Differential inversion using surface wave methods for time-lapse monitoring
Authors:   Université Gustave Eiffel, Wang Ao ,   Université Gustave Eiffel, Abraham Odile ,   Université Gustave Eiffel, Leparoux Donatienne 
Published: January 2023

Climate-changing, human activities or aging problems create variations in civil engineering structures and materials which, if monitored, bring useful information for maintenance. Time-lapse (TL) monitoring measures the present condition of a given material, named the baseline, and then repeat a successive series of measurements at different times, named repeatlines. By comparing the baseline with one of the repeatlines, material properties’ variations, including weak ones, can be inferred.

Surface wave (SW) methods are widely used for TL monitoring, because SW are very energetic and the inversion of their dispersion properties gives a depth-profile of some mechanical parameters. Classical SW inversion uses SW phase velocity (Vph) as inversion input data. It suffers from low sensitivity to the deep medium’s parameters due to high uncertainties in the measurements at low frequencies. TL monitoring can partially overcome the difficulties linked to the estimation of deep variations.

In this study, we propose a new strategy for TL monitoring using SW methods, by looking for the relation between the model parameter variations and the data difference within the frame of global inverse problems. For this purpose, we introduce differential inversion (DI) in surface wave methods. Instead of independent inversions of the baseline and repeatlines, DI uses the difference between measured data of baseline and repeatlines as inversion input data. Two approaches have been tested.

The first approach uses an innovative method to calculate the data difference, which is called the diagram difference (DD). DD is based on a statistical distance considering the area of interest of the dispersion diagram as a histogram of Vph distribution. This DI is tested experimentally on laboratory-measured data, obtained on three mortar-concrete slabs. The mortar layers of the three slabs have different water-to-cement ratios which change the mechanical properties of each slab. DI shows more concentrated results closer to the true values for both layers compared to the SW inversion using Vph as inversion input data.

The second approach uses a linear approximation of Rayleigh wave Vph in the inversion process, in order to relates the data difference with the model parameters variations by using the analytical equation of the sensitivity kernel. Numerical tests show that this approach is limited to model parameter variations less than 5%, beyond which the linear assumption of Rayleigh wave Vph is no longer valid. This approach is tested on three epoxy-resin models, with respect to the 5% variation limitation in the deep layer. The low cost of the computation time is the main feature of this second approach. Its main drawback is that it requires a good estimation of the baseline model in order to correctly calculate the sensitivity kernel. In this case, the first DI approach can be used for a prior estimate of the medium’s variations, since it has a better resolution on the inversion results compared to SW Vph inversion.