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The Gramian Method of Joint Inversion of the Gravity Gradiometry and Seismic Data

  • Wei LinEmail author
  • Michael S. Zhdanov
Article
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Abstract

Integration of multimodal geophysical data provides better constraints on the results of inversion, thus helping to obtain the most reliable information about the structure and composition of the target. The Gramian method of joint inversion uses a Gramian stabilizer to increase the correlation between the different physical parameters of the inverse model and their attributes or transforms. This paper applies the Gramian method to a joint inversion of the gravity gradiometry and seismic data with rock physics and structural constraints. In the first case we construct the Gramian stabilizer, which enforces the petrophysical relationship between the physical parameters to constrain the recovered models. In the second case, we incorporate the structural constraints in the joint inversion via a Gramian stabilizer of the gradients of velocity and density. In this case, the Gramian forces the vectors of the gradients of different model parameters to be parallel, thus implementing the structural constraints. The Gramian method of joint inversion is implemented using the Tikhonov regularization and the re-weighted conjugate gradient method. The approach is illustrated by synthetic model studies, which include a complicated SEG model of a salt dome structure located in a complex environment.

Keywords

Joint inversion seismic gravity Gramian constraints 
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Notes

Acknowledgements

The authors acknowledge support from the University of Utah’s Consortium for Electromagnetic Modeling and Inversion (CEMI) and TechnoImaging. We would like to thank Mr. Shihang Feng and Dr. Yue Zhu for their help with this research. The authors also thank Dr. Daniele Colombo and the other two anonymous reviewers for their valuable suggestions, which helped to improve the manuscript.

