3D joint inversion of gravity and magnetic data using Gramian constraint and L1-norm stabilizer

Authors

Abstract

The inversion of potential field data, gravity and magnetic, is a non-unique problem. An efficient approach to reduce the non-uniqueness of the problem, and to produce more reliable subsurface models, is based on the joint inversion of these datasets. This means gravity and magnetic data are simultaneously inserted into an inversion algorithm and, then, by relying on direct or indirect parameter interdependence, joint inversion can restrict the model space and produce results that satisfy the datasets and cross-linked characteristics of the model parameters. Here, we apply the joint inversion of gravity and magnetic data using Gramian constraints, which are based on the minimization of the determinant of the Gram matrix of a system of different model parameters. Application of the Gramian constraint enforces the linear relationships between the different model parameters, and/or their transforms. In fact, the joint inversion using Gramian constraints does not require a priori knowledge of the correlation between different model parameters, and instead provides this correlation during the inversion process, which is an important advantage for the algorithm. Furthermore, to produce sparse models with sharp boundaries, the L1-norm stabilizer is used in the presented algorithm. We applied the joint inversion algorithm on synthetic models and real data case.

Keywords

References

Blakely, R. J., 1996, Potential Theory in Gravity and Magnetic Applications, Cambridge University Press, Cambridge.
Gallardo, L. A., and M. A. Meju., 2004, Joint two-dimensional DC resistivity and seismic travel time inversion with cross-gradients constraints: Journal of Geophysical Research, 109, B03311.
Hansen, P. C., 1992, Analysis of discrete ill-posed problems by means of the L-curve, SIAM Review, 34, 561-580.
Li, Y., and Oldenburg, D. W., 1996, 3-D inversion of magnetic data, Geophysics, 61, 394–408.
Li, Y., and Oldenburg, D. W., 1998, 3D inversion of gravity data, Geophysics, 63, 109–19.
Lin, W and Zhdanov, M.S., 2018, Joint multinary inversion of gravity and magnetic data using Gramian constraints, Geophys, J. Int,  (2018) 215, 1540–1557.
Liu, S., Baniamerian, J and Fedi, M., 2020, Imaging Methods Versus Inverse Methods: An Option or An Alternative?, IEEE Transaction on Geoscience and Remote Sensing PP (99): 1-11.
Nabighian, M. N., Ander, M. E., Grauch, V. J. S., Hansen, R. O., LaFehr, T. R., Li, Y., Pearson, W. C., Peirce, J. D. and Ruder, M.E., 2005, Historical development of the gravity method in exploration, Geophysics, 70 (6), pp. 63ND-89ND.
Portniaguine, O., and Zhdanov, M. S., 1999, focusing geophysical inversion images, Geophysics, 64, 874–87.
Vatankhah, S., Renaut, R. A and Ardestani, V. E., 2017,  3D Projected L1 inversion of gravity data using truncated unbiased predictive risk estimator for regularization parameter estimation. Geophysical Journal International, 210 (3), 1872-1887.
Vatankhah, S., Liu, S., Renaut, R. A., Hu, Xi and Baniamerian, J., 2020, Improving the use of the randomized singular value decomposition for the inversion of gravity and magnetic data, Geophysics, 85, G93- G107.
Zhdanov, M. S., 2002, Geophysical Inverse Theory and Regularization Problems: Elsevier Press.
Zhdanov, M. S., Gribenko, A., and Wilson, G., 2012, Generalized joint inversion of multimodal geophysical data using Gramian constraints, Geophys, Res, Lett, 39 (9).
Volume 7, Issue 2
January 0
Pages 185-200

Files

Share

How to cite

Statistics