Learning Stratigraphically Consistent Relative Geologic Time from 3D Seismic Data via Sinusoidal Mapping

Abstract. Relative Geologic Time (RGT) estimation from seismic data underpins subsurface structural modeling, depositional analysis, and reservoir characterization, providing the basis for horizon correlation and depositional system reconstruction. Accurate RGT estimation remains challenging because RGT is a topologically constrained continuous field in which local errors readily propagate globally through topological coupling, distorting the overall result. Conventional methods depend heavily on prior information, attribute extraction, and manual interaction, resulting in cumbersome workflows with limited automation. Existing deep-learning approaches predominantly adopt a regression formulation optimized by pixel-wise MSE/MAE losses, which struggles to recover thin horizons and fails to capture the stratigraphic semantics embedded in the RGT field, yielding limited generalization, unstable stratigraphic ordering, and poor adaptability to diverse structural and depositional settings. We propose RGT-Est, a deep-learning framework that transfers the optimization target from the topologically constrained continuous field into a differentiable sinusoidal space. This representation explicitly encodes the periodic stratigraphic semantics of RGT and alleviates the over-smoothing of fine horizons inherent in direct regression. Pointwise, perceptual, and adversarial losses are jointly imposed in this space to enforce local fidelity, inter-layer consistency, and global structural plausibility, providing both fine-horizon discrimination and global stratigraphic awareness. An optional horizon-guidance module accepts sparse 2D or 3D horizons as priors to satisfy varying precision demands. Trained on synthetic data and evaluated on field seismic surveys featuring dense faulting, large unconformities, steeply dipping strata, folded deformations, and clinoforms, RGT-Est achieves state-of-the-art performance among AI-based methods, and attains substantially higher horizon-correlation accuracy and topological consistency when sparse priors are incorporated.