Free Standard AU & NZ Shipping For All Book Orders Over $80!
Register      Login
Exploration Geophysics Exploration Geophysics Society
Journal of the Australian Society of Exploration Geophysicists
RESEARCH ARTICLE

Prestack depth imaging in complex structures using VTI fast marching traveltimes

Seyed Yaser Moussavi Alashloo 1 2 Deva P. Ghosh 1
+ Author Affiliations
- Author Affiliations

1 Center of Seismic Imaging, Universiti Teknologi PETRONAS, Seri Iskandar, Perak 32610, Malaysia.

2 Corresponding author. Email: y.alashloo@gmail.com

Exploration Geophysics 49(4) 484-493 https://doi.org/10.1071/EG17013
Submitted: 15 January 2017  Accepted: 25 June 2017   Published: 17 August 2017

Abstract

The presence of sedimentary layers in the Earth’s subsurface results in seismic anisotropy, which makes wave velocity dependent on the propagation angle. This phenomenon causes complexities and errors both kinematically and dynamically in seismic imaging. Among these errors are the mispositioning of migrated events and failure to retain energy during dip-moveout. A fundamental and challenging issue in seismic imaging is the computation of seismic wave traveltime from the source to the receiver via the reflection point. A powerful method for determining traveltime is the application of finite difference to solve the eikonal equation. In this study, we employ a fast marching eikonal solver in the isotropic and vertical transverse isotropy (VTI) concepts. We also test the results by using the Kirchhoff depth migration algorithm. Instead of using a linear eikonal equation, which is commonly used in the industry, we consider a nonlinear approximation because it is more realistic and accurate than the former. The Marmousi synthetic data and a real dataset are used for testing purposes. The comparison of isotropic and VTI traveltimes demonstrates a considerable lateral difference among wavefronts. The results of Kirchhoff imaging show that the VTI algorithm generates images with perfect positioning and higher resolution than the isotropic one, specifically in deep areas. Finally, we conclude that our anisotropic approach is stable, fast, and generates high-quality images with accurate details in deep structures.

Key words: eikonal solver, fast marching method, prestack depth migration, vertical transverse isotropy.


References

Alashloo, S. Y. M., Ghosh, D., and Wan Ismail, W. Y., 2015a, One-point seismic anisotropic ray tracing in VTI media: Asia Petroleum Geoscience Conference and Exhibition 2015.

Alashloo, S. Y. M., Ghosh, D. P., and Yusoff, W. W., 2015b, VTI wave modeling using weak elastic anisotropy approximation: Proceedings of the International Conference on Integrated Petroleum Engineering and Geosciences (ICIPEG) 2014, 233–238.

Alkhalifah, T., 1995, Efficient synthetic-seismogram generation in transversely isotopic, inhomogeneous media: Geophysics, 60, 1139–1150
Efficient synthetic-seismogram generation in transversely isotopic, inhomogeneous media:Crossref | GoogleScholarGoogle Scholar |

Alkhalifah, T., and Fomel, S., 2010, An eikonal-based formulation for traveltime perturbation with respect to the source location: Geophysics, 75, T175–T183
An eikonal-based formulation for traveltime perturbation with respect to the source location:Crossref | GoogleScholarGoogle Scholar |

Alkhalifah, T., and Tsvankin, I., 1995, Velocity analysis for transversely isotropic media: Geophysics, 60, 1550–1566
Velocity analysis for transversely isotropic media:Crossref | GoogleScholarGoogle Scholar |

Babich, V., 1956, A radial method for computing the intensity of wave fronts: Doklady Akademii Nauk SSSR, 110, 355–357

Backus, G. E., 1962, Long-wave elastic anisotropy produced by horizontal layering: Journal of Geophysical Research, 67, 4427–4440
Long-wave elastic anisotropy produced by horizontal layering:Crossref | GoogleScholarGoogle Scholar |

Behera, L., Khare, P., and Sarkar, D., 2011, Anisotropic P-wave velocity analysis and seismic imaging in onshore Kutch sedimentary basin of India: Journal of Applied Geophysics, 74, 215–228
Anisotropic P-wave velocity analysis and seismic imaging in onshore Kutch sedimentary basin of India:Crossref | GoogleScholarGoogle Scholar |

Bevc, D., 1997, Imaging complex structures with semirecursive Kirchhoff migration: Geophysics, 62, 577–588
Imaging complex structures with semirecursive Kirchhoff migration:Crossref | GoogleScholarGoogle Scholar |

Biondi, B., 2006, 3D seismic imaging: Society of Exploration Geophysicists.

