Fast least-squares reverse-time migration with adaptive moment estimation
WU Dan1,2, WU Haili1,2, LI Qun1,2, ZHANG Xiangyang1,2, LIU Shuren1,2
1. Northwest Branch, Research Institute of Petroleum Exploration & Development, PetroChina, Lanzhou, Gansu 730030, China; 2. Key Laboratory of Internet of Things, CNPC, Lanzhou, Gansu 730030, China
Abstract：Least-squares reverse-time migration (LSRTM) is a seismic imaging method with high resolution and favorable amplitude fidelity. However, its computational burden is heavy since it often needs to run iterations nearly ten times and takes approximately the computational cost of two full-dataset RTMs for each iteration. Here, we introduce the adaptive moment estimation (Adam) method from the field of deep learning to improve the computational efficiency of LSRTM: At each iteration, only part of the common shot gathers are required to calculate the gradient and the resulting gradient is corrected by the momentum (AdaGrad) method; considering the nonstationary property of the gradient, the root mean square propagation (RMSProp) algorithm is used to eliminate the influence of inadequate illumination. The Adam method, combining the advantages of the AdaGrad method and the RMSProp method, not only reduces the computational burden of each iteration but also improves the convergence speed of the iterations. In addition, this method is straightforward to implement and computationally efficient with a low memory requirement, and thus it is a fast and effective gradient preconditioning method. The A-dam method not only can be applied to LSRTM directly but also is applicable to shot encoding LSRTM. Numerical tests on the SEG/EAGE salt model show that this method can provide a high-precision and high-resolution image at merely the same cost as that of two RTMs. The substantial increase in computational efficiency paves the way for the application of LSRTM in practical seismic data processing.
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