Multiobjective particle swarm inversion algorithm for two-dimensional magnetic data
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Abstract
Regularization inversion uses constraints and a regularization factor to solve ill-posed inversion problems in geophysics. The choice of the regularization factor and of the initial model is critical in regularization inversion. To deal with these problems, we propose a multiobjective particle swarm inversion (MOPSOI) algorithm to simultaneously minimize the data misfit and model constraints, and obtain a multiobjective inversion solution set without the gradient information of the objective function and the regularization factor. We then choose the optimum solution from the solution set based on the trade-off between data misfit and constraints that substitute for the regularization factor. The inversion of synthetic two-dimensional magnetic data suggests that the MOPSOI algorithm can obtain as many feasible solutions as possible; thus, deeper insights of the inversion process can be gained and more reasonable solutions can be obtained by balancing the data misfit and constraints. The proposed MOPSOI algorithm can deal with the problems of choosing the right regularization factor and the initial model.
Keywords
multiobjective inversion particle swarm optimization regularization factor global search magnetic dataPreview
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References
- Carlos, A. C. C., Gregorio, T. P., and Maximino, S. L., 2004, Handling multiple objectives with particle swarm optimization: IEEE trans on evolutionary computation, 8(3), 256–279.CrossRefGoogle Scholar
- Gribenko, A., and Zhdanov, M. S., 2007, Rigorous 3D inversion of marine CSEM data based on the integral equation method: Geophysics, 72(2), WA73–WA84.CrossRefGoogle Scholar
- Hansen, P. C., and O’Leary, D. P., 1993, The use of L-curve in the regularization of discrete ill-posed problems: SIAM Journal on Numerical Analysis, 14(6), 1487–1530.Google Scholar
- Kennedy, J., and Eberhart, R., 1995, Particle swarm optimization: IEEE Int Conf on Neural Networks, Perth, Australia, 1942–1948.Google Scholar
- Li, D. Q., Wang, G. J., Di, Q. Y., Wang, M. Y., and Wang, R., 2008, The application of genetic algorithm to CSAMT inversion for minimum structure: Chinese Journal of Geophysics (in Chinese), 51(4), 1234–1245.Google Scholar
- Nabighian, M. N., Grauch V. J. S., Hansen R. O., LaFehr, T. R., Li, Y. Peirce, J. W., Phillips, J. D., and Ruder, M. E., 2005, The historical development of the magnetic method in exploration: Geophysics, 70(6), 33ND–61ND.CrossRefGoogle Scholar
- Sen, M. K., and Stoffa, P. L., 2013, Global optimization methods in geophysical inversion: Cambridge University Press, UK.CrossRefGoogle Scholar
- Shi, X. M., Xiao, M., Fan, J. K., Yang, G. S., and Zhang, X. H., 2009, The damped PSO algorithm and its application for magnetotelluric sounding data inversion: Chinse Journal of Geophysics (in Chinese), 52(4), 1114–1120.Google Scholar
- Song, W. Q., Gao, Y. K., and Zhu, H. W., 2013, The differential evolution inversion method based on Bayesian theory for micro-seismic data: Chinese journal of geophyics (in Chinese), 56(4), 1331–1339.Google Scholar
- Stocco, S., Godio, A., and Sambuelli, L., 2009. Modelling and compact inversion of magnetic data: A Matlab code: Computers & Geosciences, 35(10), 2111–2118.CrossRefGoogle Scholar
- Telford, W. M., Gedart, L. P., and Sheriff, R. E., 1990, Applied Geophysics: Cambridge University Press, Cambridge, UK.CrossRefGoogle Scholar
- Tikhonov, A. N., 1963, Regularization of incorrectly posed problem: Soviet Mathematics Doklady, 4(6), 1624–1627Google Scholar
- Wang, Z. W., Xu, S., Liu, Y. P., and Liu, J. H., 2014, Extrapolated Tikhonov method and inversion of 3D density images of gravity data: Applied Geophysics, 11(2), 139–148.CrossRefGoogle Scholar
- Wei, C., Li, X. F., and Zhen, X. D., 2010, The group searchbased parallel algorithm for the serial Monte Carlo inversion method: Applied Geophysics, 7(2), 127–134.CrossRefGoogle Scholar
- Wierzbicki, A. P., and Qian, Y., 1982, Introduce to the methodology of multi objective optimization, Chinese Journal of Operations Research (in Chinese), 1(1), 47–52.Google Scholar
- Wu, X. P., and Xu, G. M., 1998, Improvement of Occam’s inversion for MT Data: Acta Geophysica Sinica, 41(4), 547–554.Google Scholar
- Wu, X. P., and Xu, G. M., 2000, Study on 3-D resistivity inversion using conjugate gradient method: Chinese Journal of Geophysics (in Chinese), 43(3), 420–427.Google Scholar
- Xiang, Y., Yu, P., Chen, X., and Tang, R., 2013, An improved adaptive regularized parameter selection in Magnetotelluric inversion: Journal of Tongji Universityv (Natural Science) (in Chinese), 41(9), 1429–1434.Google Scholar
- Xiong, J., Meng, X. H., Liu, C. Y., and Peng, M., 2012, Magnetotelluric inversion based on differential evolution: Geophysical and Geochemical Exploration (in Chinese), 36(3), 448–451.Google Scholar
- Xiong, J., Liu, C. Y., and Zou, C. C., 2013, The induction logging inversion based on particle swarm optimization: Geophysical and Geochemical Exploration (in Chinese), (in Chinese), 37(6), 1141–1145.Google Scholar
- Yu, P., Wang, J. L., Wu, J. S., and Wang, D. W., 2007, Constrained joint inversion of gravity and seismic data using the simulated annealing algorithm: Chinese Journal of Geophysics (in Chinese), 50(2), 529–538.Google Scholar
- Yuan, S. Y., Wang, S. X., and Tian, N., 2009, Swarm intelligence optimization and its application in geophysical data inversion: Applied Geophysics, 6(2), 166–174.CrossRefGoogle Scholar
- Zhang, H. B., Shang, Z. P., Yang, C. C., and Duan, Q. L., 2005, Estimation of regular parameters for the impedance inversion: Chinese Journal of Geophysics (in Chinese), 48(1), 181–188.Google Scholar
- Zhdanov, M. S., 2002, Geophysical Inverse Theory and Regularization problems, volume 36 (Methods in Geochemistry and Geophysics): Elsevier Science.CrossRefGoogle Scholar
- Zhdanov, M. S., Ellis, R., and Mukherjee, S., 2004, Threedimensional regularized focusing inversion of gravity gradient tensor component data: Geophysics, 69(4), 925–937.CrossRefGoogle Scholar