Cerveny, V. 2005. Seismic ray theory, Cambridge University Press.

Cristiani, E., 2009, A fast marching method for Hamilton-Jacobi equations modeling monotone front propagations: Journal of Scientific Computing, 39, 189–205
A fast marching method for Hamilton-Jacobi equations modeling monotone front propagations:Crossref | GoogleScholarGoogle Scholar |

Dellinger, J., 1991, Anisotropic finite-difference traveltimes: 61st Annual International Meeting, SEG, Expanded Abstracts, 1530–1533.

Dellinger, J., and Muir, F., 1988, Imaging reflections in elliptically anisotropic media: Geophysics, 53, 1616–1618
Imaging reflections in elliptically anisotropic media:Crossref | GoogleScholarGoogle Scholar |

Dellinger, J., Muir, F., and Karrenbach, M., 1993, Anelliptic approximations for TI media: Journal of Seismic Exploration, 2, 23–40

Fernandes, R. A. R., Pereira, R. M., Cruz, J. C. R., and Protázio, J. D. S., 2015, Anelliptic rational approximations of traveltime P-wave reflections in VTI media: 14th International Congress of the Brazilian Geophysical Society & EXPOGEF, 3–6 August 2015, Rio de Janeiro, Brazil, Brazilian Geophysical Society, 945–949.

Fomel, S., 1997, A variational formulation of the fast marching eikonal solver: Stanford Exploration Project 95, 127–147.

Fomel, S., 2004, On anelliptic approximations for qP velocities in VTI media: Geophysical Prospecting, 52, 247–259
On anelliptic approximations for qP velocities in VTI media:Crossref | GoogleScholarGoogle Scholar |

Fowler, P. J., 2003, Practical VTI approximations: a systematic anatomy: Journal of Applied Geophysics, 54, 347–367
Practical VTI approximations: a systematic anatomy:Crossref | GoogleScholarGoogle Scholar |

Hao, H., Zhang, J., Duan, P., and Cheng, J., 2011, Ray tracing and local angle domain prestack depth migration in TI medium: International Geophysical Conference, Shenzhen, China, SEG, 76–76.

Jang, S., and Kim, Y.-W., 2011, Prestack depth migration by 3D PSPI. Proceedings of the 10th SEGJ International Symposium, 20–22 November 2011, Kyoto, Japan, 1–4.

Jiang, F., and Zhou, H.-W., 2011, Traveltime inversion and error analysis for layered anisotropy: Journal of Applied Geophysics, 73, 101–110
Traveltime inversion and error analysis for layered anisotropy:Crossref | GoogleScholarGoogle Scholar |

Karal, F. C., and Keller, J. B., 1959, Elastic wave propagation in homogeneous and inhomogeneous media: The Journal of the Acoustical Society of America, 31, 694–705
Elastic wave propagation in homogeneous and inhomogeneous media:Crossref | GoogleScholarGoogle Scholar |

Koren, Z., Ravve, I., Gonzalez, G., and Kosloff, D., 2008, Anisotropic local tomography: Geophysics, 73, VE75–VE92
Anisotropic local tomography:Crossref | GoogleScholarGoogle Scholar |

Moussavi Alashloo, S. Y., Ghosh, D. P., Bashir, Y., and Wan Yusoff, W. I., 2015, A comparison on initial-value ray tracing and fast marching eikonal solver for VTI traveltime computing: IOP Conference Series: Earth and Environmental Science (EES), 30, 1–7.

Muir, F., and Dellinger, J., 1985, A practical anisotropic system: Stanford Exploration Project 44, 55–58.

Popovici, A. M., and Sethian, J. A., 2002, 3-D imaging using higher order fast marching traveltimes: Geophysics, 67, 604–609
3-D imaging using higher order fast marching traveltimes:Crossref | GoogleScholarGoogle Scholar |

Sava, P., and Fomel, S., 1998, Huygens wavefront tracing: A robust alternative to ray tracing: SEG Technical Program Expanded Abstracts, 1961–1964.

