Vector prestack depth migration based on Kirchhoff integral equation
(2.Geophysical Research and Development Department, BGP Inc., CNPC, Zhuozhou, Hebei, China 072750)
【Abstract】Conventional Kirchhoff integral migrations lead to inaccurate multi-component seismic imaging and cannot preserve true amplitude due to the scalar acoustic wave equation basis. In this paper, we put forward a vector prestack depth migration based on Kirchhoff integral equation. First we deduce Kirchhoff integral vector migration formula based on multi-component seismic vector field and homogeneous isotropic elastic wave equation. Then we apply it to the prestack depth migration of multi-component seismic data. Using wave equation vector characteristics, we recover leaked seismic information PP- and PS-wave components in the migration, and achieve PP- and PS-wave separations. The tests on 2D numerical model and real data prove that the proposed method can eliminate the mode leak and increase the imaging accuracy.
【Keywords】 prestack depth migration; Kirchhoff integral; vector; multi-component;
 Lu J, Wang Y and Yao C. Separating P- and S-waves in an affine coordinate system. Journal of Geophysics and Engineering, 2012, 9 (1): 12–18.
 Dellinger J and Etgen J. Wave-field separation in twodimensional anisotropic media. Geophysics, 1990, 55 (7): 914–919.
 Yan J, Sava P. 3D elastic wave mode separation for TTI media. SEG Technical Program Expanded Abstracts, 2009, 28: 4 292–4 298.
 Wang Zhiyang, Liu Hong. Separation of elastic wave mode based on improved interpolation algorithm. Near-Surface Asia Pacific Conference, Waikoloa, Hawaii, 2015: 108–112.
 Lou M, Campbell M, Cheng D et al. An improved parametric inversion methodology to separate P and SV wavefields from VSP data. SEG Technical Program Expanded Abstracts, 2013, 32: 5 087–5 091.
 Ma Jianqing, Li Qingchun. Seismic surface wave suppression with polarization filtering method in timefrequency domain. OGP, 2015, 50 (6): 1 089–1 097 (in Chinese).
 Cheng Bingjie, Hu Zhiquan, Xu Tianji et al. Polarization filtering constrained by classified energy in the wavelet domain. OGP, 2015, 50 (5): 815–823 (in Chinese).
 He Yinjuan, Li Wen, Liu Baojin et al. An improved vector resolution noise removal approach. OGP, 2015, 50 (2): 243–253 (in Chinese).
 Foster D J, Mosher C C. Suppression of multiple reflections using the Radon Transform. Geophysics, 1992, 57 (3): 386–395.
 Zhou B, Greeenhalgh S A. Linear and parabolic transform. Geophysics, 1994, 59 (7): 1 133–1 149.
 Huang Xinwu, Wu Lü, Song Wei. 3-D pre-stack depth migration with Radon projection. Chinese Journal of Geophysics, 2004, 47 (2): 321–326 (in Chinese).
 Guo Peng, He Bingshou, Shen Jiqian. Space domain algorithm of elastic wave-field decomposition in VTI media. OGP, 2013, 48 (4): 567–575 (in Chinese).
 Xue Yaru, Tang Huanhuan, Chen Xiaohong. Seismic data reconstruction based on high order high resolution Radon transform. OGP, 2014, 49 (1): 95–100 (in Chinese).
 Wei Shilei, Zhang Dazhou, Li Mingzhi et al. Wave field separation operator characteristics in the VTI media. OGP, 2016, 51 (3): 506–512 (in Chinese).
 Du Qizhen, Qin Tong. Multicomponent prestack reverse-time migration of elastic waves in transverse isotropic medium. Chinese Journal of Geophysics, 2009, 52 (3): 801–807 (in Chinese).
 Li Zhenchun, Yong Peng, Huang Jianping et al. Elastic wave reverse time migration based on vector wavefield separation. Journal of China University of Petroleum (Edition of Natural Science), 2016, 40 (1): 42–48 (in Chinese).
 Kuo J T, Dai Tingfan. Kirchhoff elastic wave migration for the case of noncoincident source and receiver. Geophysics, 1984, 49 (8): 1 223–1 238.
 Pao Y H, Vararharajulu V. Huygens’s principle radiation conditions and integral formulas for the scattering of elastic waves. Journal of the Acoustical Society of America, 1976, 59 (6): 1 361–1 371.
 Qin Fuhao, Guo Yaxi, Wang Miaoyue. The Kirchhoff elastic wave migration method. Chinese Journal of Geophysics, 1988, 31 (5): 577–587 (in Chinese).
 Shu Ping, Men Guangtian, Liu Qi. Re-recognize geology of Wangjiatun gas field and analyze producing performance. Natural Gas Industry, 2004, 24 (9): 108–112 (in Chinese).