Immersed boundary parametrizations for full waveform inversion

Full Waveform Inversion (FWI) is a successful and well-established inverse method for reconstructing material models from measured wave signals. In the field of seismic exploration, FWI has proven particularly successful in the reconstruction of smoothly varying material deviations. By contrast, non-destructive testing (NDT) often requires the detection and specification of sharp defects in a specimen. If the contrast between materials is low, FWI can be successfully applied to these problems as well. However, so far, the method is not fully suitable for reconstructing homogeneous Neumann boundaries such as hidden backsides of walls, crack-like defects, or internal voids, which are characterized by an infinite contrast in the material parameters. Inspired by fictitious domain methods, we introduce a dimensionless scaling function γ to model void regions in the forward and inverse scalar wave equation problem. Applying the scaling function γ to the material parameters in different ways results in three distinct formulations for mono-parameter FWI and one for two-parameter FWI. The resulting problems are solved by first-order optimization, where the gradient is computed using the adjoint state method. The corresponding Fréchet kernels are derived for each approach and the associated minimization is performed using an L-BFGS algorithm. A comparison between the different approaches shows that scaling the density with γ is most promising for parametrizing void material in forward and inverse problems. Finally, in order to consider arbitrary complex geometries known a priori, this approach is combined with an immersed boundary method, the finite cell method (FCM).