none 10.1190/geo2019-0412.1 Society of Exploration Geophysicists Society of Exploration Geophysicists 186 116807021 5981 2025121211260247500 10.1190 2025-12-12T16:26:16Z 2020-06-02T11:14:18Z 25 Geophysics 0016-8033 1942-2156 07 1 2020 85 4 Deep convolutional neural network and sparse least-squares migration Zhaolun Liu King Abdullah University of Science and Technology 1 Formerly , Department of Earth Science and Engineering, Thuwal, Saudi Arabia; presently , Department of Geosciences, Princeton, New Jersey 08544, . E-mail: zhaolunl@princeton.edu (corresponding author). USA Princeton University 1 Formerly , Department of Earth Science and Engineering, Thuwal, Saudi Arabia; presently , Department of Geosciences, Princeton, New Jersey 08544, . E-mail: zhaolunl@princeton.edu (corresponding author). USA http://orcid.org/0000-0002-1430-7914 Yuqing Chen King Abdullah University of Science and Technology 2 Formerly , Department of Earth Science and Engineering, Thuwal, Saudi Arabia; presently , Deep Earth Imaging Future Science Platform, Kensington, . E-mail: Yu. Chen@csiro.au . Australia CSIRO 2 Formerly , Department of Earth Science and Engineering, Thuwal, Saudi Arabia; presently , Deep Earth Imaging Future Science Platform, Kensington, . E-mail: Yu. Chen@csiro.au . Australia http://orcid.org/0000-0002-2480-8974 Gerard Schuster King Abdullah University of Science and Technology 3 , Department of Earth Science and Engineering, Thuwal 23955-6900, Saudi Arabia. E-mail: gerard.schuster@kaust.edu.sa . http://orcid.org/0000-0003-4746-2512 ABSTRACT We have recast the forward pass of a multilayered convolutional neural network (CNN) as the solution to the problem of sparse least-squares migration (LSM). The CNN filters and feature maps are shown to be analogous, but not equivalent, to the migration Green’s functions and the quasi-reflectivity distribution, respectively. This provides a physical interpretation of the filters and feature maps in deep CNN in terms of the operators for seismic imaging. Motivated by the connection between sparse LSM and CNN, we adopt the neural network version of sparse LSM. Unlike the standard LSM method that finds the optimal reflectivity image, neural network LSM (NNLSM) finds the optimal quasi-reflectivity image and the quasi-migration Green’s functions. These quasi-migration Green’s functions are also denoted as the convolutional filters in a CNN and are similar to migration Green’s functions. The advantage of NNLSM over standard LSM is that its computational cost is significantly less and it can be used for denoising coherent and incoherent noise in migration images. Its disadvantage is that the NNLSM quasi-reflectivity image is only an approximation to the actual reflectivity distribution. 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