Elastic Full-Waveform Inversion via Physics-Informed Recurrent Neural Network

Elastic full-waveform inversion (EFWI) has received significant attention in the industry for many years. Numerous studies have shown that parameter optimization methods based on physics-informed neural networks (PINNs) are more promising in full-waveform inversion (FWI) compared to traditional methods. Compared with surface seismic techniques, vertical seismic profiling (VSP) offers advantages such as lower acquisition costs, higher signal-to-noise ratios, and higher resolution. To address the problem of FWI for VSP, this study proposed a physics-informed recurrent neural network (RNN) method with prior knowledge constraint for elastic FWI. Our main idea is threefold. First, we mined and characterized the prior knowledge for VSP FWI, which primarily includes geological knowledge, the 1-D velocity profile around the wellbore, and the empirical relationships between compressional and shear wave velocities. Second, we implemented a PIRNN with prior knowledge constraint, using the RNN framework to optimize trainable parameters. Finally, using the PIRNN framework with prior knowledge constraint, we achieved elastic FWI for VSP. Numerical examples demonstrate that the inversion results for the salt and Marmousi models indicate that incorporating prior knowledge increases the accuracy of FWI. Compared to data-driven machine learning methods, this architecture eliminates the impact of sample quality on parameter optimization.