Seismic ray tracing for multiple reflected qP wave in tilted orthorhombic anisotropic media
WANG Di1, WU Xiang1, BAI Chaoying1,2,3, LI Xingwang1,2,3
1. School of Geological Engineering and Geomatics, Chang'an University, Xi'an, Shaanxi 710054, China; 2. Institute of Computing Geophysics, Chang'an University, Xi'an, Shaanxi 710054, China; 3. National Engineering Research Center of Offshore Oil and Gas Exploration, Beijing 100028, China
Abstract：Due to the existence of fractures，the orthorhombic anisotropic characteristics are often observed in actual strata. To determine the traveltime and ray paths of qP wave in orthorhombic anisotropic media，this paper firstly calculates the phase and group velocities of qP wave based on Christoffel equation，and the group velocity distribution of the tilted orthorhombic media is obtained by using rotation matrix. Then based on the multistage scheme incorporating the modified shortest-path method，an algorithm for tracing multiples in the tilted orthorhombic media is proposed. The computational amount for calculating the group velocity distribution can be saved to about half by introducing the spherical triangulation algorithm to determine the sampling points of phase direction which are approximately uniformly distributed. In addition，GPU parallel computing technology can further improve computational efficiency. This algorithm can be applied to direct，reflected，and multiple reflected waves，and the traveltime calculation relative error does not exceed 0.35%. The results of efficiency analysis show that the calculation of the group velocity distribution is time-consuming，which accounts for about 61% of the total time in the serial program. With the GPU parallel technology，the computing efficiency has been improved by nearly 30 times.
ČERVENÝ V.Seismic rays and ray intensities in inhomogeneous anisotropic media[J].Geophysical Journal of Royal Astronomic Society，1972，29(1)： 1-13.
[2]
TSVANKIN I，GAISER J，GRECHKA V，et al.Seismic anisotropy in exploration and reservoir characte-rization：An overview[J].Geophysics，2010，75(5)：75A15-75A29.
[3]
凌云，郭向宇，孙祥娥，等.地震勘探中的各向异性影响问题研究[J].石油地球物理勘探，2010，45(4)：606-623.LING Yun，GUO Xiangyu，SUN Xiang’e，et al.Stu-dies on the influence of anisotropy in seismic exploration[J].Oil Geophysical Prospecting，2010，45(4)：606-623.
[4]
POSTMA G W.Wave propagation in a stratified medium[J].Geophysics，1955，20(4)：780-806.
ZHANG L，ZHOU B.Calculation of slowness vectors from ray directions for qP-，qSV-，and qSH-waves in tilted transversely isotropic media[J].Geophysics，2018，83(4)：C153-C160.
[7]
孙上饶，梁锴，印兴耀，等.三维TTI介质弹性波相、群速度的近似配方表征法[J].石油地球物理勘探，2021，56(3)：496-504，518.SUN Shangrao，LIANG Kai，YIN Xingyao，et al.Approximate 3D phase and group velocities for elastic wave in TTI media based on an approximate match method[J].Oil Geophysical Prospecting，2021，56(3)： 496-504，518.
[8]
ZHOU B，GREENHALGH S A.“Shortest path” ray tracing for most general 2D/3D anisotropic media[J].Journal of Geophysics and Engineering，2005，2(1)：54-63.
[9]
张建中，安全，于建明，等.倾斜层状TI介质反射波旅行时快速计算[J].石油地球物理勘探，2022，57(1)：111-117.ZHANG Jianzhong，AN Quan，Yu Jianming，et al.Rapid calculation of reflected wave travel time in la-yered TI media with dipping interfaces[J].Oil Geophysical Prospecting，2022，57(1)：111-117.
[10]
BAKULIN A，GRECHKA V，TSVANKIN I.Stimation of fracture parameters from reflection seismic data—Part II：Fractured models with orthorhombic symmetry[J].Geophysics，2000，65(6)：1803-1817.
[11]
STOVAS A.Azimuthally dependent kinematic pro-perties of orthorhombic media[J].Geophysics，2015，80(6)：C107-C122.
