二阶应变梯度波场效应的高阶有限差分模拟优化  

Optimized high-order finite-difference modeling of second-order strain gradient wave field effects

作　　者：胡仔豪 冯海新 周之淳 李幼铭[4] 王之洋 Hu Zi-hao;Feng Hai-xin;Zhou Zhi-chun;Li You-ming;Wang Zhi-yang(College of Information Science and Technology,Beijing University of Chemical Technology,Beijing 100029,PRC;Third Research Institute of China Electronics Technology Group Company,Beijing 100015,PRC;Beijing University of Aeronautics and Astronautics,Beijing 100191,PRC;Key Laboratory of Petroleum Resources Research,Institute of Geology and Geophysics,Chinese Academy of Sciences,Beijing 100029,PRC)

机构地区：[1]北京化工大学信息科学与技术学院,北京100029 [2]中国电子科技集团公司第三研究所,北京100015 [3]北京航空航天大学,北京100191 [4]中国科学院地质与地球物理研究所,北京100029

出　　处：《Applied Geophysics》2023年第3期278-290,349,共14页应用地球物理（英文版）

基　　金：supported by The“HYXD”National Project(Nos.XJZ2023050044 and A2309002).

摘　　要：二阶应变梯度波动方程依托的公理体系是广义连续介质力学理论,其通过引入位移的二阶空间导数项,丰富了经典连续介质力学理论的内容,并同时通过附加的介质特征尺度参数以反映介质内的微结构特性,弥合微观模型和经典连续介质力学之间的差距。王之洋等人从非局部理论出发,推导单参数二阶应变梯度理论的本构方程,进而结合几何方程和运动微分方程,给出二阶应变梯度非对称弹性波动方程的数学表达式,二阶应变梯度理论可以反映以介质平均颗粒直径l为邻域的内部更小尺度的地震波传播尺度效应。考虑到较小的空间尺度效应较弱,差分算子逼近微分算子时产生的数值频散会抑制尺度效应。因此,为了更好地描述和分析尺度效应,需要对有限差分算子进行优化。本文提出了一种改进的BWOA算法来得到优化的有限差分系数,并基于二阶应变梯度理论进行了弹性波数值模拟。数值模拟分析表明,数值频散得到了很好的压制,从地震记录中可以明显地观察和提取较小的空间尺度效应。The second-order strain gradient wave equation is based on the generalized continuum mechanics theory,and it can enrich the content of classical continuum mechanics theory with the incorporation of the second-order spatial derivative term of displacement.Furthermore,this equation incorporates scale parameters of media characteristics to bridge the gap between micromodels and classical continuum mechanics to reflect the microstructural characteristics in the media.Wang used a nonlocal theory to derive a constitutive equation of single-parameter second-order strain gradient theory and provided a mathematical expression for the second-order strain gradient asymmetric elastic wave equation combined with geometric equation and differential equation of motion.The second-order strain gradient theory can reflect the small-scale effect of seismic wave propagation within the neighborhood with an average particle diameter of l of the medium.Given the relatively weak spatial-scale effect,the numerical dispersion generated when the difference operator approximates the differential operator can suppress the scale effect.Thus,the finite-difference operator must be optimized accurately to describe and analyze scale effects.In this paper,an improved black widow optimization algorithm was proposed to obtain optimized finite-difference coefficients,and numerical modeling based on the second-order strain gradient wave equation was performed.Numerical modeling results reveal the well-suppressed numerical dispersion,and seismograms display the clear extraction of small spatial-scale effects.

关 键 词：二阶应变梯度 数值模拟 BWOA算法 非对称弹性波动方程 

分 类 号：P631.4[天文地球—地质矿产勘探]