WGAN Regularized Elastic Full Waveform Inversion for Petrophysical Properties

In seismic exploration, Lame parameters ( $\lambda,\mu $ ) and density ( $\rho $ ) are often used to discriminate lithofluid types, while petrophysical parameters such as porosity ( $\phi $ ), clay content (C), and water saturation ( $S_{w}$ ) 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, multiparameter 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 multidimensional distributions of rock physical properties from well-log data. Positional encoding (PE) in the regularization helps the network integrate depth information with rock physical parameters and stabilize the inversion. Tests from synthetic data demonstrate that PE 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.