Unsupervised Seismic Acoustic Impedance Inversion Based on Conditional Latent Diffusion Model

Deep learning methods have emerged as a new paradigm for solving seismic inverse problems. However, most of these methods require large amounts of labeled training data, which limits their performance due to the scarcity of well logs in field cases. To address this issue, we propose an unsupervised deep-learning seismic impedance inversion approach based on the latent diffusion model. This model effectively captures the complex prior distribution in the training datasets, enabling the inference of missing information in the null space. Leveraging Bayes' theorem, seismic data and low-frequency information are treated as conditional inputs to the diffusion model to learn an implicit posterior distribution. Additionally, to handle test data that lies outside the distribution of the training datasets, we introduce an optimization framework to adjust the sampling process. This approach not only improves inversion accuracy but also reduces the number of sampling steps. Finally, synthetic data experiments demonstrate that our method outperforms the traditional Total Variation, supervised deep learning, and other existing unsupervised deep learning methods.