Generative Geostatistical Modeling from Incomplete Well and Imaged Seismic Observations with Diffusion Models

In this study, we introduce a novel approach to synthesizing subsurface velocity models using diffusion generative models. Conventional methods rely on extensive, high-quality datasets, which are often inaccessible in subsurface applications. Our method leverages incomplete well and seismic observations to produce high-fidelity velocity samples without requiring fully sampled training datasets. The results demonstrate that our generative model accurately captures long-range structures, aligns with ground-truth velocity models, achieves high Structural Similarity Index (SSIM) scores, and provides meaningful uncertainty estimations. This approach facilitates realistic subsurface velocity synthesis, offering valuable inputs for full-waveform inversion and enhancing seismic-based subsurface modeling.