频率域声波方程仿射25点格式高精度数值模拟  

Affine 25-point scheme for high-accuracy numerical simulation of frequency-domain acoustic wave equation

作　　者：董树立 陈景波[1,2,3] DONG ShuLi;CHEN JingBo(Key Laboratory of Petroleum Resources Research,Institute of Geology and Geophysics,Chinese Academy of Sciences,Beijing 100029,China;Innovation Academy for Earth Science,Chinese Academy of Sciences,Beijing 100029,China;University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院地质与地球物理研究所,中国科学院油气资源研究院重点实验室,北京100029 [2]中国科学院地球科学研究院,北京100029 [3]中国科学院大学,北京100049

出　　处：《地球物理学报》2024年第10期3859-3873,共15页Chinese Journal of Geophysics

基　　金：国家自然科学基金(42074159,41874163)资助。

摘　　要：构造一个高效的有限差分算子在提升频率域有限差分正演模拟的计算效率方面具有重要意义.旋转坐标系法以其良好的几何特性被广泛用于各种数值格式的构造.前人开发的广义双9点格式具有较高的数值精度且适用于任意矩形网格采样.仿射坐标系作为一种广义的坐标系统,以其不限制坐标轴彼此正交的特性而受到关注.在本研究中,我们基于仿射变换对广义双9点格式进行了深入分析,发现其并不严格遵循旋转坐标系方法.因为其在非均匀网格间隔和低波数下具有零阶截断精度.此外,考虑到广义双9点格式对有限差分模板利用不充分,我们基于仿射变换提出了一个具有更高精度的仿射25点格式.在相等或不等网格间距的情况下,仿射25点格式在低波数时都严格收敛.在高波数时,为限制相速度误差在1%以内,仿射25点格式仅需每最小波长的网格点数不多于2.2个.数值算例证明了仿射25点格式的准确性和优越性.The development of an efficacious Finite-Difference (FD) operator holds paramount significance in enhancing the computational efficiency of frequency-domain FD forward modeling. The rotated-coordinate-system method is extensively employed across numerous numerical schemes due to its advantageous geometrical attributes. The previously generalized double 9-point scheme is highly accurate and suitable for arbitrary rectangular grid sampling. Affine coordinate system, as a kind of generalized coordinate system, has gained attention because it does not restrict their axes to be orthogonal. In this study, we analyze the generalized double 9-point scheme in depth based on the affine transformation and uncover that it does not strictly adhere to the rotated-coordinate-system method. This is because it has zero-order truncation accuracy at non-uniform grid intervals and low wavenumbers. Considering the suboptimal utilization of the FD template in the generalized double 9-point scheme, we leverage the affine transformation to develop an affine 25-point scheme that boasts higher accuracy. The affine 25-point scheme converges rigorously at low wavenumbers with equal or unequal grid intervals. At high wavenumbers, the affine 25-point scheme requires less than 2.2 grid points per minimum wavelength to restrict the phase velocity error to within 1%. Numerical examples demonstrate the accuracy and superiority of the affine 25-point scheme.

关 键 词：仿射变换 双9点格式 25点格式 声波方程 频域有限差分 

分 类 号：P631[天文地球—地质矿产勘探]