Abstract
In this paper, a Pareto inversion based global optimization approach, to obtain results of joint inversion of two types of geophysical data sets, is formulated. 2D magnetotelluric and gravity data were used for tests, but presented solution is flexible enough to be used for combination of any kind of two or more target functions, as long as misfits can be calculated and forward problems solved. To minimize dimensionality of the solution, space and introduce straightforward regularization Sharp Boundary Interface (SBI) method was applied. As a main optimization engine, Particle Swarm Optimization (PSO) was used. Synthetic examples based on a real geological model were used to test proposed approach and show its usefulness in practical applications.
Article PDF
Similar content being viewed by others
References
Abdelzaher, M., J. Nishijima, G. El-Quady, E. Aboud, O. Masoud, M. Soliman, and S. Ehara (2011), Gravity and magnetotelluric investigations to elicit the origin of Hammam Faraun hot spring, Sinai Peninsula, Egypt, Acta Geophys. 59, 3, 633–656, DOI: 10.2478/s11600-011-0006-4.
Blakely, R. (1996), Potential Theory in Gravity and Magnetic Applications, Cambridge University Press, Cambridge.
Chen, J., G.M. Hoversten, K. Key, G. Nordquist, and W. Cumming (2012), Stochastic inversion of magnetotelluric data using a sharp boundary parameterization and application to a geothermal site, Geophysics 77, 4, E265–E279, DOI: 10.1190/geo2011-0430.1.
Danek, T., M. Kochetov, and M. Slawinski (2013), Uncertainty analysis of effective elasticity tensors using quaternion-based global optimization and Monte-Carlo method, Quart. J. Mech. Appl. Math. 66, 2, 253–272, DOI: 10.1093/qjmam/hbt004.
DeStefano, M. and D. Colombo (2006), Geophysical modeling through simultaneous joint inversion of seismic, gravity and magnetotelluric data. In: SEG International Exhibition and 76th Annual Meeting, Workshop on Integration of Seismic and Electromagnetic Measurements.
Fernandez Martinez, J., E. Gonzalo, J. Alvarez, H. Kuzma, and C. Menendez Perez (2010), PSO: A powerful algorithm to solve geophysical inverse problems: Application to a 1D-DC resistivity case, J. Appl. Geophys. 71, 1, 13–25, DOI: 10.1016/j.jappgeo.2010.02.001.
Gauss, C. (1809), Theoria Motus Corporum Coelestium in Sectionibus Conicis Solem Ambientium, Kunst und Industrie Comptoir.
Jegen, M.D., R.W. Hobbs, P. Tarits, and A. Chave (2009), Joint inversion of marine magnetotelluric and gravity data incorporating seismic constraints: Preliminary results of sub-basalt imaging off the Faroe Shelf, Earth Planet. Sci. Lett. 282, 1–4, 47–55, DOI: 10.1016/j.epsl.2009.02.018.
Kennedy, J., and R. Eberhart (1995), Particle swarm optimization. In: Proc. IEEE International Conference on Neural Networks, Vol. 4, 1942–1948.
Kozlovskaya, E., L. Vecsey, J. Plomerova, and T. Raita (2007), Joint inversion of multiple data types with the use of multiobjective optimization: problem formulation and application to the seismic anisotropy investigations, Geophys. J. Int. 171, 2, 761–779, DOI: 10.1111/j.1365-246X.2007.03540.x.
Kung, H., F. Luccio, and F. Preparata (1975), On finding the maxima of a set of vectors, J. ACM 22, 4, 469–476.
Legendre, A. (1805), Nouvelles Methodes pour la Determination des Orbites des Cometes, Didot Libr., Paris, 80 pp.
Liberti, L., and N. Maculan (eds.) (2006), Global Optimization: From Theory to Implementation, Springer Science and Business Media, New York.
Lines, L., A. Schultz, and S. Treitel (1988), Cooperative inversion of geophysical data, Geophysics 53, 1, 8–20, DOI: 10.1190/1.1442403.
Mehanee, S., and M. Zhdanov (2002), Two-dimensional magnetotelluric inversion of blocky geoelectrical structures, J. Geophys. Res. 107, B4, 2156–2202, DOI: 10.1029/2001JB000191.
Poli, R., J. Kennedy, and T. Blackwell (2007), Particle swarm optimization. An overview, Swarm Intell. 1, 1, 33–57, DOI: 10.1007/s11721-007-0002-0.
Sen, M., and P. Stoffa (1995), Global Optimization Methods in Geophysical Inversion, Elsevier, Amsterdam.
Smith, T., M. Hoversten, E. Gasperikova, and F. Morrison (1999), Sharp boundary inversion of 2D magnetotelluric data, Geophys. Prospect. 47, 4, 469–486, DOI: 10.1046/j.1365-2478.1999.00145.x.
Tikhonov, A. (1963), Regularization of incorrectly posed problems, Dokl. Akad. Nauk SSSR 4, 1624–1627.
Vozoff, K., and D. Jupp (1975), Joint inversion of geophysical data, Geophys. J. Int. 42, 3, 977–991, DOI: 10.1111/j.1365-246X.1975.tb06462.x.
Wannamaker, P., J. Stodt, and L. Rijo (1987), A stable finite element solution for twodimensional magnetotelluric modelling, Geophys. J. Int. 88, 1, 277–296, DOI: 10.1111/j.1365-246X.1987.tb01380.x.
Zhdanov, M. (2002), Geophysical Inverse Theory and Regularization Problems, Elsevier, Amsterdam.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Miernik, K., Bogacz, A., Kozubal, A. et al. Pareto Joint Inversion of 2D Magnetotelluric and Gravity Data — Towards Practical Applications. Acta Geophys. 64, 1655–1672 (2016). https://doi.org/10.1515/acgeo-2016-0035
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1515/acgeo-2016-0035