Controllable seismic velocity synthesis using generative diffusion models

TL;DR

The paper tackles the challenge of limited, non-representative training data and the need for flexible multi-modal priors in seismic velocity inversion. It introduces conditional denoising diffusion probabilistic models with classifier-free guidance and cross-attention to generate seismic velocity models conditioned on priors such as class labels, well logs, and reflectivity images, enabling tailored training datasets and improved inversion guidance. Experiments on the OpenFWI dataset show high-quality, diverse velocity generation under multiple conditioning schemes, including out-of-distribution scenarios (e.g., maximum mean discrepancy values like $2.6454$). The approach enables integrating multi-modal priors into diffusion-regularized FWI and provides a scalable path for data-driven geophysical methods, with potential extensions to fast sampling and ControlNet-based conditioning. Overall, the framework offers a flexible, multi-modal data synthesis tool that supports improved velocity inversion and ML-informed seismic workflows.

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 estimation, while their effectiveness hinges on access to large and diverse training datasets whose distributions generally cover the target solutions. Additionally, enhancing the precision and reliability of velocity estimation also requires incorporating prior information, e.g., geological classes, well logs, and subsurface structures, but current statistical or neural network-based methods are not flexible enough to handle such multi-modal 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 datasets 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 dataset 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 datasets for machine learning-based geophysical applications.

Figures (20)

• Figure 1: An overview of the generative diffusion model. Top: forward process; Bottom: unconditional sampling with a score function $\nabla_{\boldsymbol{x}} \log p_t\left(\boldsymbol{x}\right)$.
• Figure 2: Conditional generative diffusion models. The backbone network is U-net ronneberger2015u.
• Figure 3: Samples of velocity models corresponding to the various classes.
• Figure 4: The overall architecture of the $\boldsymbol{\epsilon}$-prediction network. Conv denotes a convolutional layer and PE denotes a sinusoidal positional encoding. The dashed box below shares the architecture of a residual block.
• Figure 5: The generated samples by diffusion models without conditioning.