Constraining Euler Deconvolution Solutions Through Combined Tilt Derivative Filters

Abstract

Local phase filters as the tilt derivative (TDR) and the horizontal tilt derivative (TDX) are extensively used to interpret magnetic data. We use two combinations of these filters, namely TDR − TDX and TDR + TDX, to design a constraining mask that guides the Euler deconvolution moving data window. The TDR − TDX filter produces sharp peaks over the centers of the sources, while the TDR + TDX filter generates plateaus over them. Motivated by previous approaches that make use of the Laplacian filter or the analytic signal to constrain the Euler deconvolution window, we compute the solutions for windows centered at points that (1) have positive values of TDR − TDX and (2) are contained in the plateaus of TDR + TDX. The use of both criteria improves the selection of source-related points while reducing the number of spurious ones. Our method is tested in synthetic anomalies due to interfering dike-like sources and field data from southeast Brazil. The experiments show that the use of a constraining mask based on combined tilt filters produce Euler solutions that are more contiguous and less sensitive to noise than the traditional located-Euler deconvolution.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

References

  1. Aziz, A. M., Sauck, W. A., Shendi, E.-A. H., Rashed, M. A., & El-Maksoud, M. A. (2013). Application of analytic signal and Euler deconvolution in archaeo-magnetic prospection for buried ruins at the ancient city of Pelusium, NW Sinai, Egypt: a case study. Surveys in Geophysics, 34(4), 395–411.

    Article  Google Scholar 

  2. Barbosa, V. C. F., Silva, J. B. C., & Medeiros, W. E. (1999). Stability analysis and improvement of structural index estimation in Euler deconvolution. Geophysics, 64(1), 48–60.

    Article  Google Scholar 

  3. Blakely, R. J. (1996). Potential theory in gravity and magnetic applications. Cambridge: Cambridge University Press.

    Google Scholar 

  4. Blakely, R. J., & Simpson, R. W. (1986). Approximating edges of source bodies from magnetic or gravity anomalies. Geophysics, 51(7), 1494–1498.

    Article  Google Scholar 

  5. Bongiolo, A. B. S., Souza, J., Ferreira, F. J. F., & Castro, L. G. (2013). GRAV MAG PRISM: a matlab/octave program to generate gravity and magnetic anomalies due to rectangular prismatic bodies. Brazilian Journal of Geophysics, 31(3), 347–363.

    Article  Google Scholar 

  6. Castro, F. R., Oliveira, S. P., de Souza, J., & Ferreira, F. J. F. (2018). Combining tilt derivative filters: new approaches to enhance magnetic anomalies. Brazilian Journal of Geophysics, 36(3), 1–9.

    Article  Google Scholar 

  7. Catalán, M., & Martín Davila, J. (2003). A magnetic anomaly study offshore the Canary Archipelago. Marine Geophysical Researches, 24(1), 129–148.

    Article  Google Scholar 

  8. Cooper, G. R. J., & Cowan, D. R. (2006). Enhancing potential field data using filters based on the local phase. Computers and Geosciences, 32(10), 1585–1591.

    Article  Google Scholar 

  9. CPRM. (2011). Aerogeophysical project Paraná-Santa Catarina: survey and processing of magnetometric and gamma-ray spectrometric data. Lasa Prospecções: Technical Report (In Portuguese).

  10. De Almeida, F. F. M. (1986). Regional distribution and tectonic relations of the post-palaeozoic magmatism in Brazil. Brazilian Journal of Geosciences, 16(4), 325–349 (In Portuguese).

    Google Scholar 

  11. Dentith, M., & Mudge, S. T. (2014). Geophysics for the mineral exploration geoscientist. Cambridge: Cambridge University Press.

    Google Scholar 

  12. Ebbing, J., Skilbrei, J. R., & Olesen, O. (2007). Insights into the magmatic architecture of the Oslo graben by petrophysically constrained analysis of the gravity and magnetic field. Journal of Geophysical Research Solid Earth, 112(B4), B04404.

    Google Scholar 

  13. Eshaghzadeh, A., Dehghanpour, A., & Kalantari, R. A. (2018). Application of the tilt angle of the balanced total horizontal derivative filter for the interpretation of potential field data. Bollettino di Geofisica Teorica ed Applicata, 59(2), 161–178.

    Google Scholar 

  14. Fairhead, J. D., Bennett, K. J., Gordon, D. R. H., & Huang, D. (1994). Euler: Beyond the “black box”. In 64th Annual International Meeting, Expanded Abstracts (pp. 422–424). SEG.

  15. FitzGerald, D., Reid, A., & McInerney, P. (2004). New discrimination techniques for Euler deconvolution. Computers and Geosciences, 30(5), 461–469.

    Article  Google Scholar 

  16. Florio, G., Fedi, M., & Pasteka, R. (2006). On the application of Euler deconvolution to the analytic signal. Geophysics, 71(6), L87–L93.

    Article  Google Scholar 

  17. Gomes, C. B., Azzone, R. G., Ruberti, E., Vasconcelos, P. M., Sato, K., & Rojas, G. E. E. (2018). New age determinations for the Banhadão and Itapirapuã complexes in the Ribeira Valley, southern Brazil. Brazilian Journal of Geology, 48(2), 403–414.

