Computations of secondary potential for 3D DC resistivity modelling using an incomplete Choleski conjugate-gradient method

Geophysical Prospecting

Volumn 51, Issue 6, 2003, Pages 567-577

  Wu, Xiaoping ^a,b   Xiao, Yifei ^a   Qi, Cheng ^a   Wang, Tongtong ^c  

^a UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b TU BERGAKADEMIE FREIBERG   (Germany)

^c Environmental Protection Agency of Anhui Province   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; FINITE DIFFERENCE METHOD; MATRIX ALGEBRA; PROBLEM SOLVING;

RESISTIVITY MODELING;

SEISMIC PROSPECTING;

ALGORITHM; ELECTRICAL RESISTIVITY; FINITE DIFFERENCE METHOD; THREE-DIMENSIONAL MODELING;

EID: 0141868578     PISSN: 00168025     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.1365-2478.2003.00392.x     Document Type: Article

References (31)

1. Ajiz M.A. and Jennings A. 1984. A robust incomplete Choleski conjugate gradient algorithm. International Journal of Numerical Methods in Engineering 20, 949-960.
2. Bentley J. 1986. Programming Pearls. Addison-Wesley Publishing Co., Reading, MA.
3. Coggon J.H. 1971. Electromagnetic and electrical modelling by the finite element method. Geophysics 36, 132-155.
4. Daniels J.J. 1977. Three-dimensional resistivity and induced polarization modelling using buried electrodes. Geophysics 42, 1006-1019.
5. Dey A. and Morrison H.F. 1979. Resistivity modelling for arbitrarily shaped three-dimensional structures. Geophysics 44, 753-780.
6. Dieter K., Paterson N.R. and Grant F.S. 1969. IP and resistivity type curves for three-dimensional bodies. Geophysics 34, 615-632.
7. Fox R.C., Hohmann G.W., Killpack T.J. and Rijo L. 1980. Topographic effects in resistivity and induced-polarization surveys. Geophysics 45, 75-93.
8. Fu Liangkui 1983. Lectures on Geoelectrical Prospecting, pp. 50-56. Geology Press, Beijing.
9. Hestense M. and Stiefel E. 1952. Methods of conjugate gradients for solving linear systems. Journal of Research of the National Bureau of Standards 49, 409-436.
10. Hohmann G.W. 1975. Three-dimensional induced polarization and electromagnetic modelling. Geophysics 40, 309-324.
11. Holcombe H.T. and Jiracek G.R. 1984. Three-dimensional terrain correction in resistivity surveys. Geophysics 49, 439-452.
12. Kershaw D.S. 1978. The incomplete Choleski conjugate gradient method for the iterative solution of systems of linear equations. Journal of Computational Physics 26, 43-65.
13. Lee T. 1975. An integral equation and its solution for some two- and three-dimensional problems in resistivity and induced polarization. Geophysical Journal of the Royal Astronomical Society 42, 81-95.
14. Loke M.H. and Barker R.D. 1996. Practical techniques for 3D resistivity surveys and data inversion. Geophysical Prospecting 44, 499-523.
15. Manteuffel T.A. 1980. An incomplete factorization technique for positive definite linear systems. Mathematics of Computation 34, 473-497.
16. Meijerink J.A. and van der Vorst H.A. 1977. An iterative solution method for linear systems of which the coefficient matrix is a symmetric matrix. Mathematics of Computation 31, 148-162.
17. Newman G.A. and Alumbaugh D.L. 2000. Three-dimensional magnetotelluric inversion using non-linear conjugate gradients. Geophysical Journal International 140, 410-424.
18. Okabe M. 1981. Boundary element method for the arbitrary inhomogeneities problem in electrical prospecting. Geophysical Prospecting 29, 39-59.
19. O'Neill D.J. et al. 1984. A digital linear filter for resistivity sounding with a generalized electrode array. Geophysical Prospecting 32, 105-123.
20. Oppliger G.L. 1984. Three-dimensional terrain corrections for mise-a-la-masse and magnetometric resistivity surveys. Geophysics 49, 1718-1729.
21. Papadrakakis M. and Dracopoulos M.C. 1991. Improving the efficiency of incomplete Choleski preconditionings. Communications in Applied Numerical Methods 7, 603-612.
22. Pratt D.A. 1972. The surface integral approach to the solution of the 3D resistivity problem. Bulletin of the Australian Society for Exploration Geophysics 3, 33-50.
23. Pridmore D.F., Hohmann G.W., Ward S.H. and Sill W.R. 1981. An investigation of finite element modelling for electrical and electromagnetic data in three dimensions. Geophysics 46, 1009-1024.
24. Scribe H. 1981. Computations of the electrical potential in the three-dimensional structure. Geophysical Prospecting 29, 790-802.
25. Smith J.T. 1996. Conservative modelling of 3D electromagnetic fields, Part II: biconjugate gradient solution as an accelerator. Geophysics 61, 1319-1324.
26. Spitzer K. 1995. A 3D finite difference algorithm for DC resistivity modelling using conjugate gradient methods. Geophysical Journal International 123, 903-914.
27. Varga R.S. 1960. Factorization and normalized iterative methods. In: Boundary Problems in Differential Equations (ed. R.E. Langer), pp. 121-142. University of Wisconsin Press, Madison, WI.
28. Xu S.Z., Guo Z.C. and Zhao S.K. 1988. An integral formulation for three-dimensional terrain modelling for resistivity surveys. Geophysics 53, 546-552.
29. Zhang J., Mackie R.L. and Madden T.R. 1995. Three-dimensional resistivity forward modelling and inversion using conjugate gradients. Geophysics 60, 1313-1325.
30. Zhao S.K. and Yedlin M.J. 1996. Some refinements on the finite-difference method for 3D DC resistivity modelling. Geophysics 61, 1301-1307.
31. Zhou B. and Greenhalgh S.A. 2001. Finite element three-dimensional direct current resistivity modelling: accuracy and efficiency considerations. Geophysical Journal International 145, 679-688.