一阶速度—胀缩—旋转弹性波方程交错网格数值模拟  

Numerical simulation of first-order velocity-dilatationrotation elastic wave equation with staggered grid

作　　者：王辉 何兵寿[1,2] 邵祥奇 WANG Hui;HE Bingshou;SHAO Xiangqi(Key Lab of Submarine Geosciences and Prospecting Techniques,MOE China,Ocean University of China,Qingdao,Shandong 266100,China;Functional Laboratory of Marine Mineral Resources Evaluation and Exploration Technology,Qingdao National Laboratory of Marine Science and Technology,Qingdao,Shandong 266100,China;Yantai Natural Resources and Planning Bureau,Yantai,Shandong 264003,China)

机构地区：[1]中国海洋大学海底科学与探测技术教育部重点实验室,山东青岛266100 [2]青岛海洋科学与技术国家实验室海洋矿产资源评价与探测技术功能实验室,山东青岛266100 [3]山东省烟台市自然资源和规划局,山东烟台264003

出　　处：《石油地球物理勘探》2022年第6期1352-1361,I0004,共11页Oil Geophysical Prospecting

基　　金：国家自然科学基金项目“OBN宽频多分量地震资料的纵横波联合逆时偏移方法研究”(41674118)资助。

摘　　要：弹性波正演在地震波传播机理研究以及多波地震资料采集、处理、解释和反演中发挥着重要作用。现有的弹性波方程正演模拟常常数值求解一阶速度—应力方程或二阶位移弹性波方程,只能直接得到同时包含纵波和横波的三个质点振动速度分量或位移分量,要想得到更直观的纯纵波和纯横波分量记录,还需要在模拟过程中采用波场解耦算子进行纵、横波分离,因此纵、横波模拟精度同时受制于模拟算法和波场解耦算法的精度。为此,推导了一阶速度—胀缩—旋转弹性波方程在三维交错网格空间中的高阶有限差分格式,并给出了相应的稳定性条件;推导了适应该方程的PML吸收边界条件,实现了一阶速度—胀缩—旋转弹性波方程的正演模拟;分析了模拟结果中各分量的物理意义。由于一阶速度—胀缩—旋转弹性波方程不仅包含了质点的振动速度矢量,而且显式地包含了横波振动速度矢量和纵波振动速度矢量,还包含了一个体应变和一个旋转矢量,因此应用该方程模拟除了能得到三个质点振动速度分量外,还可以直接得到解耦后的纵、横波分量,避免了解耦算法对模拟精度的影响。模型试算证明了该模拟方法的正确性和优越性。Elastic wave forward modeling plays an important role in seismic wave propagation mechanism research and the acquisition,processing,interpretation,and inversion of multi-wave seismic data.Present forward modeling of elastic wave equations often numerically solves first-order velocity-stress equation or second-order displacement equation to only obtain three particle vibration velocity components or displacement components containing P-and S-wave.The wave-field decoupling operator should be employed to separate Pand S-wave for a more intuitive recording of pure P-and S-wave components.Therefore,the accuracy of the wave records simulated by the methods is subject to the accuracy of both the simulation algorithm and the wavefield decoupling algorithm.This paper derives the higher-order finite-diffe-rence scheme of the first-order velocity-dilatation-rotation elastic wave equation in three-dimensional staggered grid space and gives the corresponding stability conditions.The PML absorbing boundary conditions adapted to the equation are derived,and the forward modeling of the first-order velocity-dilatation-rotation elastic wave equation is realized.The physical meaning of each component in the simulation results is analyzed.The equation not only contains the vibration velocity vector of the particles but also explicitly includes the P-and S-wave vibration velocity vectors.Additionally,an volumetric strain and a rotation vector are also involved.Therefore,in addition to the three particle vibration velocity components,the decoupled P-and S-wave components can be obtained directly by the equation.This avoids the influence of the decoupling algorithm on decoupling accuracy,and model trials prove he validity and superiority of the proposed method.

关 键 词：一阶速度—胀缩—旋转弹性波方程 交错网格 正演模拟 有限差分 PML吸收边界条件 纵、横波分离 

分 类 号：P631[天文地球—地质矿产勘探]