[12]
SONG L，EVERY A G.Approximate formulae for acoustic wave group slownesses in weakly orthorhom-bic media[J].Journal of Physics D：Applied Physics，2000，33(17)：L81-L85.
[13]
ALKHALIFAH T.An acoustic wave equation for orthorhombic anisotropy[J].Geophysics，2003，68(4)：1169-1172.
[14]
ABEDI M M，STOVAS A，IVANOV Y.Acoustic wave propagation in orthorhombic media：Phase velo-city，group velocity，and moveout approximations[J].Geophysics，2019，84(6)：C269-C279.
[15]
TSVANKIN I.Anisotropic parameters and P-wave velocity for orthorhombic media[J].Geophysics，1997，62(4)：1292-1309.
[16]
HAO Q，STOVAS A.P-wave slowness surface approximation for tilted orthorhombic media[J].Geophysics，2016，81(3)：C99-C112.
[17]
MENSCH T，FARRA V.Computation of qP-wave rays，traveltimes and slowness vectors in orthorhombic media[J].Geophysical Journal International，1999，138(1)：244-256.
[18]
PŠENÍK I，FARRA V.First-order ray tracing for qP waves in inhomogeneous，weakly anisotropic media[J].Geophysics，2005，70(6)：D65-D75.
[19]
IBANEZ-JACOME W，ALKHALIFAH T，WAHEED U B.Effective orthorhombic anisotropic mo-dels for wavefield extrapolation[J].Geophysical Journal International，2014，198(3)：1653-1661.
[20]
BLIAS E.Fast P-wave raytracing in 3D layered orthorhombic model[C].Extended Abstracts of 76th EAGE Conference & Exhibition，2014，1-5.
[21]
BLIAS E，HUGHES B.Fast P-wave ray tracing in a 3D model with dipping orthorhombic layers[C].SEG Technical Program Expanded Abstracts，2015，34：5620-5624.
[22]
MASMOUDI N，ALKHALIFAH T.Traveltime approximations and parameter estimation for orthorhombic media[J].Geophysics，2016，81(4)：C127-C137.
[23]
卢明辉，唐建侯，杨慧珠，等.正交各向异性介质P波走时分析及Thomsen参数反演[J].地球物理学报，2005，48(5)：1167-1171.LU Minghui，TANG Jianhou，YANG Huizhu，et al.P wave traveltime analysis and Thomsen parameters inversion in orthorhombic media[J].Chinese Journal of Geophysics，2005，48(5)：1167-1171.
[24]
ABEDI M M，STOVAS A.A new acoustic assumption for orthorhombic media[J].Geophysical Journal International，2020，223(2)：1118-1129.
[25]
GOODCHILD M F，YANG S R.A hierarchical spatial data structure for global geographic information systems[J].CVGIP：Graphical Models and Image Processing，1992，54(1)：31-44.
[26]
BAI C，LI X，TANG X.Seismic wavefront evolution of multiply reflected，transmitted，and converted phases in 2D/3D triangular cell model[J].Journal of Seismology，2011，15(4)：637-652.
[27]
MOSER T J.Shortest path calculation of seismic rays[J].Geophysics，1991，56(1)：59-67.
[28]
唐小平，白超英.最短路径算法下三维层状介质中多次波追踪[J].地球物理学报，2009，52(10)：2635-2643.TANG Xiaoping，BAI Chaoying.Multiple ray tracing within 3-D layered media with the shortest path me-thod[J].Chinese Journal of Geophysics，2009，52(10)：2635-2643.
[29]
SCHOENBERG M，HELBIG K.Orthorhombic media：Modeling elastic wave behavior in a vertically fractured earth[J].Geophysics，1997，62(6)：1954-1974.
[30]
VAVRYUK V.Asymptotic Green’s function in homogeneous anisotropic viscoelastic media[J].Proceedings of the Royal Society A：Mathematical, Phy-sical and Engineering Sciences，2007，463(1)：2689-2707.
