[Paper Review] CNN-tuned spatial filters for P- and S-wave decomposition and applications in elastic imaging

Wenlong Wang, Siwei Ma+1 more|arXiv (Cornell University)|Dec 21, 2021

Seismic Imaging and Inversion Techniques4 citations

TL;DR

This paper proposes CNN-tuned spatial filters for accurate, artifact-free P- and S-wave decomposition in 2D isotropic elastic wavefields, bypassing costly Fourier transforms. Trained once on synthetic data, the filters achieve superior decomposition accuracy over traditional space-domain methods and reduce imaging artifacts in elastic reverse-time migration, especially at high-velocity contrasts.

ABSTRACT

P- and S-wave decomposition is essential for imaging multi-component seismic data in elastic media. A data-driven workflow is proposed to obtain a set of spatial filters that are highly accurate and artifact-free in decomposing the P- and S-waves in 2D isotropic elastic wavefields. The filters are formulated initially by inverse Fourier transforms of the wavenumber-domain operators, and then are tuned in a convolutional neural network to improve accuracy using synthetic snapshots. Spatial filters are flexible for decomposing P-and S-waves at any time step without performing Fourier transforms over the entire wavefield snapshots, and thus are suitable for target-oriented imaging. Snapshots from synthetic data show that the network-tuned spatial filters can decompose P- and S-waves with improved decomposition accuracy compared with other space-domain PS decomposition methods. Elastic reverse-time migration using P- and S-waves decomposed from the proposed algorithm shows reduced artifacts in the presence of a high velocity contrast.

Motivation & Objective

• Address the challenge of accurate P- and S-wave decomposition in elastic seismic imaging without relying on computationally expensive Fourier transforms.
• Overcome amplitude and phase distortions caused by conventional divergence and curl operators in wavefield decomposition.
• Develop a data-driven, trainable spatial filter framework that maintains physical consistency across different velocity models.
• Enable efficient, parallelizable, and target-oriented decomposition suitable for large-scale or localized seismic imaging workflows.
• Demonstrate improved imaging quality in elastic reverse-time migration by reducing artifacts at high-velocity contrasts.

Proposed method

• Formulate initial spatial filters via inverse Fourier transforms of wavenumber-domain operators for P- and S-wave polarization.
• Implement a single-layer convolutional neural network (CNN) to tune the spatial filters using synthetic wavefield snapshots as training data.
• Train the network to minimize the difference between predicted and ground-truth P-wave snapshots decomposed in the wavenumber domain.
• Use the trained filters for direct spatial-domain decomposition without retraining, enabling application across diverse models.
• Integrate the CNN-tuned filters into elastic reverse-time migration (RTM) workflows for PS decomposition and image formation.
• Apply the filters locally to target-oriented data sets, leveraging their HPC-friendliness and parallel computation efficiency.

Experimental results

Research questions

• RQ1 Can CNN-tuned spatial filters achieve higher decomposition accuracy than conventional space-domain methods like decoupled propagation?
• RQ2 Does the proposed method reduce imaging artifacts in elastic RTM, particularly at high-velocity contrasts?
• RQ3 Can a single trained filter set be generalized across different elastic models without retraining?
• RQ4 How does the performance of the CNN-tuned filters compare to wavenumber-domain decomposition in terms of accuracy and computational cost?
• RQ5 To what extent can the spatial filters be extended to anisotropic or 3D elastic media?

Key findings

• The CNN-tuned spatial filters achieve higher decomposition accuracy than the decoupled propagation (DP) method, as evidenced by reduced artifacts in stacked PP and PS images.
• In elastic RTM using the CNN-tuned filters, image boundaries are more coherent and artifacts along high-velocity contrasts are significantly reduced compared to the DP method.
• The trained filters maintain high accuracy across different models without retraining, due to the embedded physics in the network structure.
• The computational cost of the 15×15 filter set is 225N operations, which is higher than the wavenumber-domain method’s 4N log(N) cost, but the spatial filters are more suitable for parallel and target-oriented processing.
• The method is extendable to anisotropic media by using non-stationary filters tuned at representative model points, and to 3D by extending the filter set to six components (Lx, Ly, Lz, Lxy, Lxz, Lyz).
• The ground truth for training is derived from wavenumber-domain decomposition, so the CNN-tuned filters cannot exceed the accuracy of the wavenumber method, but they match or exceed space-domain alternatives.