Coda Wave Analysis to Monitor Processes in Soils

Small-strain elastic wave propagation is a constant-fabric phenomenon ideally suited to monitor processes in soils. However, the determination of very small changes in travel time limits our ability to resolve changes in soil stiffness caused by internal processes or changes in boundary conditions. The first-arrival reflects the fastest path between the source and receiver of the propagating wave field; later arrivals in the coda correspond to longer paths after multiple boundary reflections and internal scattering. Therefore, time shifts between the codas of two consecutive signals are longer and easier to detect than between the signals’ first arrivals. Slight changes in coda waves can be determined by cross-correlating time windows, time-stretched signals, or frequency-stretched spectra. Basic coda analysis assumes a homogeneous velocity change throughout the medium, propagation modes (P, S) that are equally affected by the process and the preservation of $V_{\mathrm{P}}/V_{\mathrm{S}}$ ratio during the process. The resolving power of coda wave interferometry is explored in an experimental study conducted with quartzitic sand subjected to loading, creep, and unloading stages. The results reveal that coda wave analysis can be used to detect changes in wave velocity on the order of $\mathrm{\Delta }V/V<0.1\%$ (this corresponds to a stress change smaller than $\mathrm{\Delta }\mathrm{\sigma }\prime /\mathrm{\sigma }\prime \approx 1\%$ in uncemented soils). Such a high velocity resolution permits the study of creep, aging, and diagenetic processes even in relatively short duration tests.