Fast inversion of large-scale magnetic data using wavelet transforms and a logarithmic barrier method

Geophysical Journal International

Volumn 152, Issue 2, 2003, Pages 251-265

  Li, Yaoguo ^a   Oldenburg, Douglas W ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

3 D; Conjugate gradients; Interior point method; Inversion; Magnetic data; Positivity; Wavelet transform

Indexed keywords

DATA INVERSION; EQUATION; MAGNETIC SUSCEPTIBILITY; MATHEMATICAL CONCEPT; OPTIMIZATION; WAVELET ANALYSIS;

EID: 0037325111     PISSN: 0956540X     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1365-246X.2003.01766.x     Document Type: Article

References (18)

1. Beylkin, G., Coifman, R. & Rokhlin, V., 1991. Fast wavelet transforms and numerical algorithms I, Comm. Pure and Appl. Math., 44, 141-183.
2. Beylkin, G., 1992. On the fast algorithm for multiplication of functions in the wavelet bases. International Conference on Wavelets and applications, Toulouse. Proceedings, eds Meyer Y. & Roques S., Editions Frontieres.
3. Beylkin, G., 1993. Wavelets and fast numerical algorithms, Proceedings of Symposia in Applied Mathematics, 47, 89-117.
4. Daubechies, I., 1988. Orthonormal bases of compactly supported wavelets., Comm. Pure and Appl. Math., 41, 909-996.
5. Daubechies, I., 1992. Ten lectures on wavelets. SIAM, Philadelphia, PA.
6. Gill. P.E., Murray. W., Ponceleon, D.B. & Saunders, M., 1991. Solving reduced KKT systems in barrier methods for linear and quadratic programming. Technical Report SOL 91-7, Stanford University, Stanford, CA.
7. Golub, G.H., Heath, M. & Wahba, G., 1979. Generalized cross-validation as a method for choosing a good ridge regression parameter. Technometrics. 21, 215-223.
8. Harten, A. & Yad-Shalom, I., 1994. Fast multiresolution algorithms for matrix-vector multiplication, SIAM J. Numer. Anal., 31, 1191-1218.
9. Hutchinson, M.F., 1990. A stochastic estimator of the trace of the influence matrix for Laplacian smoothing splines, Communications in Statistics, Simulation and Computation. 19, 443-450.
10. Li, Y. & Oldenburg, D.W., 1996. 3D inversion of magnetic data, Geophysics, 61, 394-408.
11. Li, Y. & Oldenburg, D.W., 2000. Joint inversion of surface and three-component borehole magnetic data. Geophysics, 65, 540-552.
12. Mallat, S., 1989. A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans. PAMI. 11, 674-693.
13. Meyer, Y., 1993. Wavelets: Algorithms and applications, SIAM, Philadelphia, PA.
14. Oldenburg, D. W., Li, Y. & Ellis, R.G., 1997. Inversion of geophysical data over a copper-gold porphyry deposit: A case history for Mt Milligan. Geophysics. 62, 1419-1431.
15. Pilkington, M., 1997. 3-D magnetic imaging using conjugate gradients. Geophysics, 62, 1132-1142.
16. Saunders. M., 1995. Cholesky-based methods for sparse least squares: The benefits of regularization Technical Report SOL 95-1. Stanford University, Stanford, CA.
17. Wahba, G., 1990. Spline models for observational data, CBMS-NSF, regional Conference Series in Applied mathematics, 59, SIAM, Philadelphia, PA.
18. Wright, S.J., 1997. Primal-dual interior-point methods, SIAM, Philadelphia. PA.