Gabor-wavelet-activation implicit neural learning for full waveform inversion

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Seismic full waveform inversion (FWI) is an efficient imaging method for estimating subsurface physical parameters. However, when the initial models are inaccurate or seismic data lack low frequencies, most traditional discrete grid-based FWI algorithms often encounter local minimum problems. Additionally, the inversion performance and computational cost are closely related to spatial resolution. Reparameterizing velocity models using neural networks (NNs) effectively mitigates local minimum issues. However, most NN-FWI approaches perform well when overparameterized and are limited to fixed grid-like representations. In contrast, implicit neural learning (INL) enables the representation of models at any resolution using a multilayer perception (MLP) network that learns a continuous function from discrete coordinates. To enhance the capability of INL, we developed a general Gabor-wavelet-activation INL approach and applied it to FWI, referred to as wavelet implicit neural learning FWI (WinFWI), using only the vertical particle-velocity. The constructed MLP was lightweight, which reduced the computational overhead. Numerical experiments on a synthetic block model and Marmousi2 model demonstrate the robustness of the proposed method to challenges such as parameter crosstalk. This was further validated using the Chevron 2014 blind test data. All comparisons show that our method is more general and robust than traditional and INL-based FWI algorithms. Moreover, additional feature visualization and numerical analysis illustrate the potential advantages of WinFWI in balancing computational cost and inversion accuracy.