1887
image of Application of Hilbert‐like transforms for enhanced processing of full tensor magnetic gradient data

Abstract

ABSTRACT

Commonly, geomagnetic prospection is performed via scalar magnetometers that measure values of the total magnetic intensity. Recent developments of superconducting quantum interference devices have led to their integration in full tensor magnetic gradiometry systems consisting of planar‐type first‐order gradiometers and magnetometers fabricated in thin‐film technology. With these systems measuring directly the magnetic gradient tensor and field vector, a significantly higher magnetic and spatial resolution of the magnetic maps is yield than those produced via conventional magnetometers.

In order to preserve the high data quality in this work, we develop a workflow containing all the necessary steps for generating the gradient tensor and field vector quantities from the raw measurement data up to their integration into high­resolution, low­noise, and artefactless two‐dimensional maps of the magnetic field vector. The gradient tensor components are processed by superposition of the balanced gradiometer signals and rotation into an Earth‐centred Earth‐fixed coordinate frame. As the magnetometers have sensitivity lower than that of gradiometers and the total magnetic intensity is not directly recorded, we employ Hilbert‐like transforms, e.g., integration of the gradient tensor components or the conversion of the total magnetic intensity derived by calibrated magnetometer readings to obtain these values. This can lead to a better interpretation of the measured magnetic anomalies of the Earth's magnetic field that is possible from scalar total magnetic intensity measurements. Our conclusions are drawn from the application of these algorithms on a survey acquired in South Africa containing full tensor magnetic gradiometry data.

Loading

Article metrics loading...

/content/journals/10.1111/1365-2478.12518
2017-04-19
2020-07-06
Loading full text...

Full text loading...

