P and S wave speed evolution during rock deformation from coda wave interferometry and energy partitioning inversion

Seismic wave speed monitoring is important for the non-destructive evaluation of material properties in response to external forcing. Coda wave interferometry (CWI) uses travel time perturbations in multiply-scattered seismic wave trains – the seismic coda – to detect subtle perturbations in bulk wave speed. However, conventional body-wave CWI cannot separate the coupled contributions of P and S waves, which are sensitive to different material properties. We introduce energy partitioning inversion which decouples these modes by combining a scattering model with CWI measurements within non-equipartitioned coda windows. We applied this methodology to repeated ultrasonic pulse surveys during two laboratory loading experiments on Clashach sandstone: a dynamic experiment (constant strain rate until brittle failure) and a quasi-static experiment (modulating stress to maintain constant acoustic emission rate and slow down the failure process). Relative travel time perturbations and their full covariance between all pairs of surveys were measured across multiple coda windows and inverted for a single perturbation profile using a least-squares method to minimise the variance of the profile. Using an isotropic point scatterer model to predict mode partitioning with respect to the coda lapse time, we invert travel time perturbations for the scattering mean free path travel time and relative P and S wave speed perturbations via Markov-chain Monte Carlo inversion to quantify uncertainty. P and S wave speed perturbations were resolved with 95 % credible intervals of 0.025 % and 0.008 %, respectively. During the quasi-static experiment the temporal resolution was sufficient to capture a quasi-linear decrease in P and S wave speeds by ~ 50 % and ~ 14%, respectively, from peak to failure. The peak P and S wave speed perturbations were ~ 33% lower and ~ 75% higher, respectively, compared to those found in the dynamic experiment. These results demonstrate that CWI and energy partitioning inversion enables the robust, uncertainty-quantified evaluation of separate relative bulk P and S wave speed perturbations in strongly-scattering media.