Robust unsupervised 5D seismic data reconstruction on regular and irregular grids

Abstract

Seismic data reconstruction has become a central focus in seismic data processing, addressing challenges posed by sparse sampling due to physical and budgetary constraints. The advent of 5D acquisition methodologies marks a significant advancement in the quality and completeness of seismic data sets. Most traditional 5D reconstruction methods commonly use the fast Fourier transform (FFT), requiring regular grids and preliminary 4D binning before 5D interpolation. Discrete Fourier transform and nonequidistant FFT can honor the original irregular coordinates. However, when using exact locations, these methods become computationally expensive. We introduce an unsupervised deep-learning methodology to learn a continuous function across the sampling points in seismic data, facilitating reconstruction on regular and irregular grids. The network comprises a multilayer perceptron with linear layers and element-wise periodic activation functions. It excels at mapping the input coordinates to the 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 and incoherent ones during training. This characteristic mitigates incoherent noise in seismic data, such as random and erratic components. To assess the robustness of the unsupervised reconstruction technique, we conduct comprehensive evaluations using synthetic data examples sampled regularly and irregularly, as well as field-data examples with and without binning. The findings demonstrate the efficacy of our deep-learning framework in achieving resilient and accurate seismic data reconstruction across diverse sampling scenarios.