Forward modeling of ocean-bottom cable data and wave-mode separation in fluid–solid elastic media with irregular seabed
Qu Ying-Ming1,2, Sun Jun-Zhi1, Li Zhen-Chun1, Huang Jian-Ping1, Li Hai-Peng1, and Sun Wen-Zhi1
1. Department of Geophysics, School of Geosciences, China University of Petroleum, Qingdao 266580, China.
2. SINOPEC Key Laboratory of Geophysics, Nanjing 211103, China.
Abstract：
In marine seismic exploration, ocean-bottom cable techniques accurately record the multicomponent seismic wavefield; however, the seismic wave propagation in fluid–solid media cannot be simulated by a single wave equation. In addition, when the seabed interface is irregular, traditional finite-difference schemes cannot simulate the seismic wave propagation across the irregular seabed interface. Therefore, an acoustic–elastic forward modeling and vector-based P- and S-wave separation method is proposed. In this method, we divide the fluid–solid elastic media with irregular interface into orthogonal grids and map the irregular interface in the Cartesian coordinates system into a horizontal interface in the curvilinear coordinates system of the computational domain using coordinates transformation. The acoustic and elastic wave equations in the curvilinear coordinates system are applied to the fluid and solid medium, respectively. At the irregular interface, the two equations are combined into an acoustic–elastic equation in the curvilinear coordinates system. We next introduce a full staggered-grid scheme to improve the stability of the numerical simulation. Thus, separate P- and S-wave equations in the curvilinear coordinates system are derived to realize the P- and S-wave separation method.
. Forward modeling of ocean-bottom cable data and wave-mode separation in fluid–solid elastic media with irregular seabed[J]. APPLIED GEOPHYSICS, 2018, 15(3-4): 432-447.
[1]
Aki, K., and Richards, P., 2002, Quantitative seismology (second edition): University Science Books.
[2]
Bernth, H., and Chapman, C., 2011, A comparison of the dispersion relations for anisotropic elastodynamic finite-difference grids: Geophysics, 76(3), WA43−WA50.
[3]
Carcione, J. M., and Helle, H. B., 2004, The physics and simulation of wave propagation at the ocean bottom: Geophysics, 69(3), 825−839.
[4]
Choi, Y., Min, D. J., and Shin, C., 2008, Two-dimensional waveform inversion of multi- component data in acoustic-elastic coupled media: Geophysical Prospecting, 56(6), 863−881.
[5]
Dahake, G., and Gracewski, S. M., 1997, Finite difference predictions of P-SV wave propagation inside submerged solids. I. Liquid-solid interface conditions: The Journal of the Acoustical Society of America, 102(4), 2125−2137.
[6]
Dai, Y. J., 2005, Research and application of wave field separation technology of multi-wave reflection seismic exploration data acquisition: Master Thesis, Central South University, Changsha.
[7]
Dankbaar, J. W. M., 1985, Separation of P- and S waves: Geophysical Prospecting, 33(7), 970−986.
[8]
Devaney, A. J., and Oristagliot, M. L., 1986, A plane-wave decomposition for elastic wave fields applied to the separation of P-waves and S-waves in vector seismic data: Geophysics, 51(2), 419−423.
[9]
Du, Q. Z., Zhang, M. Q., Chen, X. R., Gong, X. F., and Guo, C. F., 2014, True-amplitude wavefield separation using staggered-grid interpolation in the wavenumber domain: Applied Geophysics, 11(4), 437−446.
[10]
Falk, J., Tessmer, E., and Gajewski, D., 1998, Efficient finite-difference modelling of seismic waves using locally adjustable time steps: Geophysical Journal International, 46(6), 603−616.
[11]
Fornberg, B., 1988, The pseudospectral method: accurate representation of interfaces in elastic wave calculations: Geophysics, 53(5), 625−637.
[12]
Hestholm, S. O., and Ruud, B. O., 1994, 2D finite-difference elastic wave modelling including surface topography: Geophysical Prospecting, 42(5), 371−390.
[13]
Huang, J. P., Qu, Y. M., Li, Q. Y., Li, Z. C., Li, G. L., Bu, C. C., and Teng, H. H., 2015, Variable-coordinate forward modeling of irregular surface based on dual-variable grid: Applied Geophysics, 12(1), 101−110.
[14]
Jastram, C., and Behle, A., 1992, Acoustic modeling on a vertically varying grid: Geophysical Prospecting, 40(2), 157−169.
[15]
Jastram, C., and Tessmer, E., 1994, Elastic modeling on a grid with vertically varying spacing: Geophysical Prospecting, 42(4), 357−370.
[16]
Komatitsch, D., Barnes, C., and Tromp, J., 2000, Wave propagation near a fluid-solid interface: A spectral-element approach: Geophysics, 65(2), 623−631.
