摘要
地震波传播的精确表达式能够精确表达地震波在介质中的传播特征,但由于表达式较复杂,为一些参数隐性表达式,这不利于参数反演,因此有必要研究其近似的线性表达式,以便进行参数反演,准确探测地层结构。在扰动法求解Christoffel方程,得到弱各向异性条件下qP、qS相速度、群速度近似表达式的基础上,依据介质模型坐标与观测坐标,各种介质弹性系数矩阵关系式推导出裂隙介质中地震波相速度、偏振向量及群速度的近似表达。数值计算结果表明,当各向异性系数在0.3以内时,对一般裂隙各向异性介质都适用,且具有较高的精度,在各向异性系数大于0.3时,纵波(P波)仍然具有较高的精度,但横波(S波)的误差增大到50%,主要是因为扰动解是在弱各向异性条件下推导的,因此在介质各向异性系数较小的情况下,为地震波速度分析及参数反演奠定了基础。
The precise expression of seismic wave propagation can accurately express the propagation characteristics of seismic waves in the medium.Because the expression is complicated and it’s implicit expression of some parameters,which is not conducive to parameter inversion,so it is necessary to study its approximate linear expression.The study helps to perform parameter inversion and accurately detect stratigraphic structure.Based on the solution of the Christoffel equation by the perturbation method,the approximate expressions of the phase and group velocities of qP and qS wave under weak anisotropy in extreme anisotropic media were obtained firstly.Based on the relation sheep between media coordinates and observation coordinates,and relations between the elasticity matrix of various media,approximate expressions of seismic wave phase velocity,polarization vector,and group velocity in fractured media were derived then.The numerical calculation results show that when the anisotropy coefficient is within 0.3,it is suitable for general fracture anisotropic media and has high accuracy.When the anisotropy coefficient is greater than 0.3,the P wave still has high accuracy.However,the error of the S wave increases to 50%,mainly because the perturbation solution is derived under weakly anisotropic conditions.Therefore,when the medium anisotropy coefficient is small,it lays the groundwork for seismic wave velocity analysis and parameter inversion.
作者
何现启
彭凌星
朱自强
鲁光银
HE Xian-qi;PENG Ling-xing;ZHU Zi-qiang;LU Guang-yin(Hunan Provincial Communications Planning, Survey & Design Institute Co., Ltd., Changsha 410200, China;School of Geosciences and Info Physics, Central South University, Changsha 410083, China)
出处
《科学技术与工程》
北大核心
2020年第22期8868-8874,共7页
Science Technology and Engineering
基金
国家自然科学基金(41374120)。
关键词
裂隙介质
地震波
传播特征
相速度
fracture media
seismic wave
propagation characteristics
phase velocity
