WGAN Regularized Elastic Full Waveform Inversion for Petrophysical Properties

In seismic exploration, Lame parameters (λ, μ) and density (ρ) are often used to discriminate litho-fluid types, while petrophysical parameters such as porosity (ϕ), clay content (C), and water saturation (Sw) provide a more detailed characterization of reservoir rock properties. The direct inversion of high-resolution rock physical profiles from seismic data is becoming popular by combining waveform inversion with rock physics modeling, especially for complex reservoirs. However, multi-parameter waveform inversions are notoriously difficult because of crosstalks between different parameters. Rock physics theories largely increase the nonlinearity of the inversion, making a direct inversion of rock physical properties extremely unstable. To alleviate the problem, we propose a regularization term utilizing positional encoded Wasserstein generative adversarial networks (WGAN-PE). The network learns multi-dimensional distributions of rock physical properties from well-log data. Positional encoding in the regularization helps the network integrate depth information with rock physical parameters and stabilize the inversion. Tests from synthetic data demonstrate that positional encoding significantly enhances the performance of WGAN regularization. Numerical experiments on three models are compared with different regularizations. The results suggest that the improved WGAN regularization gives satisfactory results for direct rock physical properties inversions.