[17]
Komatitsch, D., and Tromp, J., 2002, Spectral-element simulations of global seismic wave propagation-I. Validation: Geophys. J. Int. 149(2), 390−412.
[18]
Lan, H. Q., and Zhang, Z. J., 2012, Research on seismic survey design for doubly complex areas, Applied Geophysics, 9(3), 301− 312.
[19]
Lebedev, V. I., 1964, Difference analogues of orthogonal decompositions, basic differential operators and some boundary problems of mathematical physics: USSR Computational Mathematics and Mathematical Physics, 4(3), 36-45.
[20]
Levander, A., 1988, Fourth-order finite-difference P-SV seismograms: Geophysics, 53(11), 1425−1436.
[21]
Li, Z. C., Zhang, H., Liu, Q. M., and Han, W. G., 2007, Numieric simulation of elastic wavefield separation by staggering grid high-order finite-difference algorithm: Oil Geophysical Prospecting, 42(5), 510−515.
[22]
Lu, J., and Wang, Y., and Yao, C., 2012, Separating P- and S-waves in an affine coordinate system: J. Geophys. Eng., 9(1), 12−18.
[23]
Ma, J. T., Sen, K. M., Chen, X. H., and Yao, F. C., 2011, OBC multiple attenuation technique using SRME theory: Chinese J. Geophys. (in Chinese), 54(11), 2960−2966.
[24]
Mirko, V. D. B., 2006, PP/PS Wavefield separation by independent component analysis: Geophys. J. Int., 166(1), 339-348.
[25]
Moczo, P., Bystricky, E., Kristek, J., Carcione, J. M., and Bouchon, M., 1997, Hybrid modeling of P-SV seismic motion at inhomogeneous viscoelastic topographic structures: Bull. seism. Soc. Am., 87(5), 1305−1323.
[26]
Qu, Y., Huang, J., Li, Z., Li, Q., Zhao, J., and Li, X., 2015, Elastic wave modeling and pre-stack reverse time migration of irregular free-surface based on layered mapping method: Chinese J. Geophys., 58(8), 2896−2911.
[27]
Qu, Y., Huang, J., Li, Z., and Li, J., 2017, A hybrid grid method in an auxiliary coordinate system for irregular fluid-solid interface modeling: Geophys. J. Int., 208(3), 1540−1556.
[28]
Qu, Y., Li, Z., Huang, J., and Li, J., 2017, Elastic full waveform inversion for surface topography: Geophysics, 82(5), R269−R285.
[29]
Qu, Y., Li, Z., and Huang, J., Li, J., 2018, Multi-scale full waveform inversion for areas with irregular surface topography in anauxiliary coordinate system: Exploration Geophysics., 49(1),70−82.
[30]
Soares, J. D., and Mansur, W. J., 2006, Dynamic analysis of fluid-soil-structure interaction problems by the boundary element method: Journal of Computational Physics, 219(2), 498−512.
[31]
Sun, R., Chow, J., and Chen, K. J., 2001, Phase correction in separating P-and S-waves in elastic data: Geophysics, 66(5), 1515-1518.
[32]
Sun, R., McMechan, G. A., and Chuang, H., 2011, Amplitude balancing in separating P- and S-waves in 2D and 3D elastic seismic data: Geophysics, 76(3), S103-S113.
[33]
Tessmer, E., 2000, Seismic finite-difference modeling with spatially varying time steps: Geophysics, 65(4), 1290−1293.
[34]
Tessmer, E., Kosloff, D., and Behle, A., 1992, Elastic wave propagation simulation in the presence of surface topography: Geophysical Journal International, 108(2), 621−632.
[35]
Tessmer, E., and Kosloff, D., 1994, 3D elastic modelling with surface topography by a Chebychev spectral method: Geophysics, 59(3), 464−473.
Wang, Y. B., Satish, C. S., and Penny J. B., 2002, Separation of P- and SV-wavefields from multi-component seismic data in the τ−p domain: Geophys. J. Int., 151(2), 663−672.
[39]
Yang, J. J., He B. S., and Zhang J. Z., 2014, Multicomponent seismic forward modeling of gas hydrates beneath the seafloor: Applied Geophysics, 11(4), 418−428.
[40]
Yang, J. H., Liu, T., Tang, G. Y., and Hu, T. Y., 2009, Modeling seismic wave propagation within complex structures: Applied Geophysics, 6(1), 30−41.
[41]
Zhang, B. Q., Zhou, H., Li, G. F., and Guo, J. Q., 2016, Geophone-seabed coupling effect and its correction: Applied Geophysics, 13(1), 145−155.
[42]
Zhang, J., 2004, Wave propagation across fluid-solid interfaces: a grid method approach: Geophysical Journal International, 159(1), 240−252.
2018, Vol. 15 
