Experimental detection of inclusions for the time-harmonic elastic wave equation
For researchers in nondestructive testing and geophysics, this work improves inclusion detection in elastic materials by using time-harmonic waves, but the method is incremental as it extends existing monotonicity-based approaches to a new wave regime.
The authors solve the inverse problem of reconstructing inclusions in elastic bodies using time-harmonic elastic wave equation measurements, achieving better reconstructions than the stationary approach despite noisy data. They introduce a modified linearized monotonicity method and demonstrate numerical reconstructions.
We are concerned with the reconstruction of inclusions in elastic bodies based on measurements from a laboratory experiment. In doing so, we solve the inverse problem of the time-harmonic elastic wave equation, in contrast to the stationary wave equation and the corresponding lab experiment proposed earlier in Eberle and Moll (2021). The investigation of the harmonic problem leads to a better reconstruction compared to the stationary one. Since we deal with real measurement data, we have to take into account, that those measurements always include measurement errors, so that we have to handle noisy data. Thus, we consider the linearized monotonicity method for noisy data and introduce a modified version of this method. Based on this, we reconstruct the inclusions numerically.