Abstract
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.