Time-lapse global inversion for surface-waves: A differential approach using a linear approximation of the Rayleigh wave phase velocity

Surface-wave methods have a wide range of possible applications in the monitoring of near-surface media. In classical monitoring methods, data measured at different times are inverted separately and independently, and the difference in the inversion results reflects the temporal changes in the medium. However, the results obtained in this way can be affected by the reproducibility of experimental measurements, measurement and inversion uncertainties, etc. In this study, we introduce Differential Inversion in surface-wave methods, which uses the difference between measured data as inversion input data, instead of the measured data themselves. More precisely, a linear approximation of Rayleigh wave phase velocity associated with its sensitivity kernel is used to relate the data difference with the model variations. This differential inversion approach is firstly tested with numerical data generated in a series of two-layer models in order to estimate the limitations of the linear approximation with a global inversion approach. It is shown that when the shear-wave velocity variation is more than 5%, the linear assumption is no longer relevant. With respect to the 5% of variation, we apply the differential inversion approach on laboratory data, obtained from three reduced-scale epoxy-resin two-layer models. The results show the feasibility of the differential inversion to estimate the shear-wave velocity differences between epoxy-resin models. The short calculation time is one of its advantages. However, a good estimation on the baseline is required in order to calculate the sensitivity kernel. Finally, the robustness of the proposed approach is verified by numerical data, using the Spectral Element Method to simulate wave propagation in the presence of an under-surface cavity.(c) 2023 Elsevier B.V. All rights reserved.