1. State Key Laboratory of Shale Oil and Gas Enrichment Mechanisms and Effective Development, Beijing 100083, China; 2. SINOPEC Key Laboratory of Seismic Elastic Wave Technology, Beijing 100083, China; 3. Unconventional Petroleum Research Institute, China University of Petroleum (Beijing), Beijing 102249, China; 4. SINOPEC Petroleum Exploration and Production Research Institute, Beijing 100083 China
Abstract：According to the geometric relationship between the tilted symmetry axis of 3D TTI media and the observation coordinate system, the TTI media can be regarded as 3D VTI media through coordinate rotation. The wavefield decomposition method for VTI can be applied to TTI media. Therefore, on the basis of the 3D anisotropic elastic wave equation, this paper built a 3D VTI wavefield decomposition operator by solving the eigenvectors of the Christoffel equation. Then a 3D TTI decomposition operator is derived by coordinate rotation. Finally, the elastic wavefield decomposition of 3D TTI can be realized by Poisson’s equation. An improved fast algorithm is introduced to avoid solving Poisson’s equation directly. The derived decomposition operator is suitable for the complex 3D TTI media because it considers the varying elastic parameters and tilted symmetry axis with space. When the anisotropic parameters and tilted angle of the symmetry axis are zero，this operator can be degraded into isotropic form. Numerical results show the derived TTI operator can obtain more accurate decomposition results than isotropic or VTI operators, and efficiently realize 3D anisotropic vector elastic wave field decomposition.
CALDWELL J. Marine multicomponent seismology[J]. The Leading Edge，1999，18(11): 1274-1282.
[2]
GRANLI J，ARNTSEN B，SOLLID A，et al. Imaging through gas-filled sediments using marine shear-wave data[J]. Geophysics，1999，64(3): 668-677.
[3]
ZHAO Y，ZHANG H Z，YANG J D，et al. Reducing artifacts of elastic reverse time migration by the de-primary technique[J]. Geophysics，2018，83(6): S569-S577.
DENG F，MCMECHAN G A. Viscoelastic true-amplitude prestack reverse-time depth migration[J]. Geophysics，2008，73(4): S143-S155.
[6]
DU Q Z，GONG X F，ZHANG M Q，et al. 3D PS-wave imaging with elastic reverse-time migration[J]. Geophysics，2014，79(5): S173-S184.
[7]
张婧，张文栋，张铁强，等. 应用τ-p域矢量旋转的地震数据波场分离[J]. 石油地球物理勘探，2020，55(1): 46-56.ZHANG Jing，ZHANG Wendong，ZHANG Tieqiang，et al. Seismic wave field decomposition method based on vector rotation in τ-p domain[J]. Oil Geophysical Prospecting，2020，55(1): 46-56.
[8]
LU J，WANG Y，YAO C. Separating P- and S-waves in an affine coordinate system[J]. Journal of Geophysics and Engineering，2012，9(1): 12-18.
[9]
LU J，WANG Y，CHEN J Y，et al. P- and S-mode separation of three-component VSP data[J]. Exploration Geophysics，2019，50(4): 430-448.
[10]
杜文波，黄文凯，朱红涛，等. 台湾海峡西部海域沉积体系、地层架构与油气勘探前景[J]. 中国地质，2020，47(5): 1542-1553.DU Wenbo，HUANG Wenkai，ZHU Hongtao，et al. Sedimentary system，stratigraphic architecture and petroleum exploration prospect analysis in the western Taiwan Strait[J]. Geology in China，2020，47(5): 1542-1553.
[11]
MORSE P M，FESHBACH H. Methods of Theoretical Physics[M]. McGraw-Hill Book Co.，New York，1953.
[12]
SUN R，CHOW J，CHEN K J. Phase correction in separating P- and S-waves in elastic data[J]. Geophysics，2001，66(5): 1515-1518.
[13]
周熙焱，常旭，王一博，等. 基于纵横波解耦的三维弹性波逆时偏移[J]. 地球物理学报，2018，61(3): 1038-1052.ZHOU Xiyan，CHANG Xu，WANG Yibo，et al. 3D elastic reverse time migration based on P- and S-wave decoupling[J]. Chinese Journal of Geophysics，2018，61(3): 1038-1052.
[14]
THOMSEN L. Weak elastic anisotropy[J]. Geophysics，1986，51(10): 1954-1966.
[15]
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.
[16]
吴潇，刘洋，蔡晓慧. 弹性波波场分离方法对比及其在逆时偏移成像中的应用[J]. 石油地球物理勘探，2018，53(4): 710-721.WU Xiao，LIU Yang，CAI Xiaohui. Elastic wavefield separation methods and their applications in reverse time migration[J]. Oil Geophysical Prospecting，2018，53(4): 710-721.
[17]
DELLINGER J，ETGEN J. Wave-field separation in two-dimensional anisotropic media[J]. Geophysics，1990，55(7): 914-919.
[18]
YAN J，SAVA P. Elastic wave-mode separation for VTI media[J]. Geophysics，2009，74(5): WB19-WB32.
[19]
ZHANG Q S，MCMECHAN G A. 2D and 3D elastic wavefield vector decomposition in the wavenumber domain for VTI media[J]. Geophysics，2010，75(3): D13-D26.
[20]
CHENG J B，FOMEL S. Fast algorithms for elastic-wave-mode separation and vector decomposition using low-rank approximation for anisotropic media[C]. SEG Technical Program Expanded，Abstracts 2013，32: 991-997.
[21]
ZUO J H，NIU F L，LIU L，et al. 3D anisotropic P- and S-mode wavefields separation in 3D elastic reverse-time migration[J]. Surveys in Geophysics，2022，43(3): 673-701.
[22]
YAN J，SAVA P. Elastic wave mode separation for tilted transverse isotropic media[J]. Geophysical Prospecting，2012，60(1): 29-48.
[23]
YANG J D，ZHANG H Z，ZHAO Y，et al. Elastic wavefield separation in anisotropic media based on eigenform analysis and its application in reverse-time migration[J]. Geophysical Journal International，2019，217(2): 1290-1313.
[24]
ZHU H J. Elastic wavefield separation based on the Helmholtz decomposition[J]. Geophysics，2017，82(2): S173-S183.
[25]
ZHANG L L，LIU L，NIU F L，et al. A novel and efficient engine for P/S wave-mode vector decomposition for VTI elastic reverse time migration[J]. Geophysics，2022，87(4): S185-S207.
