摘要 基于泰勒级数的P波旅行时方程的计算精度受到具有垂直对称轴的横向各向同性（Transverse Isotropy Medium with Vertical Symmetry Axis，VTI）介质的影响，为了改善这种情况，提出一种基于平方处理与系数匹配的计算方法。首先，利用平方处理将非平方形式的基于泰勒级数的旅行时公式转换为包含高阶项的平方形式；再使用系数匹配法处理旅行时平方公式的高阶项，保持方程炮检距的最高阶为常用的4阶；然后，在简化参数形式与优化旅行时平方公式计算的基础上，得到与各向异性参数相关的新系数y；最后，形成了含有y的基于平方处理与系数匹配的4阶P波旅行时计算方法。基于水平层状VTI介质模型的实验结果表明，与有理近似算法、三射线广义时差近似计算法和扩展广义时差计算法相比，该方法计算误差更小，同时远炮检距处的计算能力得到一定提高，从而给以旅行时方程为基础的应用提供了更多选择。
Abstract：The calculation accuracy of P-wave traveltime equations based on the Taylor series is affected by the transverse isotropy medium with vertical symmetry axis(VTI). In order to improve this situation, a calculation method based on square processing and coefficient matching is proposed. In this method, the square processing is used to transform the traveltime equation of the non-square form based on the Taylor series into the square form containing high-order terms, and then the coefficient matching method is used to deal with the high-order terms of the traveltime square equation so that the highest order of the equation offset is the commonly used fourth order. Then, on the basis of simplifying the form of parameters and optimizing the traveltime square equation, a new coefficient y, which is related to the anisotropic parameter, is obtained. Finally, a fourth-order P-wave traveltime calculation method with y based on square processing and coefficient matching is formed. The experimental results based on the horizontally layered VTI medium model show that compared with the rational approximation method, the generalized moveout approximation method based on three rays, and the extended generalized moveout approximation method, this method has smaller errors, and the calculation ability at the far offset is improved to some extent, which provides more options for the applications based on traveltime equations.
ABEDI M M, STOVAS A. Extended generalized nonhyperbolic moveout approximation[J]. Geophysical Journal International, 2019, 216(2):1428-1440.
[2]
樊中海, 胡渤, 宋吉杰, 等. 地震反演储层描述精度影响因素分析[J]. 石油地球物理勘探, 2022, 57(2):441-451.FAN Zhonghai, HU Bo, SONG Jijie, et al. Analysis of influencing factors in reservoir description accuracy by seismic inversion[J]. Oil Geophysical Prospecting, 2022, 57(2):441-451.
[3]
蔡志东, 王世成, 韦永祥, 等. VSP波场研究与应用现状[J]. 石油物探, 2021, 60(1):81-91.CAI Zhidong, WANG Shicheng, WEI Yongxiang, et al. Research and application status of VSP wavefields[J]. Geophysical Prospecting for Petroleum, 2021, 60(1):81-91.
[4]
TANER M T, KOEHLER F. Velocity spectra-digital computer derivation and applications of velocity functions[J]. Geophysics, 1969, 34(6):859-881.
[5]
MAY B T, STRALEY D K. Higher-order moveout spectra[J]. Geophysics, 1979, 44(7):1193-1207.
[6]
ALKHALIFAH T, TSVANKIN I. Velocity analysis for transversely isotropic media[J]. Geophysics, 1995, 60(5):1550-1566.
[7]
胡中平. 优化6次项NMO校正方法研究[J]. 石油地球物理勘探, 2003, 38(6):603-607.HU Zhongping. Study of NMO correction method by optimized sixth-order term[J]. Oil Geophysical Prospecting, 2003, 38(6):603-607.
[8]
STOVAS A, URSIN B. New travel-time approximations for a transversely isotropic medium[J]. Journal of Geophysics and Engineering, 2004, 1(2):128-133.
[9]
URSIN B, STOVAS A. Traveltime approximations for a layered transversely isotropic medium[J]. Geophysics, 2006, 71(2):D23-D33.
[10]
SONG H, ZHANG J, YAO Z. Normal moveout for long offset in isotropic media using the Padé approximation[J]. Applied Geophysics, 2016, 13(4):658-666.
