Full waveform inversion based on normalized energy spectrum objective function

The L2 norm-based conventional Full Waveform Inversion (FWI) method is a strong nonlinear functional, it is easy to fall into a local minimum during the inversion process. In this paper, the Normalized Energy Spectrum based Full Waveform Inversion (NESFWI) is proposed to alleviate the strong nonlinear problem and reduce the dependence of high Signal to Noise Ratio (SNR) seismic data and source wavelet. The objective function of NESFWI is to match the energy spectrum of the observed and synthetic data in the frequency domain, which ignores the waveform and phase oscillation characteristics of the seismic data. It can effectively mitigate the waveform mismatching problem during the inversion process, while reducing dependence of seismic source wavelet and high SNR seismic data. Numerical examples show that NESFWI results are better than the Normalized Full Waveform Inversion (NFWI) in building an initial velocity model, noise immunity and source wavelet dependence. Tests on a metallic deposit model show that even if the seismic data lack low frequency components, it still can get better inversion results than the conventional FWI method.