Controllable Seismic Velocity Synthesis Using Generative Diffusion Models

Abstract Accurate seismic velocity estimations are vital to understanding Earth's subsurface structures, assessing natural resources, and evaluating seismic hazards. Machine learning‐based inversion algorithms have shown promising performance in regional (i.e., for exploration) and global velocity estimations, while their effectiveness hinges on access to large and diverse training data sets whose distributions generally cover the target solutions. Additionally, enhancing the precision and reliability of velocity estimation also requires incorporating prior information, for example, geological classes, well logs, and subsurface structures, but current statistical or neural network‐based methods are not flexible enough to handle such multimodal information. To address both challenges, we propose to use conditional generative diffusion models for seismic velocity synthesis in which we readily incorporate those priors. This approach enables the generation of seismic velocities that closely match the expected target distribution, offering data sets informed by both expert knowledge and measured data to support training for data‐driven geophysical methods. We demonstrate the flexibility and effectiveness of our method through training diffusion models on the OpenFWI data set under various conditions, including class labels, well logs, reflectivity images, and the combination of these priors. The performance of the approach under out‐of‐distribution conditions further underscores its generalization ability, showcasing its potential to provide tailored priors for velocity inverse problems and create specific training data sets for machine learning‐based geophysical applications.