Controllable Seismic Velocity Synthesis Using Generative Diffusion Models

• Published in: Journal of geophysical research. Machine learning and computation Vol. 1; no. 3
• Main Authors: Wang, Fu, Huang, Xinquan, Alkhalifah, Tariq
• Format: Journal Article
• Language: English
• Published: 01.09.2024
• Subjects: diffusion models; geological priors; machine learning; velocity generation
• ISSN: 2993-5210; 2993-5210
• DOI: 10.1029/2024JH000153

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. Plain Language Summary Estimating the Earth's subsurface velocity is vital to understanding geological formations, evaluating natural resources, and assessing earthquake risks. Traditional methods, for example, full waveform inversion (FWI), often face challenges with limited data. They tend to be also computationally expensive. Machine learning‐based inversion offers a potential solution but requires large and diverse training data sets whose distribution includes the target solution. Typically, it is hard and expensive to acquire such data sets. Moreover, to further improve the accuracy of the velocity estimation, incorporating prior information—such as geological data from well logs and seismic images—into the inversion is promising. However, it is challenging to handle multimodal information in velocity synthesis. To address these challenges, our research introduces a novel approach utilizing a conditional diffusion model that can adapt to different geological priors. The proposed method allows controllable velocity synthesis and ensures the generated seismic velocities align with specific features that we are interested in. We have trained various models using different types of priors (e.g., geological classes, well logs, reflectivity images, and their integrations) and analyzed how well they perform in creating the maps from given priors to the velocity models. Our tests, conducted using the OpenFWI data set, show that our method can effectively guide the creation of seismic velocity models. This innovation offers a promising new tool for geophysicists, allowing controllable data sets for training data‐driven geophysical methods and providing a key component for an FWI that incorporates multimodal priors. Key Points We propose to use diffusion models for velocity synthesis We develop the framework for controllable velocity synthesis with velocity classes, well log information, and reflectivity images Numerical examples demonstrate that we can use any condition to generate high‐quality velocities even for out‐of‐distribution models