References

  1. AbramowitzM. and StegunI.A.1972. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th edn. Dover.
    [Google Scholar]
  2. BroydenC.G.1970. The convergence of a class of double‐rank minimization algorithms. Journal of the Institute of Mathematics and its Applications6, 76–90.
    [Google Scholar]
  3. ClarkeJ. and BraginskiA.I.2004. The SQUID Handbook: Fundamentals and Technology of SQUIDs and SQUID Systems, Vol. 1. Weinheim, Germany: Wiley‐VCH.
    [Google Scholar]
  4. CooperG.R.J.2000. Gridding gravity data using an equivalent layer. Computers & Geosciences26(2), 227–233.
    [Google Scholar]
  5. DampneyC.N.G.1969. The equivalent source technique. Geophysics34, 39–53.
    [Google Scholar]
  6. DelaunayB.1934. Sur la sphère vide. A la mémoire de Georges Voronoï;. Bulletin de l'Académie des Sciences de l'URSS, Classe des sciences mathématiques et naturelles6, 793–800.
    [Google Scholar]
  7. Eastern Platinum Limited
    Eastern Platinum Limited2010. Technical Report Update on the Mareesburg Platinum Project in Limpopo, South Africa. http://eastplats.com/_resources/reports/Technical_Report_Update_-_Mareesburg_Project_December_2010.pdf [Retrieved February 27, 2012].
  8. FinlayC.C., MausS., BegganC.D., Bondar, T.N., ChambodutA., ChernovaT.A.et al. 2010. International geomagnetic reference field: the eleventh generation. Geophysical Journal International183, 1216–1230.
    [Google Scholar]
  9. FitzGeraldD.J. and HolsteinH.2006. Innovative data processing methods for gradient airborne geophysical data sets. The Leading Edge25, 87–92.
    [Google Scholar]
  10. GoldsteinH.1980. Classical Mechanics, 2nd edn. Reading, UK: Addison–Wesley.
    [Google Scholar]
  11. HoodP.1965. Gradient measurements in aeromagnetic surveying. Geophysics30, 891–902.
    [Google Scholar]
  12. JacobsJ.A.1987. Geomagnetism, Vol. 1. Academic Press Ltd.
    [Google Scholar]
  13. LiY. and OldenburgD.W.2010. Rapid construction of equivalent sources using wavelets. Geophysics75(3), L51–L59.
    [Google Scholar]
  14. LourencoJ.S. and MorrisonH.F.1973. Vector magnetic anomalies derived from measurements of a single component of the field. Geophysics38(2), 359–368.
    [Google Scholar]
  15. LuoY., Al‐DossaryS., MarhhonM. and AlfarajM.2003. Generalized Hilbert transform and its applications in geophysics. The Leading Edge22, 198–202.
    [Google Scholar]
  16. MastelloneD., FediM., IalongoS. and PaolettiV.2014. Volume continuation of potential fields from the minimum‐length solution: an optimal tool for continuation through general surfaces. Journal of Applied Geophysics111, 346–355.
    [Google Scholar]
  17. MausS.2010. An ellipsoidal harmonic representation of Earth's lithospheric magnetic field to degree and order 720. Geochemistry, Geophysics, Geosystems11, Q06015.
    [Google Scholar]
  18. MausS. and ManojC.2010. Geomagnetic field models for exploration and directional drilling. SEG Expanded Abstracts30, 2344–2347.
    [Google Scholar]
  19. MohanN.L., SundararajanN. and Seshagiri RaoS.V.1982. Interpretation of some two‐dimensional magnetic bodies using Hilbert transforms. Geophysics47, 376–387.
    [Google Scholar]
  20. MunschyM. and FleuryS.2011. Scalar, vector, tensor magnetic anomalies: measurement or computation? Geophysical Prospection59, 1035–1045.
    [Google Scholar]
  21. NabighianM.1972. The analytic signal of two‐dimensional magnetic bodies with polygonal cross‐section: its properties and use for automated interpretation. Geophysics37, 507–517.
    [Google Scholar]
  22. NabighianM.1984. Toward a three‐dimensional automatic interpretation of potential field data via generalized Hilbert transforms: fundamental relations. Geophysics49, 780–786.
    [Google Scholar]
  23. NabighianM. and HansenR.O.2001. Unification of Euler and Werner deconvolution in three dimensions via the generalized Hilbert transform. Geophysics66, 1805–1810.
    [Google Scholar]
  24. NelsonJ.B.1986. An alternate derivation of the three‐dimensional Hilbert transform relations from first principles. Geophysics51, 1014–1015.
    [Google Scholar]
  25. NelsonJ.B.1988. Calculation of the magnetic gradient tensor from total‐field gradient measurements and its application to geophysical interpretation. Geophysics53, 957–966.
    [Google Scholar]
  26. OlsenN., Toffner‐ClausenL., RisboT., BrauerP., MerayoJ., PrimdahlF.et al. 2001. In‐flight calibration methods used for the Ørsted mission. In: Ground and In‐Flight Space Magnetometer Calibration Techniques, ESA SP‐490 (eds A.Balogh and F.Primdahl ).
    [Google Scholar]
  27. PressW.H., FlanneryB.P., VetterlingW.T. and TeukolskyS.A.1992. Numerical Recipes in C: The Art of Scientific Computing, 2nd edn. Cambridge University Press.
    [Google Scholar]
  28. ReidA.B.2007. Euler deconvolution. In: Encyclopaedia of Geomagnetism and Paleomagnetism (eds D.Gubbins and E.Herrero‐Bervera ), pp. 263–266. Berlin, Germany: Springer.
    [Google Scholar]
  29. ReynoldsJ.M.1997. An Introduction to Applied and Environmental Geophysics. Wiley.
    [Google Scholar]
  30. Ridsdill‐SmithT.A.2000. The application of the wavelet transform to the processing of aeromagnetic data. PhD thesis, The University of Western Australia, Australia.
    [Google Scholar]
  31. SchifflerM., QueitschM., StolzR., ChwalaA., KrechW., MeyerH.‐G.et al. 2014. Calibration of SQUID vector magnetometers in full tensor gradiometry systems. Geophysical Journal International198, 954–964.
    [Google Scholar]
  32. SchneiderM., StolzR., LinzenS., SchifflerM., ChwalaA., SchulzM.et al. 2013. Inversion of geo‐magnetic full‐tensor gradiometer data. Journal of Applied Geophysics92, 57–67.
    [Google Scholar]
  33. ShinE.‐H.2005. Estimation techniques for low‐cost inertial navigation. PhD thesis, University of Calgary, Canada.
    [Google Scholar]
  34. ShinE.‐H. and El‐SheimyN.2007. Unscented Kalman filter and attitude errors of low‐cost inertial navigation systems. Navigation54(1), 1–9.
    [Google Scholar]
  35. StolzR.2006. Supraleitende Quanteninterferenzdetektor‐Gradiometer‐Systeme für den geophysikalischen Einsatz. PhD thesis, Isle Verlag, Germany.
    [Google Scholar]
  36. StolzR., ZakosarenkoV., SchulzM., ChwalaA., FritzschL., MeyerH.G.et al. 2006. Magnetic full‐tensor SQUID gradiometer system for geophysical applications. The Leading Edge25, 178–180.
    [Google Scholar]
  37. SundararajanN. and SrinivasY.1996. A modified Hilbert transform and its application to self potential interpretation. Journal of Applied Geophysics36, 137–143.
    [Google Scholar]
  38. TelfordW.M., GeldartL.P. and SheriffR.E.1990. Applied Geophysics, 2nd edn. Cambridge University Press.
    [Google Scholar]
  39. VrbaJ.1996. SQUID gradiometers in real environments. In: NATO ASI Series E: Applied Sciences, SQUIDs: Fundamentals, Fabrication and Applications (ed. H.Weinstock ). Kluwer Academic Publishers.
    [Google Scholar]
  40. ZhdanovM.S., CaiH. and WilsonG.2012. 3D inversion of SQUID magnetic tensor data. Journal of Geology and Geosciences1, 1000104.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/1365-2478.12518
Loading
/content/journals/10.1111/1365-2478.12518
Loading

Data & Media loading...

  • Article Type: Research Article
Keywords: Data processing; Magnetics; Computing aspects
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error