce an improved version of a spectral technique known as the method of ‘rotated coordinate frames’, which allows global evaluation of the Green's function of the radiative transfer equation in a finite domain. The method is validated through direct pointwise comparison with Green's functions obtained by the Monte Carlo method. To illustrate the theory, we consider a series of scattering media displaying increasing levels of scattering anisotropy and discuss the impact on the traveltime and decorrelation kernels. We also consider the related problem of imaging variations of scattering properties based on intensity perturbations observed in the coda. The impact of anisotropy is particularly pronounced for the scattering and decorrelation sensitivity kernels, which probe spatial/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. 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.