摘要
各向异性和黏滞性在地球介质中广泛存在,会对地震波的运动学和动力学特征产生影响,因此研究地震波在地下空间中传播时应该对其予以充分考虑.现有的各向异性波场外推方法主要采用基于声学近似的伪声波方程,该类方程在非声学假设条件下容易出现伪横波污染及传播不稳定.针对此问题,本文应用优化方案对原始的耦合各向异性纯声波频散关系式进行近似展开,进而发展了针对三维TI(横向各向同性)介质和OA(正交各向异性)介质的优化纯声波方程,结合有限差分和泊松算法对其进行了有效求解.同时,考虑到介质对地震波的吸收衰减效应,本文结合发展的纯声波方程和标准线性体模型,推导了黏滞各向异性优化纯声波方程.相速度分析表明优化方案能够产生高精度近似结果.数值模型算例证明优化黏滞纯声波方程在产生精确稳定P波响应的前提下,能够有效模拟各向异性介质中纯声波的振幅衰减和相位频散.整体而言,本文推导的方程能够为各向异性衰减介质成像和反演提供有效帮助.
The anisotropy and viscosity are widely existed in earth media,which affect the kinematic and dynamic characteristics during seismic wave propagation.Therefore,it should be taken into full consideration when studying the propagation of seismic wave in underground media.The existing anisotropic wavefield extrapolation methods mainly use pseudo-acoustic wave equations based on the acoustic approximation,which are easy to encounter pseudo-shear wave pollution and instability when the medium parameters can't meet approximated conditions.To address this problem,this paper applies an optimization scheme to expand the original coupled anisotropic pure acoustic wave dispersion relation,and then Proposes Optimized Pure Acoustic Wave Equations(PAWEs)in 3D TI(Transversely Isotropy)and OA(Orthorhombic Anisotropy)media.The derived PAWEs are computed by combining finite-difference and Poisson solver effectively.Meanwhile,considering the absorption and attenuation effect of underground media,the Viscous Anisotropic PAWEs(VAPAWEs)are exploited by combining the developed PAWEs and standard linear solid model.Phase velocity analysis indicates that the optimized scheme can produce high accuracy approximated results.Several numerical examples demonstrate that the proposed VAPAWEs can produce accurate and stable P-wave response,and availably simulate the amplitude loss and phase dispersion of pure acoustic wave.In conclusion,the proposed equations can provide effective assistances for seismic imaging and inversion in anisotropic attenuation media.
作者
包乾宗
谭崔文
BAO QianZong;TAN CuiWen(Chang'an University,School of Geological Engineering and Geomatics,Department of Geophysics,Xi'an 710054,China;National Engineering Research Center of Offshore Oil and Gas Exploration,Beijing 100028,China)
出处
《地球物理学报》
SCIE
EI
CAS
CSCD
北大核心
2024年第6期2415-2428,共14页
Chinese Journal of Geophysics
基金
国家重点研发计划项目(2021YFA0716902)资助。
关键词
各向异性
黏滞性
波动方程
数值模拟
Anisotropy
Attenuation
Wave equation
Numerical modeling
