Imaging Spatio-temporal Changes of the Earth with Coda Waves

Coda-wave interferometry is a powerful technique which exploits waveform perturbations observed in the coda to monitor changes of the propagation medium. In this work, we use a radiative transfer approach to model two relevant observables which may be employed for monitoring purposes: travel-time shifts and de-correlation of waveforms. These observables are sensitive to weak changes of the background velocity or to the addition of mechanical defects, respectively. We develop specific sensitivity functions for each type of observable and evaluate them numerically using analytical solutions of the radiative transfer equation. Our theory can model arbitrarily anisotropic wave fields and is not limited by a diffusion approximation. We show that the coherent wave plays a crucial role in the sensitivity of coda waves in the weak scattering regime. In particular, the coherent wave is responsible for the algebraic divergence of both the travel time and de-correlation sensitivity kernels at the source and receiver. The de-correlation kernel shows an additional zone of high sensitivity in the vicinity of the single-scattering ellipse. These sensitivity functions may be employed to develop a linearized tomographic approach to the monitoring of medium changes in the weak scattering regime.