矩形/长方体网格单元时间高阶有限差分波场数值模拟  

Seismic wavefield numerical simulation by temporal high-order finite difference method based on rectangular/cuboid grid elements

作　　者：徐世刚 黄兴国 韩丽 包乾宗[1,2] 任志明 XU Shigang;HUANG Xingguo;HAN Li;BAO Qianzong;REN Zhiming(Department of Geophysics,School of Geological Engineering and Geomatics,Chang’an University,Xi’an,Shaanxi 710054,China;National Engineering Research Center of Offshore Oil and Gas Exploration,Beijing 100028,China;College of Instrumentation and Electrical Engineering,Jilin University,Changchun,Jilin 130061,China)

机构地区：[1]长安大学地质工程与测绘学院地球物理系,陕西西安710054 [2]海洋油气勘探国家工程研究中心,北京100028 [3]吉林大学仪器科学与电气工程学院,吉林长春130061

出　　处：《石油地球物理勘探》2024年第5期976-988,共13页Oil Geophysical Prospecting

基　　金：国家重点研发计划项目“高铁地震学研究与应用示范”(2021YFA0716902);国家自然科学基金项目“基于高精度时空域有限差分的正交各向异性弹性波数值模拟新方法研究”(42004119)联合资助。

摘　　要：有限差分法在求解不同类型地震波动方程中广泛应用,提高有限差分在时间域和空间域的地震波场数值模拟精度十分重要。为了提高现有时间—空间域高阶差分方法的精度和灵活性,提出了基于矩形/长方体网格单元的改进时间—空间高阶有限差分方案,分别求解二维和三维声波方程。改进差分法主要通过联合旁轴网格节点和传统轴向节点来共同完成偏导数近似,进一步结合平面波理论和泰勒级数展开求取改进模板中的高阶差分系数。数值精度分析表明,改进差分方案相较于传统方法具有更高的数值精度和稳定性。多个模型算例表明,在相同参数条件下,改进差分方法在兼顾空间模拟精度的前提下能够提高时间模拟精度。此外,改进模板沿不同空间方向可以选用不同的网格步长,有效增加了波场模拟的灵活性,能够为后续的地震成像和反演提供有效波场延拓工具。The finite difference(FD)method is widely used to solve different types of seismic wave equations.It’s crucial to simultaneously improve the FD accuracy for seismic wavefield simulation in the temporal domain and the spatial domain.To promote the accuracy and flexibility of the existing high‐order FD method in the spatiotempral domain,this paper proposes an improved spatio‐tempral high‐order FD method based on rectangular/cuboid grid elements and solves the 2D and 3D acoustic equations,respectively.The improved FD method combines off‐axis grid nodes and traditional axial nodes to jointly approximate partial derivatives and further applies plane wave theory and Taylor series expansion method to compute the high‐order FD coefficients of the improved stencils.Numerical accuracy analysis indicates that the improved FD method presents higher numerical accuracy and stability than the traditional one.Several computational examples by models demonstrate that under the identical conditions of model parameters,the proposed FD method can generate higher temporal‐domain simulation accuracy while keeping satisfactory spatial‐domain simulation accuracy.In addition,the improved stencil can adopt different grid spacing along different spatial directions,which effectively increases the flexibility of wavefield simulation and can provide an effective wavefield extrapolation tool for seismic imaging and inversion.

关 键 词：地震波动方程 正演模拟 高阶有限差分 矩形/长方体网格 差分系数 

分 类 号：P631[天文地球—地质矿产勘探]