[11]
邓怀群, 刘雯林. 横向各向同性介质中地震波旅行时的计算[J]. 石油地球物理勘探, 2000, 35(4):508-516.DENG Huaiqun, LIU Wenlin. Computation of seismic travel times in transversely isotropic medium[J]. Oil Geophysical Prospecting, 2000, 35(4):508-516.
[12]
SONG H, GAO Y, ZHANG J, et al. Long-offset moveout for VTI using Padé approximation[J]. Geophysics, 2016, 81(5):C219-C227.
[13]
SRIPANICH Y, FOMEL S, STOVAS A, et al. 3D generalized nonhyperboloidal moveout approximation[J]. Geophysics, 2017, 82(2):C49-C59.
[14]
XU S, STOVAS A, MIKADA H. Traveltime and relative geometric spreading approximation in elastic orthorhombic medium[J]. Geophysics, 2020, 85(5):C153C162.
[15]
ABEDI M M, STOVAS A. A new parameterization for generalized moveout approximation, based on three rays[J]. Geophysical Prospecting, 2019, 67(5):1243-1255.
[16]
BLIAS E. VSP extension of the generalized FomelStovas approximation[C]. SEG Technical Program Expanded Abstracts, 2012, 31:1-5.
[17]
ABEDI M M, RIAHI M A, STOVAS A. Threeparameter normal moveout correction in layered anisotropic media:a stretch-free approach[J]. Geophysics, 2019, 84(3):C129-C142.
[18]
ABEDI M M. Rational approximation of P-wave kinematics-part 1:transversely isotropic media[J]. Geophysics, 2020, 85(5):C163-C173.
[19]
FARRA V, PŠENČÍK I. P-wave reflection-moveout approximation for horizontally layered media of arbitrary moderate anisotropy[J]. Geophysics, 2020, 85(2):C61-C70.
[20]
ABEDI M M, PARDO D. Large-offset P-wave traveltime in layered transversely isotropic media[J]. Geophysics, 2021, 86(3):C65-C74.
[21]
魏建, 孙祥娥. VTI介质中基于降阶补偿处理的旅行时计算方法[J]. 山东科技大学学报(自然科学版), 2022, 41(1):86-91.WEI Jian, SUN Xiang'e. A method of traveltime calculation based on descending order compensation processing in VTI medium[J]. Journal of Shandong University of Science and Technology (Natural Science), 2022, 41(1):86-91.
[22]
STOVAS A, URSIN B. Improved geometricspreading approximation in layered transversely isotropic media[J]. Geophysics, 2009, 74(5):D85-D95.
[23]
BANIK N C. An effective anisotropy parameter in transversely isotropic media[J]. Geophysics, 1987, 52(12):1654-1664.
[24]
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 layered TI media with dipping interfaces[J]. Oil Geophysical Prospecting, 2022, 57(1):111-117.
[25]
陈占国, 曾昭翰, 杨心超. 基于VSP数据的任意弱各向异性参数反演方法[J]. 石油地球物理勘探, 2022, 57(2):311-319.CHEN Zhanguo, ZENG Zhaohan, YANG Xinchao. An inversion method for arbitrary weak anisotropy parameters based on VSP data[J]. Oil Geophysical Prospecting, 2022, 57(2):311-319.
[26]
杨飞龙, 任广莹, 姚凤鸣, 等. 井间地震逆菲涅尔束叠加成像及其应用[C]. 2022年中国石油物探学术年会论文集(下册), 2022, 207-210.YANG Feilong, REN Guangying, YAO Fengming, et al. Inverse fresnel beam stack imaging of cross-well seismic and its application[C]. Proceedings of the 2022 China Petroleum Geophysical Exploration Academic Annual Conference (Volume 2), 2022, 207-210.
[27]
秦宁. 弹性波各向异性高斯束逆时偏移[J]. 石油物探, 2022, 61(2):321-328.QIN Ning. Elastic reverse time migration with Gaussian beams in anisotropic media[J]. Geophysical Prospecting for Petroleum, 2022, 61(2):321-328.
[28]
秦宁, 王常波, 梁鸿贤, 等. 一次波和层间多次波联合成像方法[J]. 石油地球物理勘探, 2022, 57(6):1375-1383.QIN Ning, WANG Changbo, LIANG Hongxian, et al. Joint imaging method of primaries and internal multiples[J]. Oil Geophysical Prospecting, 2022, 57(6):1375-1383.
