一种简化的计算频域有限差分自适应系数的方法  

A simplified calculation for adaptive coefficients of finite-difference frequency-domain method

作　　者：徐文豪 巴晶[1] Jose M.Carcione 杨志芳[3,4] 晏信飞[3,4] Xu Wen-Hao;Ba Jing;Carcione Jose Maria;Yang Zhi-Fang;Yan Xin-Fei(School of Earth Science and Engineering,Hohai University,Nanjing,Jiangsu,211000;National Institute of Oceanography and Applied Geophysics(OGS),Sgonico,Trieste 34010;China National Petroleum Corporation Exploration and Development Research Institute,Beijing,100083;China National Petroleum Corporation Key Laboratory of Geophysics,Beijing,100083)

机构地区：[1]河海大学地球科学与工程学院,江苏南京211000 [2]National Institute of Oceanography and Applied Geophysics(OGS),Sgonico,Trieste 34010 [3]中国石油天然气股份有限公司勘探开发研究院,北京100083 [4]中国石油天然气股份有限公司地球物理重点实验室,北京100083

出　　处：《Applied Geophysics》2023年第3期262-277,348,349,共18页应用地球物理（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.42174161,No.41974123);China Postdoctoral Science Foundation(No.2022M711004);China National Petroleum Corporation Exploration and Development Research Institute Open Fund(No.822102016);the Jiangsu Province Science Fund for Distinguished Young Scholars(No.BK20200021).

摘　　要：频域有限差分(finite difference frequency domain,FDFD)方法是地震波场模拟的常用方法,FDFD地震波场模拟的关键之一是构造能有效压制数值频散的FDFD系数。在已有的构造地震波场模拟FDFD系数的方法中,随一个网格内的波长个数变化的自适应FDFD系数可以最大程度地压制数值频散。目前计算自适应FDFD系数的方法涉及角度积分、共轭梯度优化、顺序初值选取、光滑正则化等问题,不仅较难实现而且计算效率较低。为了简化自适应FDFD系数的计算并提高相应计算效率,本文提出一种新的计算自适应FDFD系数的方法。所提方法首先将不同离散传播角度的平面波解代入FDFD格式,构造相应的最小二乘问题。由于该最小二乘问题较为病态,常规的基于正规方程组的求解方法难以得到光滑的自适应FDFD系数,本文提出通过QR矩阵分解求解相应超定线性方程组来求解该最小二乘问题。相比已有的基于角度积分、共轭梯度优化、顺序初值选取的计算自适应FDFD系数的方法,所提方法在可以得到光滑自适应FDFD系数的基础上,不仅计算过程更简洁,且计算效率明显提高。数值波场模拟结果表明,基于QR矩阵分解的自适应系数FDFD方法可以达到与基于角度积分、共轭梯度优化、顺序初值选取的自适应系数FDFD方法相同的精度,同时所需的计算时间更少。The finite-difference frequency domain(FDFD)method is widely applied for simulating seismic wavefields,and a key to achieving successful FDFD simulation is to construct FDFD coefficients that can effectively suppress numerical dispersion.Among the existing FDFD coefficients for seismic wavefield simulation,adaptive FDFD coefficients that vary with the number of wavelengths per grid can suppress numerical dispersion to the maximum extent.The current methods for calculating adaptive FDFD coefficients involve numerical integration,conjugate gradient(CG)optimization,sequential initial value selection,and smooth regularization,which are difficult to implement and inefficient in calculations.To simplify the calculation of adaptive FDFD coefficients and improve the corresponding computational efficiency,this paper proposes a new method for calculating adaptive FDFD coefficients.First,plane-wave solutions with different discrete propagation angles are substituted in the FDFD scheme,and the corresponding least-squares problem is constructed.As this problem is ill-conditioned and obtaining smooth adaptive FDFD coefficients by the conventional solving method based on normal equations is difficult,this paper proposes solving the least-squares problem by solving the corresponding overdetermined linear system of equations through QR matrix decomposition.Compared with the existing methods for calculating adaptive FDFD coefficients based on numerical integration,CG optimization,and sequential initial value selection,the proposed method allows for a simplified computational process and considerably higher computational efficiency.Numerical wavefield simulation results show that the adaptive-coefficient FDFD method based on QR matrix decomposition can achieve the same accuracy as those based on numerical integration,CG optimization,and sequential initial value selection while requiring less computation time.

关 键 词：地震波场模拟 频域有限差分 自适应系数 数值频散 QR分解 

分 类 号：P631.4[天文地球—地质矿产勘探]