References

  1. Abubakar, A., Gao, G., Habashy, T. M., & Liu, J. (2012). Joint inversion approaches for geophysical electromagnetic and elastic full-waveform data. Inverse Problems, 28(5), 055016.CrossRefGoogle Scholar
  2. Aki, K., & Richards, P. G. (2009). Quantitative seismology. Mill Valley: University Science Books.Google Scholar
  3. Bleistein, N. (2012). Mathematical methods for wave phenomena. Cambridge: Academic Press.Google Scholar
  4. Brekhovskikh, L. M. (1976). Mathematical methods for wave phenomena. Cambridge: Academic Press.Google Scholar
  5. Chen, J., Hoversten, G. M., Vasco, D., Rubin, Y., & Hou, Z. (2007). A Bayesian model for gas saturation estimation using marine seismic AVA and CSEM data. Geophysics, 72(2), WA85–WA95.CrossRefGoogle Scholar
  6. Colombo, D., & De Stefano, M. (2007). Geophysical modeling via simultaneous joint inversion of seismic, gravity, and electromagnetic data: Application to prestack depth imaging. The Leading Edge, 26(3), 326–331.CrossRefGoogle Scholar
  7. Colombo, D., Mantovani, M., Hallinan, S., & Virgilio, M. (2008). Sub-basalt depth imaging using simultaneous joint inversion of seismic and electromagnetic (MT) data: A CRB field study. SEG Technical Program Expanded Abstracts, 2008, 2674–2678.Google Scholar
  8. Colombo, D., & Rovetta, D. (2018). Coupling strategies in multiparameter geophysical joint inversion. Geophysical Journal International, 215(2), 1171–1184.CrossRefGoogle Scholar
  9. De Stefano, M., Golfré Andreasi, F., Re, S., Virgilio, M., & Snyder, F. F. (2011). Multiple-domain, simultaneous joint inversion of geophysical data with application to subsalt imaging. Geophysics, 76(3), R69–R80.CrossRefGoogle Scholar
  10. Dell’Aversana, P. (2014). Cognition in geosciences—The feeding loop between geo-disciplines, cognitive sciences and epistemology. Cambridge: Academic Press.Google Scholar
  11. French, W. (1974). Two-dimensional and three-dimensional migration of model experiment reflection profiles. Geophysics, 39, 265–277.CrossRefGoogle Scholar
  12. Gallardo, L. A., Fontes, S. L., Meju, M. A., Buonora, M. P., & Lugão, P. P. (2012). Robust geophysical integration through structure-coupled joint inversion and multispectral fusion of seismic reflection, magnetotelluric, magnetic, and gravity images: Example from Santos Basin, offshore Brazil. Geophysics, 77(5), B237–B251.CrossRefGoogle Scholar
  13. Gallardo, L. A., & Meju, M. A. (2003). Characterization of heterogeneous near-surface materials by joint 2D inversion of DC resistivity and seismic data. Geophysical Research Letters, 30(13), 1–4.CrossRefGoogle Scholar
  14. Gallardo, L. A., & Meju, M. A. (2004). Joint two-dimensional DC resistivity and seismic travel-time inversion with cross-gradients constraints. Journal of Geophysical Research: Solid Earth, 109(B03311), 1–11.Google Scholar
  15. Gallardo, L. A., & Meju, M. A. (2007). Joint two-dimensional cross-gradient imaging of magnetotelluric and seismic traveltime data for structural and lithological classification. Geophysical Journal International, 169(3), 1261–1272.CrossRefGoogle Scholar
  16. Gallardo, L. A., & Meju, M. A. (2011). Structure-coupled multi-physics imaging in geophysical sciences. Reviews of Geophysics, 49(1), RG1003.CrossRefGoogle Scholar
  17. Gallardo, L. A., Meju, M. A., & Pérez-Flores, M. A. (2005). A quadratic programming approach for joint image reconstruction: mathematical and geophysical examples. Inverse Problems, 21(2), 435.CrossRefGoogle Scholar
  18. Gao, G., Abubakar, A., & Habashy, T. M. (2012). Joint petrophysical inversion of electromagnetic and full-waveform seismic data. Geophysics, 77(3), WA3–WA18.CrossRefGoogle Scholar
  19. Gardner, G. H. F., Gardner, L. W., & Gregory, A. R. (1974). Formation velocity and density—The diagnostic basics for stratigraphic traps. Geophysics, 39(6), 770–780.CrossRefGoogle Scholar
  20. Haber, E., & Oldenburg, D. (1997). Joint inversion: A structural approach. Inverse Problems, 13(1), 63–67.CrossRefGoogle Scholar
  21. Hoversten, G. M., Cassassuce, F., Gasperikova, E., Newman, G. A., Chen, J., Rubin, Y., et al. (2006). Direct reservoir parameter estimation using joint inversion of marine seismic AVA and CSEM data. Geophysics, 71(3), C1–C13.CrossRefGoogle Scholar
  22. Hoversten, G. M., Gritto, R., Washbournez, J., & Daley, T. (2003). Pressure and fluid saturation prediction in a multicomponent reservoir using combined seismic and electromagnetic imaging. Geophysics, 68(5), 1580–1591.CrossRefGoogle Scholar
  23. Hu, W. Y., Abubakar, A., & Habashy, T. M. (2009). Joint electromagnetic and seismic inversion using structural constraints. Geophysics, 74(6), R99–R109.CrossRefGoogle Scholar
  24. Jegen, M. D., Hobbs, R. W., Tarits, P., & Chave, A. (2009). Joint inversion of marine magnetotelluric and gravity data incorporating seismic constraints: Preliminary results of sub-basalt imaging off the Faroe Shelf. Earth and Planetary Science Letters, 282(1–4), 47–55.CrossRefGoogle Scholar
  25. Lelièvre, P. G., Farquharson, C. G., & Hurich, C. A. (2012). Joint inversion of seismic traveltimes and gravity data on unstructured grids with application to mineral exploration. Geophysics, 77(1), K1–K15.CrossRefGoogle Scholar
  26. Lippmann, B. A., & Schwinger, J. (1950). Variational principles for scattering processes I. Physical Review Letters, 79(3), 469.Google Scholar
  27. Malovichko, M., Khokhlov, N., Yavich, N., & Zhdanov, M. S. (2017). Approximate solutions of acoustic 3D integral equation and their application to seismic modeling and full-waveform inversion. Journal of Computational Physics, 346, 318–339.CrossRefGoogle Scholar
  28. Malovichko, M., Khokhlov, N., Yavich, N., & Zhdanov, M. S. (2018). Acoustic 3D modeling by the method of integral equations. Computers and Geosciences, 111, 223–234.CrossRefGoogle Scholar
  29. Meju, M. A., & Gallardo, L. A. (2016). Structural coupling approaches in integrated geophysical imaging. In M. Moorkamp, P. G. Lelièvre, N. Linde, & A. Khan (Eds.), Integrated imaging of the earth: Theory and applications (Vol. 218, pp. 49–67). Hoboken: Wiley.CrossRefGoogle Scholar
  30. Meqbel, N. M., & Ritter, O. (2012). New weighting schemes for joint inversion of land magnetotelluric and controlled source EM data. AGU Fall Metting Abstracts.Google Scholar
  31. Moorkamp, M., Heincke, B., Jegen, M., Robert, A. W., & Hobbs, R. W. (2011). A framework for 3-D joint inversion of MT, gravity and seismic refraction data. Geophysical Journal International, 184(1), 477–493.CrossRefGoogle Scholar
  32. Moorkamp, M. (2017). Integrating electromagnetic data with other geophysical observations for enhanced imaging of the earth: A tutorial and review. Surveys in Geophysics, 38(5), 935–962.CrossRefGoogle Scholar
  33. Pica, A., Diet, L. P., & Tarantola, A. (1990). Nonlinear inversion of seismic reflection data in a laterally invariant medium. Geophysics, 55, 284–292.CrossRefGoogle Scholar
  34. Sheriff, R. E., & Geldart, L. P. (1995). Exploration seismology (2nd ed.). Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  35. Sunwall, D., Cox, L., & Zhdanov, M. S. (2013). Joint 3D inversion of time- and frequency- domain airborne electromagnetic data. SEG Technical Program Expanded Abstracts, 2013, 713–717.Google Scholar
  36. Tarantola, A. (1984). Inversion of seismic reflection data in the acoustic approximation. Geophysics, 49, 1259–1266.CrossRefGoogle Scholar
  37. Tarantola, A. (2004). Inverse problem theory (1st ed.). Philadelphia: SIAM.Google Scholar
  38. Zhdanov, M. S. (2002). Geophysical inverse theory and regularization problems (Vol. 36). Amsterdam: Elsevier.CrossRefGoogle Scholar
  39. Zhdanov, M. S., Gribenko, A. V., & Wilson, G. (2012a). Generalized joint inversion of multimodal geophysical data using Gramian constraints. Geophysical Research Letters, 39(9), L09301.CrossRefGoogle Scholar
  40. Zhdanov, M. S., Gribenko, A. V., Wilson, G., & Funk, C. (2012b). 3D joint inversion of geophysical data with Gramian constraints: A case study from the Carrapateena IOCG deposit, South Australia. The Leading Edge, 31(11), 1382–1388.CrossRefGoogle Scholar
  41. Zhdanov, M. S. (2015). Inverse theory and applications in geophysics (Vol. 36). Amsterdam: Elsevier.Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Geology and GeophysicsUniversity of UtahSalt Lake CityUSA
  2. 2.Minmetals Exploration & Development Co.BeijingChina
  3. 3.TechnoImagingSalt Lake CityUSA

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