Amplitude-balanced curvatures of geophysical data


Many different fields, such as terrain analysis, medical imaging, and of course the Geosciences, have used the curvature of their data for many years to enhance subtle details. Despite the fact that the calculations of the curvature are based on second-order derivatives of the data and are therefore sensitive to noise, curvature has proved itself to be a useful aid to the interpretation of the data. Although there are many different curvatures that can be computed from a 2D (map) dataset, they all have a response that depends on the amplitude of the data, so that small-amplitude features can be missed. This manuscript shows how amplitude-balanced curvatures can be computed, and the technique is demonstrated on synthetic data and also on gravity and magnetic datasets from South Africa.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Data availability

The gravity and magnetic data used belongs to the Council for Geoscience, Pretoria.


  1. Al-Dossary S, Marfurt KJ (2006) 3D volumetric multispectral estimates of reflector curvature and rotation. Geophysics 71(5):P41–P51

    Article  Google Scholar 

  2. Blakely RJ (1995) Potential theory in gravity and magnetic applications. Cambridge University Press 441pp

  3. Blumentritt CH, Marfurt KJ, Sullivan EC (2006) Volume-based curvature computations illuminate fracture orientations — Early to mid-Palaeozoic, Central Basin Platform, west Texas. Geophysics 71:159–166

    Article  Google Scholar 

  4. Cevallos C, Kovac P, Lowe S (2013) Application of curvatures to airborne gravity gradient data in oil exploration. Geophysics 78(4):G81–G88

    Article  Google Scholar 

  5. Cooper GRJ, Cowan DR (2009) Terracing potential field data. Geophys Prospect 57:1057–1061

    Article  Google Scholar 

  6. Eales HV (2001) A first introduction to the geology of the Bushveld complex and those aspects of geology that relate to it. Council for Geoscience, Pretoria 84pp

    Google Scholar 

  7. Gonzalez RC, Woods RE (2008) Digital image processing, 3rd edn. Pearson 976pp

  8. Lee MD, Morris M, Leblanc G, Harris J (2013) Curvature analysis to differentiate magnetic sources for geologic mapping. Geophys Prospect 61:572–585

    Article  Google Scholar 

  9. Li X (2015) Curvature of a geometric surface and curvature of gravity and magnetic anomalies. Geophysics 80(1):G15–G26

    Article  Google Scholar 

  10. Miller HG, Singh V (1994) Potential field tilt – a new concept for location of potential field sources. J Appl Geophys 32:213–217

    Article  Google Scholar 

  11. Mitasova H, Jarosalav H (1993) Interpolation by regularized spline with tension: II. Application to terrain modelling and surface geometry analysis. Math Geol 25:657–669

    Article  Google Scholar 

  12. Phillips JD, Hansen RO, Blakely RJ (2007) The use of curvature in potential-field interpretation. Explor Geophys 38:111–119

    Article  Google Scholar 

  13. Roberts A (2001) Curvature attributes and their applications to 3D interpreted horizons. First Break 19(2):85–100

    Article  Google Scholar 

  14. Therriault A, Grieve RAF, Reimold WU (1997) Original size of the Vredefort structure: implications for the geological evolution of the Witwatersrand Basin. Meteorit Planet Sci 32:71–77

    Article  Google Scholar 

Download references


The Council for Geoscience, Pretoria, are thanked for permission to use the data that is shown in Figs. 3 and 4. The reviewers and editors are thanked for their constructive comments which have improved the manuscript.

Code availability

The code for this project is not available.

Author information



Corresponding author

Correspondence to Gordon Robert John Cooper.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Responsible Editor: Narasimman Sundararajan

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Cooper, G.R.J. Amplitude-balanced curvatures of geophysical data. Arab J Geosci 14, 280 (2021).

Download citation


  • Geophysics
  • Aeromagnetics
  • Curvature
  • Tilt angle