Adaptively subtracting multiple model from the initial data is an essential assignment for the successful elimination of seismic surface-related multiples. Conventional expanded multichannel linear regression (EMLR) method has been proposed to address this challenge by utilizing multi-pattern multiple model. These patterns include the multiple model itself and its first derivative, its Hilbert transform and its first derivative of the Hilbert transform, which are matched with the initial data in the EMLR method. It may lead to inaccurate primary preservation or give rise to residual multiples by using the LR model. The existing U-Net method effectively mitigates complex disparities between the multiple model and actual multiples through integrating adaptive subtraction into the non-LR architecture. Nevertheless, residual multiples are produced by this method using the multiple model itself, especially in complex media contexts. In order to improve surface-related multiple removal’s accuracy, we propose the expanded multichannel U-Net (EMUN) method with multi-pattern multiple model. In the proposed method, the initial data is matched with the multi-pattern multiple model through U-Net in the way of self-supervised training without true primaries as labels. The proposed method incorporates rich information from expanded multichannel of U-Net, enabling better U-Net training for adaptive subtraction. In contrast to the EMLR method and the existing U-Net method, the proposed EMUN method exhibits exceptional efficacy in protecting primaries and eliminating surface-related multiples, as evidenced by its outstanding performance in both synthetic and field data tests.

Transformer has shown great capability in remote sensing and automatic target recognition (ATR). Due to the self-attention mechanism, the Transformer could extract global features while parallelizing training. However, the computational costs and power consumption are challenging the electronic computing techniques. Here, we develop a Transformer-based optronic neural network (TOPNN) for synthetic aperture radar (SAR) target recognition. We implement the self-attention mechanism in optics, significantly reducing the network computational costs. Compared with digital techniques, the TOPNN promises the speed of light, low computational costs, and low power consumption. Experiments on the Moving and Stationary Target Acquisition and Recognition (MSTAR) dataset demonstrate the feasibility and efficiency of TOPNN for SAR target recognition.

Effectively suppressing seismic multiples relies heavily on the crucial task of adaptively subtracting the simulated multiples from the initial recorded data. By executing adaptive subtraction within the non-linear regression (non-LR) framework the U-net method has shown superior capability in mitigating the intricate disparities between the simulated and actual multiples when compared to the LR method. The low, medium and high frequency-bands of simulated multiples have been employed to effectively address frequency-dependent inconsistencies in the LR method. To further improve multiple suppression accuracy three frequency-bands of simulated multiples are employed as three channels of the U-net input, which are matched with the initial recorded data during self-supervised training in this letter. Compared to the LR method inputting simulated multiples alone, the LR method inputting three frequency-bands of simulated multiples and the U-net method inputting simulated multiples alone, the proposed U-net method inputting three frequency-bands of simulated multiples improves the signal-to-noise ratio (SNR) by 4.41, 2.07 and 1.99 in the synthetic data example, and demonstrates superior improvement in preserving primaries and eliminating residual multiples in the field data example.

Adaptive subtraction plays a crucial role in the multiple removal method that involves modeling and subtraction steps. The linear regression (LR) based method utilizes the fast iterative shrinkage thresholding algorithm (FISTA) to solve the optimization problem that contains L1 norm minimization constraint of primaries. It selects the regularization factor and shrinkage thresholding value through trial and error. Under the non-LR framework the U-net is used for adaptive subtraction of modeled multiples from the original recorded data. Since U-net has large network capacity, it is prone to overfit to the original recorded data and lead to primary damage. In this paper, we unfold the iterative steps of FISTA to construct FISTA-Net, which takes the original recorded data and modeled multiples as input data and outputs the estimated primaries. The FISTA-Net based method does not require true primaries as labels and uses L1 norm minimization constraint of primaries for unsupervised training. It can adaptively estimate the regularization factor and shrinkage thresholding value, which is replaced by U-net. FISTA-Net introduces the nonlinear mapping ability of U-net into its structure, which can be interpreted as the iterative steps of FISTA. As a result, the proposed FISTA-Net based method can better attenuate residual multiples, avoid overfitting, and preserve primaries compared to the LR-based and U-net based methods.