Gravity-magnetic cross-gradient joint inversion by the cyclic gradient method. (English) Zbl 1458.86004
Summary: In this paper, we consider a joint-inversion problem using different types of geophysical data: gravity and magnetism. We first formulate two kinds of inverse problems in the famework of the first kind Fredholm integral equations, and then build up a sparse inversion model combining the two inverse problems as well as the cross-gradient term. The cyclic gradient method for quadratic function minimization is extended for solving the corresponding optimization problem. We update the stepsizes in a cyclic way, by combining the approximated Cauchy steps and the fixed steplengths. Theoretical analysis shows that the algorithm converges R-linearly. Experimental tests show that the proposed joint inversion sparse model as well as the proposed cyclic gradient method improve the numerical performances effectively, compared to the state of the art.
MSC:
| 86-08 | Computational methods for problems pertaining to geophysics |
| 65K05 | Numerical mathematical programming methods |
| 86A25 | Geo-electricity and geomagnetism |
| 86A20 | Potentials, prospecting |
References:
| [1] | De Asmundis, R.; di Serafino, D.; Hager, W. W.; Toraldo, G.; Zhang, H.-C., An efficient gradient method using the Yuan steplength, Comput. Opt. Appl., 59, 541-563 (2014) · Zbl 1310.90082 |
| [2] | Barzilai, J.; Borwein, J. M., Two point step size gradient methods, IMA J. Numer. Anal., 8, 141-148 (1988) · Zbl 0638.65055 |
| [3] | Cauchy, A., Methode generale pour la resolution des systems dequations simultanees, Comp. Rend. Sci. Paris, 25, 46-89 (1847) |
| [4] | Dai, Y.-H., Alternate step gradient method, Optimization, 52, 395-415 (2003) · Zbl 1056.65055 |
| [5] | Dai, Y.-H.; Fletcher, R., On the asymptotic behaviour of some new gradient methods, Math. Program., 103, 541-559 (2005) · Zbl 1099.90038 |
| [6] | Dai, Y.-H.; Liao, L.-Z., R-linear convergence of the Barzilai and Borwein gradient method, IMA J. Numer. Anal., 22, 1-10 (2002) · Zbl 1002.65069 |
| [7] | Dai, Y.-H.; Yuan, Y.-X., Analysis of monotone gradient methods, J. Ind. Manage. Optim., 1, 181-192 (2005) · Zbl 1071.65084 |
| [8] | Fletcher, R., A limited memory steepest descent method, Math. Program. Ser. A, 135, 413-436 (2012) · Zbl 1254.90113 |
| [9] | Fregoso, E.; Gallardo, L. A., Cross-gradients joint 3D inversion with applications to gravity and magnetic data, Geophysics, 74, 4, L31-L42 (2009) |
| [10] | Gallardo, L. A., Multiple cross-gradient joint inversion for geospectral imaging, Geophys. Res. Lett., 34, 19, 517-524 (2007) |
| [11] | Gallardo., L. A.; Meju, M. A., Joint two-dimensional cross-gradient imaging of magnetotelluric and seismic traveltime data for structural and lithological classification, Geophys. J. R. Astron. Soc., 169, 3, 1261-1272 (2010) |
| [12] | Gallardo, L. A.; Meju, M. A.; Pérezflores, M. A., A quadratic programming approach for joint image reconstruction: Mathematical and geophysical examples, Inverse Probl., 21, 2, 435-452 (2005) · Zbl 1070.65050 |
| [13] | Gallardo, L. A.; Pérez-Flores, M. A.; Gómez-Treviño, E., A versatile algorithm for joint 3D inversion of gravity and magnetic data, Geophysics, 68, 3, 949-959 (2003) |
| [14] | Gao, J.; Zhang, H. J., An efficient sequential strategy for realizing cross-gradient joint inversion: Method and its application to two-dimensional cross borehole seismic travel time and DC resistivity tomography, Geophys. J. Int., 213, 2, 1044-1055 (2018) |
| [15] | Hu, W. Y.; Abubakar, A.; Habashy, T. M., Joint electromagnetic and seismic inversion using structural constraints, Geophysics, 74, 74, R99-R109 (2009) |
| [16] | Jegen, M. D.; Hobbs, R. W.; Tarits, P.; Chave, A., Joint inversion of marine magnetotelluric and gravity data incorporating seismic constraints: Preliminary results of sub-basalt imaging off the faroe shelf, Earth Planetary Sci. Lett., 282, 1, 47-55 (2009) |
| [17] | Li, Y. G.; Oldenburg, D. W., 3-D inversion of magnetic data, Geophysics, 61, 2, 394-408 (1996) |
| [18] | Linde, N.; Tryggvason, A.; Peterson, J. E.; Hubbard, S. S., Joint inversion of crosshole radar and seismic traveltimes acquired at the south oyster bacterial transport site, Geophysics, 73, 73, G29-G37 (2008) |
| [19] | Liu, G. D., General Theory of Geophysics (2018), Shanghai Science and Technology Press: Shanghai Science and Technology Press, Shanghai |
| [20] | Shu, M. C.; Wang, Y. F., The posterior constrained regularization method on reservoir density inversion, Chinese J. Geophys., 58, 6, 2079-2086 (2015) |
| [21] | Sun, C. and Liu, J.P., New stepsizes for the gradient method, accepted by Optimization Letters, 2020. Available at doi:10.1007/s11590-019-01512-y. |
| [22] | Sun, W.-Y.; Yuan, Y.-X., Optimization Theory and Methods: Nonlinear Programming (2006), Springer: Springer, New York · Zbl 1129.90002 |
| [23] | Telford, W. M.; Geldart, L. P.; Sheriff, R. E., Applied Geophysics (1990), Cambridge University Press, New York |
| [24] | Tikhonov, A. N., Inverse and Improperly Posed Problems, 3 (2009), Nauka: Nauka, Moscow |
| [25] | Wang, Y. F., Computational Methods for Inverse Problems and their Applications (2007), Higher Education Press (in Chinese), Beijing |
| [26] | Wang, Y. F.; Cao, J. J.; Yang, C. C., Recovery of seismic wavefields based on compressive sensing by an \(####\)-norm constrained trust region method and the piecewise random sub-sampling, Geophys. J. Int., 187, 199-213 (2011) |
| [27] | Yagola, A. G.; Wang, Y.; Stepanova, I. E.; Titarenko, V. N., Inverse Problems and Recommended Solutions Applications to Geophysics (2014), BINOM: BINOM, Moscow |
| [28] | Yu, P.; Wang, J. L.; Wu, J. S.; Yang, H., Research status and analysis of geophysical joint inversion, Progress Explor. Geophys., 29, 2, 87-93 (2006) |
| [29] | Yuan, Y.-X., A new stepsize for the steepest descent method, J. Comput. Math., 24, 149-156 (2006) · Zbl 1101.65067 |
| [30] | Zhang, Y. P.; Wang, Y. F., Three-dimensional gravity-magnetic cross-gradient joint inversion based on structural coupling and a fast gradient method, J. Comput. Math., 37, 6, 758-777 (2019) · Zbl 1463.86001 |
| [31] | Zhdanov, M. S., Geophysical Inverse Theory and Regularization Problems (2002), Elsevier: Elsevier, Amsterdam |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
