Regularized derivatives of potential fields and their role in semi‐automated interpretation methods

References

1. BarbosaV.C.F., SilvaJ.B.C. and MedeirosW.E.1999. Stability analysis and improvement of structural index estimation in Euler deconvolution. Geophysics64, 48–60.
   [Google Scholar]
2. BathM.1968. Mathematical Aspects of Seismology . Elsevier.
   [Google Scholar]
3. BerdichevskiM.N. and DmitrievV.I.2002. Magnetollurics in the Context of the Theory of Ill‐posed Problems . SEG.
   [Google Scholar]
4. CooperR.J.2004. Euler deconvolution applied to potential field gradients. Exploration Geophysics35, 165–170.
   [Google Scholar]
5. CooperG.R.J. and CowanD.R.2006. Enhancing potential field data using filters based on the local phase. Computers and Geosciences32, 1585–1591.
   [Google Scholar]
6. DmitrievV.I., MorozovV.A., ZhdanovM.S., NikitinA.A., BrusnetzovN.P., PavlovB.M. et al . 1990. Numerical Mathematics and Techniques in Exploration Geophysics . Nedra, Moscow (in Russian).
   [Google Scholar]
7. FediM. and FlorioG.2001. Detection of potential fields source boundaries by enhanced horizontal derivative method. Geophysical Prospecting49, 40–58. doi:DOI: 10.1046/j.1365-2478.2001.00235.x
   [Google Scholar]
8. FitzGeraldD., ReidA. and McInerneyP.2004. New discrimination techniques for Euler deconvolution. Computers and Geosciences30, 461–469.
   [Google Scholar]
9. GuspíF. and IntrocasoB.2000. A sparse spectrum technique for gridding and separating potential field anomalies. Geophysics65, 1154–1161.
   [Google Scholar]
10. HansenP.C.1994. Regularization tools. A MatLab package for analysis and solution of discrete ill‐posed problems. Numerical Algorithms6, 1–35.
    [Google Scholar]
11. HansenP.C.1998. Rank‐deficient and Discrete Ill‐posed Problems: Numerical Aspects of Linear Inversion . SIAM, Philadelphia .
    [Google Scholar]
12. HartmanR.R., TeskeyD.J. and FriedbergJ.1971. A system for rapid digital aeromagnetic interpretation. Geophysics36, 891–918.
    [Google Scholar]
13. MikhailovV., GaldeanoA., DiamentM., GvishianiA., AgayanS., BogoutdinovS. et al . 2006. Application of artificial intelligence for Euler solutions clustering. Geophysics68, 168–180.
    [Google Scholar]
14. MushayandebvuM.F., Van DrielP., ReidA.B. and FairheadJ.D.2001. Magnetic source parameters of two‐dimensional structures using extended Euler deconvolution. Geophysics66, 814–823.
    [Google Scholar]
15. MushayandebvuM.F., LesurV., ReidA.B. and FairheadJ.D.2004. Grid Euler deconvolution with constraints for 2D structures. Geophysics69, 489–496.
    [Google Scholar]
16. NabighianM.N.1972. The analytic signal of two‐dimensional magnetic bodies with polygonal cross‐section: Its properties and use for automated anomaly interpretation. Geophysics37, 507–517.
    [Google Scholar]
17. NabighianM.N.1974. Additional comments on the analytic signal of two‐dimensional magnetic bodies with polygonal cross‐section. Geophysics39, 85–92.
    [Google Scholar]
18. NabighianM.N.1984. Toward a three‐dimensional automatic interpretation of potential field data via generalised Hilbert transforms: Fundamental relations. Geophysics49, 780–786.
    [Google Scholar]
19. NabighianM.N. and HansenR.O.2001. Unification of Euler and Werner deconvolution in three dimensions via the generalized Hilbert transform. Geophysics66, 1805–1810.
    [Google Scholar]
20. PawlowskiR.S. and HansenR.O.1990. Gravity anomaly separation by Wiener filtering. Geophysics55, 539–548.
    [Google Scholar]
21. PortniaguineP. and ZhdanovM.1999. Focusing geophysical inversion images. Geophysics64, 874–887.
    [Google Scholar]
22. PortniaguineP. and ZhdanovM.2002. 3‐D magnetic inversion with data compression and image focusing. Geophysics67, 1532–1541.
    [Google Scholar]
23. ReidA.B., AllsopJ.M., GranserH., MilletA.J. and SomertonI.W.1990. Magnetic interpretation in three dimensions using Euler deconvolution. Geophysics55, 80–91.
    [Google Scholar]
24. RoestW.R., VerhoefJ. and PilkingtonM.1992. Magnetic interpretation using the 3D analytic signal. Geophysics57, 116–125.
    [Google Scholar]
25. SacchiM.D. and UlrychT.J.1996. Estimation of the discrete Fourier transform, a linear inversion approach. Geophysics61, 1128–1136.
    [Google Scholar]
26. SalemA. and RavatD.2003. A combined analytic signal and Euler method (AN‐EUL) for the automatic interpretation of magnetic data. Geophysics68, 1952–1961.
    [Google Scholar]
27. SalemA., WilliamsS., FairheadJ.D., RavatD. and SmithR.2007. Tilt‐depth method: A simple depth estimation method using first‐order magnetic derivatives. The Leading Edge26, 1502–1505.
    [Google Scholar]
28. ThompsonD.T.1982: EULDPH. A new technique for making computer‐assisted depth estimates from magnetic data. Geophysics47, 31–37.
    [Google Scholar]
29. TikhonovA.N. and ArseninB.J.1977. Solutions of Ill‐posed Problems . John Wiley & Sons.
    [Google Scholar]
30. TikhonovA.N. and GlaskoV.B.1965. Application of the regularization method to nonlinear problems. Zh. vychislit. matem. i matem. fiz.5, 463–473.
    [Google Scholar]
31. TikhonovA.N., GlaskoV.B., LitvinenkoO.K. and MelichovV.P.1968. Analytic continuation of a potential in the direction of disturbing masses by the regularization method. Izv., Earth Physics12, 30–48 (in Russian; English translation: 738–747).
    [Google Scholar]
32. TroutmanJ.L.1983. Variational Calculus with Elementary Convexity . Springer
    [Google Scholar]
33. WijnsC., PerezC. and KowalczykP.2005. Theta Map: Edge detection in magnetic data. Geophysics70, L39–L43.
    [Google Scholar]
34. ZhdanovM.S.2002. Geophysical Inverse Theory and Regularization Problems . Elsevier.
    [Google Scholar]