用神经算子和生成先验，快速生成高精度地下速度模型。

Velocity model building serves as a crucial component for achieving high precision subsurface imaging. However, conventional velocity model building methods are often computationally expensive and time consuming. In recent years, with the rapid advancement of deep learning, particularly the success of generative models and neural operators, deep learning based approaches that integrate data and their statistics have attracted increasing attention in addressing the limitations of traditional methods. In this study, we propose a novel framework that combines generative models with neural operators to obtain high resolution velocity models efficiently. Within this workflow, the neural operator functions as a forward mapping operator to rapidly generate time lag reverse time migration (RTM) extended images from the true and migration velocity models. In this framework, the neural operator is acting as a surrogate for modeling followed by migration, which uses the true and migration velocities, respectively. The trained neural operator is then employed, through automatic differentiation, to gradually update the migration velocity placed in the true velocity input channel with high resolution components so that the output of the network matches the time lag images of observed data obtained using the migration velocity. By embedding a generative model, trained on a high-resolution velocity model distribution, which corresponds to the true velocity model distribution used to train the neural operator, as a regularizer, the resulting predictions are cleaner with higher resolution information. Both synthetic and field data experiments demonstrate the effectiveness of the proposed generative neural operator based velocity model building approach.