Frequency-aware seismic velocity inversion via Long-Range Dependency learning

Abstract

Seismic velocity inversion is a highly non-linear problem, and achieving efficient and accurate velocity modeling remains challenging due to the complexity of seismic wavefields. This process is primarily constrained by cycle-skipping and the loss of macroscopic structural trends. To overcome these limitations, we introduce FAR-UNet (Frequency-Aware Reasoning UNet), a frequency-aware framework that redefines velocity reconstruction as a hierarchical spectral reasoning task. By integrating multi-head attention with relative position biases, the model functions as a set of adaptive spectral filters to honor geologically-consistent priors. This mechanism captures long-range spatial dependencies that are typically lost in conventional convolutional operators, furthermore bridging the gap between global geological context and fine-scale stratigraphic details to ensure both structural continuity and interface sharpness. To ensure wavefield integrity, we prioritize data integrity by utilizing raw shot gathers and linear Layer Normalization. This “raw-input” strategy strictly preserves relative amplitude ratios and acoustic impedance contrasts, allowing the network to honor true wavefield dynamics without distortions from manual gain adjustments. Numerical benchmarks demonstrate that FAR-UNet significantly enhances reconstruction fidelity. On the Simulated dataset, the proposed method achieves a PSNR of 27.20 dB and an SSIM of 68.30 %, representing a 3.20 dB PSNR gain and an 8.87 % SSIM improvement over the Swin-Unet baseline. These results confirm that our architecture effectively resolves complex velocity anomalies while maintaining a reduced computational footprint of 19.54 G FLOPs.