High-resolution velocity model estimation with neural operator and the time-shift imaging condition

TL;DR

The paper addresses the challenge of seismic velocity inversion, which is ill-posed and computationally expensive with traditional FWI. It proposes a neural-operator framework, specifically a Fourier Neural Operator coupled with CNNs, to learn a direct mapping from initial velocity and time-lag RTM images to high-resolution velocity fields in a mesh-independent, data-driven manner. Training on synthetic data guided by field RTM results, including salt structures, the approach achieves accurate recovery of mid- and high-wavenumber content and demonstrates strong generalization to out-of-distribution scenarios, including real field data, with predictions completed in seconds. This method offers a fast, scalable alternative to FWI for rapid velocity model building and can provide robust initial models for subsequent inversion and imaging tasks in practical exploration.

Abstract

Extracting subsurface velocity information from seismic data is mainly an undetermined problem that requires injecting a priori information to constrain the inversion process. Machine learning has offered a platform to do so through the training process, as we formulate our training dataset to inject as much prior knowledge as possible in the trained ML model. Here, we use a neural-operator-based framework for high-resolution seismic velocity model building, which integrates Neural Operators with time-lag reverse time migration imaging. Unlike conventional full waveform inversion (FWI) methods that rely on iterative forward and adjoint-state computations, our approach learns a direct mapping from initial velocity models and extended seismic images to high-resolution velocity estimates through supervised learning. The network architecture enables mesh-independent generalization by learning mappings in infinite-dimensional function spaces, while synthetic velocity models and time-lag reverse time migration (RTM) images provide complementary high-frequency information critical for recovering mid- and high-wavenumber velocity components. Synthetic experiments demonstrate that the proposed method accurately reconstructs fine-scale structures and complex geologies, including out-of-distribution features such as salt bodies. Applications to real seismic field data acquired offshore Australia further validate the method's robustness and resolution capability. The predicted models show enhanced structural details and improved consistency with well-log data, outperforming traditional multi-scale FWI in both accuracy and computational efficiency. The entire prediction process is completed within seconds, making the proposed approach highly suitable for rapid and scalable velocity model building in practical exploration scenarios.

Figures (14)

• Figure 1: (a) and (b) show the background velocity model and the corresponding RTM image derived from field data, respectively. The structural features evident in the RTM image serve as valuable references for constructing synthetic seismic datasets used in training.
• Figure 2: (a) and (b) illustrate two distinct types of synthetic velocity models along with their corresponding migration velocity and time-lag RTM images, samples from the training set. The migration velocity and the three RTM images form a four-channel input to the neural operator, while the true velocity acts as the label.
• Figure 3: (a) presents the overall architecture of the neural operator proposed in this study, including the Fourier operator layers and the encoder-decoder framework. (b) provides a detailed view of the internal structure of each individual component within the neural operator.
• Figure 4: During the training stage, the background velocity model together with the corresponding three time-lag images are fed into the neural network. The loss is then computed between the operator’s output and the label, and the parameters of the neural operator are updated through backpropagation until the output closely matches the label.
• Figure 5: Training and validation losses during the training phase.