Compact Full Waveform Inversion by Model Space Re-Parameterization

Full waveform inversion is an ill-posed optimization problem. To address this issue, we propose a novel compact full waveform inversion (CFWI) scheme. For that purpose, we re-parameterize the problem in an alternative model space, which is the result of two transformations, namely a 2D Fourier transformation (Hartley transform), followed by a wavelet transformation (Haar transform). In this model space, the waveform inversion problem can be appropriately parameterized using only a small number of model parameters. As a result, we can improve the robustness of FWI. We demonstrate this with a simple crosshole example, where we obtain excellent results while reducing the number of model parameters by 98%. Besides this considerable reduction of model parameters, CFWI offers new opportunities to analyze the spatial resolution, which can be extremely valuable for optimized experimental design purposes.