Robust unsupervised 5D seismic data reconstruction on both regular and irregular grid

Seismic data reconstruction in five dimensions (5D) has become a central focus in seismic data processing, addressing challenges posed by irregular sampling due to physical and budgetary constraints. Most traditional high-dimensional reconstruction methods commonly utilize the fast Fourier transform (FFT), requiring regular grids and preliminary 4D binning before 5D interpolation. Discrete Fourier transform and non-equidistant FFT can honour original irregular coordinates. However, when using exact locations, these methods become computationally expensive. This study introduces an unsupervised deep-learning methodology to learn a continuous function across sampling points in seismic data, facilitating reconstruction on both regular and irregular grids. The network comprises a multilayer perceptron (MLP) with linear layers and element-wise periodic activation functions. It excels at mapping input coordinates to corresponding seismic data amplitudes without relying on external training sets. The network’s intrinsic low-frequency bias is crucial in prioritizing acquiring self-similar features over high-frequency, incoherent ones during training. This characteristic mitigates incoherent noise in seismic data, including random and erratic components. To assess the robustness of the unsupervised reconstruction technique, we conduct comprehensive evaluations using synthetic data examples sampled both regularly and irregularly, as well as field-data examples with and without binning. The findings demonstrate the efficacy of the proposed deep-learning framework in achieving resilient and accurate seismic data reconstruction across diverse sampling scenarios.