Diffusion priors enhanced velocity model building from time-lag images using a neural operator

TL;DR

This work addresses the high computational cost and limited-resolution of traditional velocity model building by coupling a neural-operator forward model with a diffusion prior to perform fast, high-fidelity velocity inversions from time-lag RTM images. The neural operator, based on a Fourier Neural Operator architecture, maps two-channel velocity inputs to time-lag RTM images, enabling differentiable forward modeling that guides inversion via automatic differentiation. A conditional DDPM diffusion prior is trained to learn high-wavenumber velocity distributions and is used to regularize the inversion, suppressing artifacts and enhancing fine-scale structure; a single-step generation is used to keep the approach efficient. Results on synthetic and field datasets demonstrate substantial speedups (roughly 300× over full RTM in forward passes) and improved reconstruction of high-frequency content and geological features, with successful data matching in field-scale scenarios, suggesting practical value for seismic imaging workflows.

Abstract

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.

Figures (19)

• Figure 1: Schematic of the proposed workflow. (a) The data preparation and training stage: Seismic data are simulated using the true velocity model. The migrated velocity model is obtained by applying a Gaussian smoothing and is combined with the simulated data to generate time-lag RTM images. The neural operator is trained in a supervised manner to predict these images, with gradients backpropagated to minimize the loss. (b) The inversion stage: the channel of the true velocity model is replaced by the migration velocity. The pre-trained neural operator is used to predict the time-lag RTM images. The loss between simulated and observed data (images) is backpropagated to update the migration velocity iteratively.
• Figure 2: The two columns (a and b) represent two sampled velocity models used during neural network training. From top to bottom, each row corresponds to the true velocity model, the migration velocity model, and the associated time-lag RTM images, respectively.
• Figure 3: The detailed neural operator architecture. The input of the neural operator consists of two channels: the first channel corresponds to the true velocity model, and the second channel represents migration velocity. The output of the operator is the time-lag RTM images. The input data are first processed by an FNO layer, which captures the global spectral representation of the inputs. Subsequently, the features are passed through four encoder blocks and four decoder blocks to extract and reconstruct the hierarchical spatial features. Finally, the resulting feature maps are fed into another FNO layer to produce the final prediction. Each encoder block is built upon the ResNet-101 backbone, which facilitates efficient feature extraction through residual connections. The decoder block consists of three convolutional kernels that progressively reconstruct the spatial details of the feature maps during the upsampling process. During the skip connection stage, we incorporate an attention block that combines both channel attention and spatial attention mechanisms. The detailed architecture of each block is illustrated in (b).
• Figure 4: In the inversion phase, in the first input channel, we use the migration velocity model, and the neural operator is kept fixed to serve as a differentiable forward model (operator). The network output is compared with the observed seismic data, and gradients are backpropagated via automatic differentiation to iteratively update the velocity model. We continue the iterative process until the predicted images converge to the observed ones.
• Figure 5: Schematic illustration of the Neural-Operator-Guided DDPM framework. First, the neural operator is trained to rapidly predict the time-lag RTM images, serving as a differentiable forward operator. Next, an unconditional diffusion model is trained, which possesses the capability to generate new velocity samples that follow the desired velocity distribution. In the third stage, the diffusion model is integrated into the inversion framework, where the inversion result at each iteration serves as the guidance (condition) for the diffusion model to generate a new velocity model. The generated velocity model is then used as the initial model for the next round of inversion, progressively refining the reconstruction through iterative updates.