A linear traveltime interpolation method with hybrid meshes for VTI medium under rugged interface conditions
(2.China National Aviation Fuel Northwest China Company, Xi’an, Shaanxi , China 710082)
【Abstract】In order to calculate the seismic wave traveltime in VTI medium under rugged interface conditions, we divide a model with a hybrid mesh composed by rectangular meshes and irregular quadrilateral meshes to better fit rugged interface conditions. In the hybrid mesh, the relationship between group velocity and group angle is transformed into the relationship between group velocity and interpolated point coordinates to find the local traveltime. Then with the multi-stage multi-step calculation technique, the ray tracing algorithm is extended to VTI medium to realize the traveltime calculation of seismic waves (first arrival, reflection, multiple reflection, multiple transmission conversion, and multiple reflection conversion) in VTI medium. Compared with the irregular cell shortest path method, the numerical simulations show that the proposed algorithm is more accurate and can better adapt the complex-structure models.
【Keywords】 vertical transverse isotropic ; ray tracing ; rugged interface ; hybrid mesh ; seismic wave traveltime ;
 Tsvankin I. Seismic Signatures and Analysis of Reflection Data in Anisotropic Media. Elsevier, 2001.
 Charles S. Data-driven tomographic velocity analysis in tilted transversely isotropic media: A 3D case history from the Canadian Foothills. Geophysics, 2008, 73 (5): VE261–VE268.
 Thomsen L. Weak elastic anisotropy. Geophysics, 1986, 51 (10): 1954–1966.
 Sena A G. Seismic traveltime equations for azimuthally anisotropic and isotropic media: Estimation of interval elastic properties. Geophysics, 1991, 56 (12): 2090–2101.
 Faria E L and Stoffa P L. Traveltime computation in transversely isotropic media. Geophysics, 1994, 59 (2): 272–281.
 Deng Huaiqun, Liu Wenlin. Computation of seismic travel times in transversely isotropic medium. OGP, 2000, 35 (4): 508–516 (in Chinese with English abstract).
 Alkhalifah T. Traveltime computation with the linea-rized eikonal equation for anisotropic media. Geophysical Prospecting, 2002, 50 (4): 373–382.
 Zhou B, Greenhalgh S A. “Shortest path” ray tracing for most general 2D/3D anisotropic media. Journal of Geophysics & Engineering, 2005, 2 (1): 54–63.
 Zhao Aihua, Zhang Meigen, Ding Zhifeng. Seismic traveltime computation for transversely isotropy media. Chinese Journal of Geophysics, 2006, 49 (6): 1762–1769 (in Chinese with English abstract).
 Ma Detang, Zhu Guangming. Computation of traveltime of seismic first breaks in transversely isotropic medium. OGP, 2006, 41 (1): 26–31 (in Chinese with English abstract).
 Li Jianguo, Li Yanpeng, Guo Xiaoling. VTI media test-firing ray tracing. OGP, 2010, 45 (4): 491–496 (in Chinese with English abstract).
 Ma Detang, Zhu Guangming, Fan Tingen. A search algorithm for first break traveltime in 2D TTI medium. OGP, 2011, 46 (5): 710–714 (in Chinese with English abstract).
 Bai Haijun, Sun Zandong, Wang Xuejun. Ray tracing in TTI media using wavefront construction. OGP, 2011, 46 (S1): 1–6 (in Chinese with English abstract).
 Li Xiaoling, Bai Chaoying, Hu Guangyi. Multiple ray tracing in an undulated layered TI media. OGP, 2013, 48 (6): 924–931 (in Chinese with English abstract).
 Farra V. Ray tracing in complex media. Journal of Applied Geophysics, 1993, 30 (1–2): 55–73.
 Berryman J G. Long-wave elastic anisotropy in transversely isotropy media. Geophysics, 1979, 44 (5): 896–917.
 Li Qingchun, Ye Pei. Joint tomography of first break and reflection traveltime with multi-scale netsize method. OGP, 2013, 48 (4): 536–544 (in Chinese with English abstract).
 Li Yongbo, Li Qingchun, Wu Qiong et al. Improved fast marching method for higher calculation accuracy and efficiency of traveltime. OGP, 2016, 51 (3): 467–473 (in Chinese with English abstract).
 Ye Pei, Li Qingchun. Improvements of linear traveltime interpolation ray tracing for the accuracy and efficiency. Journal of Jilin University (Earth Science Edition), 2013, 43 (1): 291–298 (in Chinese with English abstract).
 Qin Ning, Wang Yanguang, Yang Xiaodong et al. Gaussian bean prestack depth migration for undulating-surface area in piedmont zone. OGP, 2017, 52 (1): 81–86 (in Chinese with English abstract).
 Huang Guojiao, Bai Chaoying. Simultaneous inversion with multiple traveltime within 2-D complex layered media. Chinese Journal of Geophysics, 2010, 53 (12): 2972–2981 (in Chinese with English abstract).
 Asakawa E, Kawanaka T. Seismic ray tracing using linear traveltime interpolation. Geophysics Prospecting, 1993, 41 (4): 99–111.
 Li X G, Uirych T J. LTI formulations and application to curved wavefronts. Journal of Seismic Exploration, 1993, 2 (1): 239–246.
Zhao Gaishan, Hao Shouling. Seismic ray tracing algorithm based on the linear traveltime interpolation. GPP, 1998, 32 (2): 14–24 (in Chinese with English abstract).
 Cardarelli E and Cerreto A. Ray tracing in elliptical anisotropic media using the linear traveltime interpolation (LTI) method applied to traveltime seismic tomography. Geophysical Prospecting, 2002, 50 (1): 55–72.
 Nie Jianxin, Yang Huizhu. Quadrarical linear travel time interpolation of seismic ray-tracing. Journal of Tsinghua University, 2003, 43 (11): 1495–1498 (in Chinese with English abstract).
 Kumar D, Sen M K, Ferguson R J. Traveltime calculation and prestack depth migration in tilted transversely isotropic media. Geophysics, 2004, 69 (1): 37–44.
 Zhang Saimin, Zhou Zhusheng, Chen Lingjun et al. Seismic ray tracing method of applying parabolic interpolation to travel time. Progress in Geophysics, 2007, 22 (1): 43–48 (in Chinese with English abstract).
 Zhang Dong, Xie Baolian, Yang Yan et al. A ray tracing method based on improved linear traveltime interpolation. Chinese Journal of Geophysics, 2009, 52 (1): 200–205 (in Chinese with English abstract).
 Zhang Dong, Fu Xiangru, Yang Yan et al. 3-D seismic ray tracing algorithm based on LTI and partition of grid interface. Chinese Journal of Geophysics, 2009, 52 (9): 2370–2376 (in Chinese with English abstract).
 Byun B S, Corrigan D and Gaiser J E. Anisotropicvelocity analysis for lithology discrimination. Geophysics, 1989, 54 (12): 1564–1574.
 Zhao Aihua, Ding Zhifeng. New approximate expressions of seismic group velocities for weakly anisotropic media. Progress in Geophysics, 2005, 20 (4): 916–919 (in Chinese with English abstract).
 Wu Guochen, Liang Kai, Qi Yanping. Phase velocity and group velocity in 3D TTI media. Progress in Geophysics, 2009, 24 (6): 2097–2105 (in Chinese with English abstract).
 Zhao Rui, Bai Chaoying. Fast multiple ray tracing within complex layered media: the shortest path method based on irregular grid cells. Acta Seismologica Sinica, 2010, 32 (4): 433–444 (in Chinese with English abstract).