    Article  Google Scholar 

  18. Keating, P., & Pilkington, M. (2004). Euler deconvolution of the analytic signal and its application to magnetic interpretation. Geophysical Prospecting, 52(3), 165–182.

    Article  Google Scholar 

  19. Machado Junior, D. L. (2000). Structural conditioning and tectonic context of the Guapiara lineament. Ph.D. thesis, Universidade de São Paulo, São Paulo (In Portuguese).

  20. McGrath, P. H., & Hood, P. J. (1970). The dipping dike case: A computer curve-matching method of magnetic interpretation. Geophysics, 35(5), 831–848.

    Article  Google Scholar 

  21. Melo, F. F., Barbosa, V. C. F., Uieda, L., Oliveira, V. C, Jr., & Silva, J. B. C. (2013). Estimating the nature and the horizontal and vertical positions of 3D magnetic sources using Euler deconvolution. Geophysics, 78(6), J87–J98.

    Article  Google Scholar 

  22. Miller, H. G., & Singh, V. (1994). Potential field tilt—a new concept for location of potential field sources. Journal of Applied Geophysics, 32(2–3), 213–217.

    Article  Google Scholar 

  23. Nelson, J. B. (1988). Comparison of gradient analysis techniques for linear two-dimensional magnetic sources. Geophysics, 53(8), 1088–1095.

    Article  Google Scholar 

  24. Olesen, O., Smethurst, M. A., Torsvik, T. H., & Bidstrup, T. (2004). Sveconorwegian igneous complexes beneath the Norwegian-Danish basin. Tectonophysics, 387(1), 105–130.

    Article  Google Scholar 

  25. Pawlowski, J., Lewis, R., Dobush, T., & Valleau, N. (1995). An integrated approach for measuring and processing geophysical data for the detection of unexploded ordnance. In Symposium on the Application of Geophysics to Engineering and Environmental Problems (pp. 965–977). SEG.

  26. Reid, A. B. (1995). Euler deconvolution: Past, present, and future—a review. In 65th Annual International Meeting, Expanded Abstracts (pp. 272–273). SEG.

  27. Reid, A. B., Allsop, J. M., Granser, H., Millett, A. J., & Somerton, I. W. (1990). Magnetic interpretation in three dimensions using Euler deconvolution. Geophysics, 55(1), 80–91.

    Article  Google Scholar 

  28. Reid, A. B., Ebbing, J., & Webb, S. J. (2014). Avoidable Euler errors—the use and abuse of Euler deconvolution applied to potential fields. Geophysical Prospecting, 62(5), 1162–1168.

    Article  Google Scholar 

  29. Roest, W. R., Verhoef, J., & Pilkington, M. (1992). Magnetic interpretation using the 3-D analytic signal. Geophysics, 57(1), 116–125.

    Article  Google Scholar 

  30. Ruppel, A., Jacobs, J., Eagles, G., Läufer, A., & Jokat, W. (2018). New geophysical data from a key region in east Antarctica: Estimates for the spatial extent of the Tonian Oceanic Arc Super Terrane (TOAST). Gondwana Research, 59, 97–107.

    Article  Google Scholar 

  31. Salem, A., & Ravat, D. (2003). A combined analytic signal and Euler method (AN-EUL) for automatic interpretation of magnetic data. Geophysics, 68(6), 1952–1961.

    Article  Google Scholar 

  32. Santos, T. A. & de Sousa, M. A. (2003). Euler deconvolution applied to potential field data from the Parnaíba basin, Brazil. In 8th International Congress of the Brazilian Geophysical Society (pp. 1–4). Brazilian Geophysical Society.

  33. Silva, J. B. C., & Barbosa, V. C. F. (2003). 3D Euler deconvolution: Theoretical basis for automatically selecting good solutions. Geophysics, 68(6), 1962–1968.

    Article  Google Scholar 

  34. Thompson, D. T. (1982). EULDPH: A new technique for making computer-assisted depth estimates from magnetic data. Geophysics, 47(1), 31–37.

    Article  Google Scholar 

  35. Williams, S., Fairhead, J. D., & Flanagan, G. (2003). Grid based Euler deconvolution: Completing the circle with ’2D constrained Euler’. In 73th Annual International Meeting, Expanded Abstracts (pp. 576–579). SEG.

  36. Williams, S. E., Fairhead, J. D., & Flanagan, G. (2005). Comparison of grid Euler deconvolution with and without 2D constraints using a realistic 3D magnetic basement model. Geophysics, 70(3), L13–L21.

    Article  Google Scholar 

Download references

Acknowledgements

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior/Brasil (CAPES) - Finance Code 001, through Programa de Pós-Graduação em Geologia/UFPR. The authors thank Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq, grants 313100/2017-9, 113897/2018-9, and 303826/2018-5) and Companhia de Pesquisa de Recursos Minerais (CPRM, Geological Survey of Brazil) for permission to use the aeromagnetic data.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Saulo P. Oliveira.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Castro, F.R., Oliveira, S.P., de Souza, J. et al. Constraining Euler Deconvolution Solutions Through Combined Tilt Derivative Filters. Pure Appl. Geophys. (2020). https://doi.org/10.1007/s00024-020-02533-w

Download citation

Keywords

  • Potential methods
  • Euler deconvolution
  • tilt derivative
  • magnetic anomaly