应用自适应矩估计的快速最小二乘逆时偏移

最小二乘逆时偏移(LSRTM)是一种高分辨率和振幅相对保真的地震成像方法,但是该方法往往需要迭代近十次,而每次迭代大约需要两次所有炮逆时偏移(RTM)的计算成本,因此计算量非常大。文中应用深度学习领域中的自适应矩估计方法提高LSRTM的计算效率:每次迭代只采用部分共炮点道集计算梯度,利用动量法对梯度进行修正;考虑梯度的非稳态性,通过均方根传播算法消除照明不足带来的影响。自适应矩估计方法结合了这两种方法的优点,不仅降低了每次迭代的计算量,而且提高了迭代收敛的速度。该方法易于实现、计算效率高、占用内存小,是一种快速有效的梯度预条件方法。自适应矩估计方法不仅可以直接用于LSRTM,也可应用于炮编码的LSRTM。SEG/EAGE盐丘模型数值试验表明,自适应矩估计方法仅需两倍的RTM计算成本就能够获得高精度、高分辨率的成像结果。计算效率的大幅度提升有助于将LSRTM方法推广应用于实际地震数据处理。

Fast least-squares reverse-time migration with adaptive moment estimation

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.