An unsupervised inversion framework in the frequency domain using a Wasserstein generative adversarial network

Summary Reconstructing subsurface structures with high resolution is one of the main goals and potentials of full waveform inversion (FWI). However, FWI is a highly nonlinear and ill-posed problem. Conventional physics-based FWI methods, which rely on gradient-based optimization to minimize the difference between observed and synthetic data face cycle-skipping challenge. Although numerous deep-learning inversion approaches have shown promise, they typically focus on latent representations of time-domain seismic data. This often causes an unstable inversion process due to waveform mismatches. To overcome these limitations, we introduce FFT-InversionGAN, an unsupervised seismic inversion framework that integrates physics-based forward modeling with adversarial learning of the frequency-domain data based on Wasserstein generative adversarial network with gradient penalty (WGAN-GP). Fast Fourier transformer (FFT) is employed to transfer the time and phase information of time-domain seismic data into the spectrum and amplitude distributions to modify the feature space and sensitivity of the adversarial loss to different types of mismatches. By leveraging Wasserstein distance constraints, this method can naturally operate on the spectral distributions of seismic data. Compared with L2 norm, Wasserstein distance is far less sensitive to the linear variations in the phase spectrum. And our proposed method eliminates the need for network pre-training while improving stability and flexibility. FFT-InversionGAN demonstrates enhanced accuracy and resilience in numerical experiments on noise-free, noisy and missing low-frequency benchmarks. This was observed when applied to the Marmousi and overthrust models, where it consistently outperformed conventional FWI and FWIGAN. These findings highlight that FFT-InversionGAN has superior inversion effectiveness.