Deep learning-based off-the-grid seismic data reconstruction and regularization: Preliminary research

ABSTRACT During field seismic data acquisition, sources and receivers are commonly positioned off the Cartesian grids (off-the-grid). Irregularities in the observed seismic data can negatively affect subsequent migration and inversion processes, which assume that the data are acquired on regular grids (on-the-grid). Most seismic interpolation algorithms assign off-the-grid samples to their nearest regular grid points using a binning strategy, easily introducing reconstruction errors. To improve the reconstruction accuracy of off-the-grid seismic data, we conduct preliminary research on supervised deep learning-based seismic data reconstruction and regularization. Initially, we determine a nonuniform discrete Fourier transform (NDFT) operator based on the observed off-the-grid and the regularized on-the-grid trace locations. Then, we apply the adjoint NDFT operator to transform the observed off-the-grid data into the blurry on-the-grid conjugate solutions, which implicitly contain the original off-the-grid information. The conjugate solutions and their corresponding on-the-grid complete data serve as the training inputs and labels, respectively. We adopt a designed U-net to learn the nonlinear mapping between the training inputs and the labels. Upon training convergence, we input the on-the-grid conjugate solutions of unlabeled off-the-grid test data into the optimized network for reconstruction and regularization. During the training phase, we use the L1 norm to measure the data misfit in the frequency-wavenumber domain as the loss function, and its advantages are thoroughly demonstrated in the “Discussion” section. Furthermore, we explore the potential of our method for off-the-grid ocean-bottom node reconstruction and regularization through self-supervised learning. The effectiveness and superiority of our deep learning-based off-the-grid seismic data reconstruction and regularization algorithm are validated by numerical results of synthetic and field data, particularly compared with the curvelet transform-based sparse inversion method.