Real-Data-Guided Seismic Forward Modeling in Latent Space

Seismic forward modeling (SFM) predicts wave responses from subsurface velocity fields, but learning this mapping accurately remains challenging because seismic responses are high-dimensional and paired real-world velocity–response data are scarce. Nevertheless, we argue that real earthquake records can still provide informative waveform trends for data-driven SFM. Motivated by this insight, we apply Parallel Symbolic Enumeration (PSE) to event–station records to discover empirical relationships. After offline physics-based screening with assistance from a large language model (LLM), the retained relationships can be transformed into normalized trend templates that regularize training at no additional inference cost. Building on this real-data-derived guidance, we propose Latent Seismic Predictor (LSP), a coarse-to-refined latent framework that separates dominant response prediction from oscillatory detail recovery. LSP first maps the subsurface velocity field into a coarse response latent capturing principal arrivals, reflection geometry, and broad energy distribution, and then applies attention-guided spectral residual refinement to recover unresolved waveform components through tapered sine–cosine basis functions. Moreover, learnable tapering suppresses spurious oscillations before residual synthesis, after which the refined latent representation is decoded into the complete seismic response. Across ten OpenFWI subsets, LSP achieves the best average rank in MAE, MSE, and SSIM, reducing average MAE and MSE on the challenging Style subsets by 11.4% and 26.2%, respectively, over the strongest baseline. When transferred from Style-B to Marmousi and Overthrust without fine-tuning, it reduces average MAE by 24.5%. The leading performance on GlobalTomo also supports its extension to high-dimensional 3D acoustic wave prediction. Codes are attached.