Suppressing Seismic Multiples Based on Deep Residual Fourier Neural Operator

Multiples are interfering waves that seriously affect seismic imaging, which is one of the key problems for seismic data processing needed to be commonly concerned with how to suppress multiples effectively. Based on Fourier Neural Operator (FNO) and Residual network (ResNet), this paper proposes a seismic multiple suppressing method using Deep Residual Fourier Neural Operator (DRFNO). DRFNO is a weakly constrained model + data -driven Artificial Intelligence (AI) algorithm. In order to supervise the training of DRFNO, full wavefield data is used as input and primary data is utilized as labels. The objective is to obtain the optimal weights and biases in DRFNO, considering the characteristics of seismic wavefield data as well as the physical mechanism of wave equation forward modeling. The parameters are optimized through the minimizing of the error between the predicted and target label wavefield. Once trained, DRFNO can effectively suppress multiples from the full wavefield and reconstruct primaries. To address the issue of inconsistent seismic events energies within shot gathers for the proposed method, a Seismic Data Activation Function (SDAF) is used in data preprocessing. This function is derived from the traditional machine learning approach with setting activation functions and has been layered medium models effectiveness, the noise specifically defined to enable successful network training for seismic data. Next, two synthetic and a complex synthetic Sigsbee2B examples are applied to demonstrate the immunity and the generalization ability of DRFNO based on the results of multiples suppressing. Finally, a real seismic data example shows that this proposed DRFNO method has some good results to suppress multiples within the real complex seismic wavefields.