The process of seismic multiple removal in oil seismic exploration is crucial for the imaging of underground structures with primary reflections. The inclusion of prediction and subtraction in the multiple removal method requires adaptive subtraction to remove the complex differences between the true and modeled multiples. The traditional adaptive subtraction method is generally expressed as a linear regression (LR) problem. In this article, we introduce U-net, a popular deep learning tool, to represent the complex differences between the true and modeled multiples in a nonlinear relationship. Thus, we present adaptive subtraction as a non-LR problem. The modeled multiples and full recorded seismic response with multiples and primaries are used as the input and labels to train U-net. The proposed U-net method is able to avoid over-fitting of the primaries due to the sufficient number of 2-D data windows for the training of U-net, as well as the network parameter regularization and the L1 norm minimization constraint on the primaries. The proposed U-net method attains 20.5 dB and 2.5 dB improvement in the signal-to-noise ratio (SNR) using the first synthetic data and second synthetic (Sigsbee2B) data set, respectively, compared with the traditional LR method, and a qualitative improvement for a real data set test.

Multichannel predictive deconvolution can accommodate the lateral variations of subsurface structures to some extent and better preserve primaries than can single-channel predictive deconvolution. To solve the 2D predictive filter, traditional multichannel predictive deconvolution uses the least-squares (LS) algorithm, which requires orthogonality between primaries and multiples. In areas where primaries and multiples overlap, traditional LS-based multichannel predictive deconvolution can cause distorted primaries and residual multiples. To avoid the orthogonality assumption required by the LS algorithm, the iterative reweighted LS (IRLS) algorithm and the fast iterative shrinkage-thresholding (FIST) algorithm can be used to solve the prediction filter using the $l_1$ norm. The FIST algorithm uses the shrinkage-thresholding operator to promote the sparsity of estimated primaries and solves the predictive filter with iterative steps. Compared with the IRLS algorithm, the FIST algorithm can reduce the computation burden effectively while achieving similar accuracy. We have used the FIST algorithm for multichannel predictive deconvolution using the $l_1$ norm. Compared with traditional FIST-based single-channel predictive deconvolution and LS-based multichannel predictive deconvolution, our method can better balance primary preservation and multiple removal. Tests using synthetic and field data sets proved the effectiveness of the proposed method.

After multiple prediction, adaptive multiple subtraction is essential for the success of multiple removal. The 3D blind separation of convolved mixtures (3D BSCM) method, which is effective in conducting adaptive multiple subtraction, needs to solve an optimization problem containing L1-norm minimization constraints on primaries by the iterative reweighted least-squares (IRLS) algorithm. The 3D BSCM method can better separate primaries and multiples than the 1D/2D BSCM method and the method with energy minimization constraints on primaries. However, the 3D BSCM method has high computational cost because the IRLS algorithm achieves nonquadratic optimization with an LS optimization problem solved in each iteration. In general, it is good to have a faster 3D BSCM method. To improve the adaptability of field data processing, the fast iterative shrinkage thresholding algorithm (FISTA) is introduced into the 3D BSCM method. The proximity operator of FISTA can solve the L1-norm minimization problem efficiently. We demonstrate that our FISTA-based 3D BSCM method achieves similar accuracy of estimating primaries as that of the reference IRLS-based 3D BSCM method. Furthermore, our FISTA-based 3D BSCM method reduces computation time by approximately 60% compared with the reference IRLS-based 3D BSCM method in the synthetic and field data examples.

Anelasticity of the earth subsurface medium, which is quantified by the quality factor $Q$ , causes the dissipation of seismic energy. Strong attenuation effect resulting from geology such as gas clouds (gas-filled sandstone) is a challenging problem for high-resolution imaging. To compensate the attenuation effect, first we need to accurately estimate the attenuation parameter. However, it is difficult to directly derive a heterogeneous attenuation Q model. This research letter proposes a method to derive a Q model corresponding to strong attenuative media from marine reflection seismic data using convolutional neural network (CNN), a popular deep learning framework. We treat Q anomaly detection problem as a semantic segmentation task and train a network to perform a pixel-by-pixel prediction to invert a pixel group that belongs to the strong level of attenuation probability. The proposed method uses a volume of marine 3-D reflection seismic data for network training and validation, which needs only a small part of real data as the training set due to the feature of U-Net. In the final stage, to evaluate the attenuation model, we validate the predicted heterogeneous Q model using deabsorption prestack depth migration (Q-PSDM), a high-resolution imaging result in depth domain with appropriate compensation is obtained.