张庆朝^1,2,,
朱国维^1,2,,,
何登科^1,2,
秦良³,
呼邦兵^1,2
1. 中国矿业大学(北京) 煤炭资源与安全开采国家重点实验室, 北京 100083
2. 中国矿业大学(北京) 地球科学与测绘工程学院, 北京 100083
3. 中交(天津)生态环保设计研究院有限公司, 天津 300461

基金项目: 国家重点研发计划项目"煤矿隐蔽致灾地质因素动态智能探测技术研究"（2018YFC0807801）


详细信息

作者简介: 张庆朝, 男, 1988年生, 在读博士研究生, 主要从事地震波正演与偏移成像研究.E-mail:yiuyiusiu@gmail.com

通讯作者: 朱国维, 男, 教授, 博导, 主要从事工程地质、工程物探、矿井物探等方面的教学和科研工作.E-mail:zhugwcumtb@126.com

中图分类号: P631

收稿日期:2018-09-02
修回日期:2019-07-05
上线日期:2019-11-05

A decoupled qP-wave and qSV-wave equation in TI media with arbitrary spatial oriented symmetry axis

ZHANG QingChao^1,2,,
ZHU GuoWei^1,2,,,
HE DengKe^1,2,
QIN Liang³,
HU BangBing^1,2
1. State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Beijing 100083, China
2. College of Geoscience and Surveying Engineering, China University of Mining and Technology, Beijing 100083, China
3. CCCC(Tianjin) Eco-Environmental Protection Design & Research Institute Co., Ltd., Tianjin 300461, China


More Information

Corresponding author: ZHU GuoWei,E-mail:zhugwcumtb@126.com

MSC: P631

--> Received Date: 02 September 2018
Revised Date: 05 July 2019
Available Online: 05 November 2019


摘要
摘要:由于构造运动等作用，TI介质对称轴往往沿空间任意方向分布，具有任意空间取向对称轴的TI（ATI）介质更符合实际地质情况.VTI介质与ATI介质的相速度在形式上具有一致性，VTI介质中地震波的相角对应ATI介质对称轴与地震波传播方向的夹角.本文基于Tsvankin的VTI介质精确相速度公式，利用TI介质对称轴和地震波传播方向上单位向量的数量积和向量积来计算ATI介质的精确相速度.根据弱各向异性假设，导出qP波和qSV波的近似相速度，分析了近似公式的误差，讨论总结了ATI介质qP波和qSV波的相速度特征.本文中的单位向量采用观测坐标系表示，通过相角关系，可以较为方便地由ATI介质近似相速度导出频散关系，然后借助傅里叶逆变换推导出时间-波数域qP波和qSV波解耦的波动方程.数值算例表明本文的波动方程是qP波和qSV波解耦的，波场计算结果稳定，未出现明显的数值频散，验证了本文方法的有效性.
关键词: TI介质/
qP-qSV波波动方程/
相速度/
伪谱法

Abstract:Due to the tectonic deformation and other geological factors,the symmetry axis direction of transversely isotropic media is arbitrary. Formally,the phase angle of plane waves travelling in VTI (transversely isotropic media with a vertical symmetry axis) media is consistent with the angle between the symmetry axis and the direction of plane waves travelling in ATI media. With the accurate phase velocity derived by Tsvankin in VTI media,we calculate the accurate phase velocity of quasi-P and quasi-SV waves for ATI media (transversely isotropic media with arbitrary spatial orientation symmetry axis) in terms of the dot product and cross product of the unit vectors of the symmetry axis and the direction of wave propagation. According to the weak anisotropy assumption and Taylor's formula,we derive the approximate formulas of phase velocity of qP- and qSV-waves. The errors of the approximate formulas are analyzed. The phase velocity characteristics of qP-wave and qSV-wave in ATI media are discussed. The unit vectors are represented by the observational coordinate system. Based on the approximate phase velocity formulas of ATI media,the decoupled qP and qSV-wave equations in the time-wavenumber domain are derived with the phase angle relations by using inverse Fourier transform. Numerical examples demonstrate that the qP and qSV wavefields are decoupled and stable without obvious numerical dispersion,showing the validity of the method proposed in this study.
Key words:TI media/
qP-qSV wave equations/
Phase velocity/
Pseudo-spectral method



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