3D impedance inversion based on a gradient-enhanced diffusion model

Traditional model-driven inversion methods rely on prior information and regularization, which often lead to oversimplification of geological features. With the rapid development of deep learning, diffusion models have emerged as a powerful alternative for solving inverse problems, as they can learn the complex data distribution characteristics and provide better prior information. Inspired by this, this paper introduces diffusion models to enhance the reliability and stability of inversion results. The method learns the data distribution through the processes of noise addition and denoising applied to a synthetic impedance model. Subsequently, by utilizing posterior sampling conditioned on seismic data, it incorporates low-frequency model constraints, 3D lateral constraints, and momentum estimation to improve lateral continuity and the stability of gradient updates, thereby achieving a robust mapping between seismic data and the impedance model. Application results on both synthetic and real data demonstrate that the new method can recover impedance models that are both detailed and geologically plausible. Compared to traditional model-driven methods, the proposed method improves the accuracy of single-trace inversion by 5%. The new inversion framework reduces reliance on prior information and significantly enhances generalizability and reliability, while also providing new approaches for solving other complex geophysical inverse problems.