Skip to main content
SpringerLink
Log in

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

  • Published:
Pure and Applied Geophysics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • 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.

    Article  Google Scholar 

  • Aki, K., & Richards, P. G. (2009). Quantitative seismology. Mill Valley: University Science Books.

    Google Scholar 

  • Bleistein, N. (2012). Mathematical methods for wave phenomena. Cambridge: Academic Press.

    Google Scholar 

  • Brekhovskikh, L. M. (1976). Mathematical methods for wave phenomena. Cambridge: Academic Press.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • Colombo, D., & Rovetta, D. (2018). Coupling strategies in multiparameter geophysical joint inversion. Geophysical Journal International, 215(2), 1171–1184.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Dell’Aversana, P. (2014). Cognition in geosciences—The feeding loop between geo-disciplines, cognitive sciences and epistemology. Cambridge: Academic Press.

    Google Scholar 

  • French, W. (1974). Two-dimensional and three-dimensional migration of model experiment reflection profiles. Geophysics, 39, 265–277.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • Gallardo, L. A., & Meju, M. A. (2011). Structure-coupled multi-physics imaging in geophysical sciences. Reviews of Geophysics, 49(1), RG1003.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Gao, G., Abubakar, A., & Habashy, T. M. (2012). Joint petrophysical inversion of electromagnetic and full-waveform seismic data. Geophysics, 77(3), WA3–WA18.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Haber, E., & Oldenburg, D. (1997). Joint inversion: A structural approach. Inverse Problems, 13(1), 63–67.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Hu, W. Y., Abubakar, A., & Habashy, T. M. (2009). Joint electromagnetic and seismic inversion using structural constraints. Geophysics, 74(6), R99–R109.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Lippmann, B. A., & Schwinger, J. (1950). Variational principles for scattering processes I. Physical Review Letters, 79(3), 469.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Meqbel, N. M., & Ritter, O. (2012). New weighting schemes for joint inversion of land magnetotelluric and controlled source EM data. AGU Fall Metting Abstracts.

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Pica, A., Diet, L. P., & Tarantola, A. (1990). Nonlinear inversion of seismic reflection data in a laterally invariant medium. Geophysics, 55, 284–292.

    Article  Google Scholar 

  • Sheriff, R. E., & Geldart, L. P. (1995). Exploration seismology (2nd ed.). Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • 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 

  • Tarantola, A. (1984). Inversion of seismic reflection data in the acoustic approximation. Geophysics, 49, 1259–1266.

    Article  Google Scholar 

  • Tarantola, A. (2004). Inverse problem theory (1st ed.). Philadelphia: SIAM.

    Google Scholar 

  • Zhdanov, M. S. (2002). Geophysical inverse theory and regularization problems (Vol. 36). Amsterdam: Elsevier.

    Book  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Zhdanov, M. S. (2015). Inverse theory and applications in geophysics (Vol. 36). Amsterdam: Elsevier.

    Google Scholar 

Download references

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.

Author information

Authors and Affiliations

  1. Department of Geology and Geophysics, University of Utah, Salt Lake City, UT, 84112, USA

    Wei Lin & Michael S. Zhdanov

  2. Minmetals Exploration & Development Co., Beijing, 100010, China

    Wei Lin

  3. TechnoImaging, Salt Lake City, UT, 84107, USA

    Michael S. Zhdanov

Authors
  1. Wei Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael S. Zhdanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei Lin.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lin, W., Zhdanov, M.S. The Gramian Method of Joint Inversion of the Gravity Gradiometry and Seismic Data. Pure Appl. Geophys. 176, 1659–1672 (2019). https://doi.org/10.1007/s00024-018-02088-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00024-018-02088-x

Keywords

Search

Navigation