Five-Dimensional Seismic Data Reconstruction via Coordinate-Guided Transformer

Abstract

Irregular acquisition geometries in field seismic surveys lead to non-uniform spatial sampling, which introduces spatial aliasing, reduces spectral utilization and degrades the accuracy of subsequent wavefield reconstruction and imaging. Seismic data regularization aims to resample such irregularly acquired data onto a uniform grid, serving as a critical preprocessing step. In this study, we propose an unsupervised deep learning framework for five-dimensional (5D) seismic data regularized reconstruction that integrates implicit neural representation with a Transformer backbone and short-time Fourier transform based time–frequency feature learning. The seismic wavefield is parameterized as a continuous mapping from four-dimensional (4D) spatial coordinates to amplitudes. A novel 4D positional encoding scheme, extending sinusoidal Transformers to shot and receiver coordinates, is designed to enhance the representation of high-dimensional spatial structures. The Transformer architecture captures global long-range dependencies through self-attention, while the model predicts the real and imaginary components of the time–frequency spectrum, from which waveforms are reconstructed via the inverse short-time Fourier transform (ISTFT), thereby improving spectral recovery and amplitude-phase consistency. Experiments on synthetic data demonstrate that the proposed method achieves lower normalized root-mean-square errors and superior reconstruction of reflection structures, spectra and detailed waveform features compared with projection onto convex sets, damped rank reduction, robust damped rank reduction, and a baseline implicit neural representation approach. Field 5D data experiments further confirm the method's effectiveness in recovering amplitude, phase and azimuthally anisotropic characteristics on regular grids, with only a small incremental ISTFT cost for the tested workload. The proposed framework enables high-accuracy, self-supervised reconstruction of 5D seismic data under irregular sampling conditions without requiring labelled training data.