Sethian, J. A., and Popovici, A. M., 1999, 3-D traveltime computation using the fast marching method: Geophysics, 64, 516–523
3-D traveltime computation using the fast marching method:Crossref | GoogleScholarGoogle Scholar |

Sethian, J. A., and Vladimirsky, A., 2001, Ordered upwind methods for static Hamilton–Jacobi equations: Proceedings of the National Academy of Sciences of the United States of America, 98, 11069–11074
Ordered upwind methods for static Hamilton–Jacobi equations:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD3MXnt1yqsLo%3D&md5=96e391516565a2175e5eedd995e6b99eCAS |

Stovas, A., and Alkhalifah, T., 2012, A new traveltime approximation for TI media: Geophysics, 77, C37–C42
A new traveltime approximation for TI media:Crossref | GoogleScholarGoogle Scholar |

Stovas, A., and Fomel, S., 2012, Generalized nonelliptic moveout approximation in τ-p domain: Geophysics, 77, U23–U30
Generalized nonelliptic moveout approximation in τ-p domain:Crossref | GoogleScholarGoogle Scholar |

Thomsen, L., 1986, Weak elastic anisotropy: Geophysics, 51, 1954–1966
Weak elastic anisotropy:Crossref | GoogleScholarGoogle Scholar |

Thomsen, L., 2002, Understanding seismic anisotropy in exploration and exploitation: Society of Exploration Geophysicists.

Tsvankin, I., 1996, P-wave signature and notation for transversely isotropic media: an overview: Geophysics, 61, 467–483
P-wave signature and notation for transversely isotropic media: an overview:Crossref | GoogleScholarGoogle Scholar |

Waheed, U. B., Alkhalifah, T., and Stovas, A., 2013a, Diffraction traveltime approximation for TI media with an inhomogeneous background: Geophysics, 78, WC103–WC111
Diffraction traveltime approximation for TI media with an inhomogeneous background:Crossref | GoogleScholarGoogle Scholar |

Waheed, U. B., Pšen Ík, I., Ervený, V., Iversen, E., and Alkhalifah, T., 2013b, Two-point paraxial traveltime formula for inhomogeneous isotropic and anisotropic media: tests of accuracy: Geophysics, 78, WC65–WC80
Two-point paraxial traveltime formula for inhomogeneous isotropic and anisotropic media: tests of accuracy:Crossref | GoogleScholarGoogle Scholar |

Waheed, U., Yarman, C. E., and Flagg, G., 2015a, An iterative, fast-sweeping-based eikonal solver for 3D tilted anisotropic media: Geophysics, 80, C49–C58
An iterative, fast-sweeping-based eikonal solver for 3D tilted anisotropic media:Crossref | GoogleScholarGoogle Scholar |

Waheed, U. B., Alkhalifah, T., and Wang, H., 2015b, Efficient traveltime solutions of the acoustic TI eikonal equation: Journal of Computational Physics, 282, 62–76
Efficient traveltime solutions of the acoustic TI eikonal equation:Crossref | GoogleScholarGoogle Scholar |

Wang, Y., 2014. Seismic ray tracing in anisotropic media – a modified Newton algorithm for solving nonlinear systems: 76th Conference and Exhibition, EAGE, Extended Abstracts.

Whiting, P., Klein-Helmkamp, U., Notfors, C., and Khan, O., 2003, Anisotropic prestack depth migration in practice: ASEG Extended Abstracts 2003, 1–3.

Zhang, Y.-T., Zhao, H.-K., and Qian, J., 2006, High order fast sweeping methods for static Hamilton–Jacobi equations: Journal of Scientific Computing, 29, 25–56
High order fast sweeping methods for static Hamilton–Jacobi equations:Crossref | GoogleScholarGoogle Scholar |

Zhao, H., 2005, A fast sweeping method for eikonal equations: Mathematics of Computation, 74, 603–627
A fast sweeping method for eikonal equations:Crossref | GoogleScholarGoogle Scholar |

Zhao, A.-H., Zhang, M.-G., and Ding, Z.-F., 2006, Seismic traveltime computation for transversely isotropic media: Chinese Journal of Geophysics, 49, 1603–1612

Zhu, T., Gray, S., and Wang, D., 2005, Kinematic and dynamic raytracing in anisotropic media: theory and application: SEG Technical Program Expanded Abstracts, 96–99.