Skip to main content
Log in

Detecting and analyzing fault edges in sampled ground movements

  • Original Paper
  • Published:
Applied Geomatics Aims and scope Submit manuscript

Abstract

For describing height changes, ground movement models (bivariate polynomials) are used. These models approximate the ground movement measured at discrete bench marks by high-precision levelings. Because fault edges can be existent in the regions of investigation, they have to be detected and separated from the smooth ground movement. The present study proposes an algorithm that is able to detect and analyze subregions where fault edges are most likely. This algorithm is investigated based on a simulated example and tested using real sample regions: subregions containing a fault edge most likely can be identified. Furthermore, this fault edge is analyzed by revealing outliers in the approximation. If the spatial distribution and magnitude of these outliers is inconspicuous, the existence of a significant fault edge is very unlikely. Based on first considerations, the likeliness of a fault edge can even be analyzed by calculating curvature radii if using denser sampled measurements of remote sensors. These curvature radii can afterwards be used to quantify the damage-potential of the fault edge.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  • Burger W, Burge M (2008) Digital image processing: an algorithmic introduction using Java. Springer, Berlin

    Book  Google Scholar 

  • Cignoni P, Rocchini C, Scopigno R (1998) Metro: measuring error on simplified surfaces. Comp Graph Forum 17(2):167–174

    Article  Google Scholar 

  • Edelsbrunner H (1995) Smooth surfaces for multi-scale shape representation. Lect. Notes Comput Sc 1026:391–412

    Google Scholar 

  • Holst C, Eling C, Kuhlmann H (2013) Anforderungen und Grenzen von Bodenbewegungsmodellen zur Beschreibung des Bodensenkungsverhaltens im Rheinischen Braunkohlenrevier. Markscheidewesen 120(1–2):13–22

    Google Scholar 

  • Holst C, Eling C, Kuhlmann H (2013) Automatic optimization of height network configurations for detection of surface deformations. J Appl Geodesy 7(2):103–113

    Article  Google Scholar 

  • Holst C, Zeimetz P, Nothnagel A, Schauerte W, Kuhlmann H (2012) Estimation of focal length variations of a 100-m radio telescope’s main reflector by laser scanner measurements. J Surv Eng 138(3):126–135

    Article  Google Scholar 

  • Jaboyedoff M, Oppikofer T, Abellán A, Derron MH, Loye A, Metzger R, Pedrazzini A (2012) Use of lidar in landslide investigations: a review. Nat Hazards 61(1):5–28

    Article  Google Scholar 

  • Keys RG (1981) Cubic convolution interpolation for digital image processing. IEEE T Acoust Speech 29:1153–1160

    Article  Google Scholar 

  • Kratzsch H. (2008) Bergschadenskunde, 5edn. Deutscher Markscheider-Verein e.V. Bochum, Germany

    Google Scholar 

  • Lague D, Brodu N, Leroux J (2013) Accurate 3D comparison of complex topography with terrestrial laser scanner: application to the Rangitikei Canyon (n-z). ISPRS J Photogramm 82:10–26

    Article  Google Scholar 

  • Lancaster P, Salkauskas K (1986) Curve and surface fitting - an introduction. Academic Press LTD., London

    Google Scholar 

  • Pressley A (2001) Elementary differential geometry. Springer, London, Berlin, Heidelberg

    Book  Google Scholar 

  • Preusse A, Schulte R (2012) Bodenbewegungen im Rheinischen Braunkohlenrevier. In: Bergschadensforum. Elsdorf, Germany

  • Rasche H, Fenk J (1987) Senkung der Tagesoberflache durch Grundwasserentzug im Braunkohlenbergbau der Deutschen Demokratischen Republik̈. Neue Bergbautechnik 17(4):128–131

    Google Scholar 

  • Ritter GX, Wilson JN (2001) Handbook of computer vision algorithms in image algebra, 2nd edn. CRC Press, Boca Raton, London, New York

    Google Scholar 

  • Sandwell D T (1987) Biharmonic spline interpolation of geos-3 and seasat altimeter data. Geophys Res Lett 14(2):139–142

    Article  Google Scholar 

  • Scaioni M, Roncella R, Alba M (2013) Change detection and deformation analysis in point clouds: application to rock face monitoring. Photogramm Eng Remote Sens 79(5):441–456

    Article  Google Scholar 

  • Solomon C, Breckon T (2010) Fundamentals of digital image processing: a practical approach with examples in Matlab. John Wiley & Sons

  • Zeimetz P., Kuhlmann H. (2011) Use of parametric models for analyzing ground movement measurements in the rhenish lignite mining area. World of Mining—Surface and Underground 5:256–264

    Google Scholar 

  • Ziou D, Tabbone S (1998) Edge detection technique—an overview. Int J Pattern Recognit Image Anal 8:537–559

    Google Scholar 

Download references

Acknowledgments

The writers thank the anonymous reviewers for their valuable comments and suggestions that helped to significantly improve the quality of the paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Christoph Holst.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Holst, C., Kuhlmann, H. Detecting and analyzing fault edges in sampled ground movements. Appl Geomat 7, 103–114 (2015). https://doi.org/10.1007/s12518-014-0145-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12518-014-0145-9

Keywords

Navigation