Mathematical Geology

, Volume 37, Issue 4, pp 357–372 | Cite as

Artificial Lineaments in Digital Terrain Modelling: Can Operators of Topographic Variables Cause Them?

  • Igor V. Florinsky


Digital terrain modeling is widely used in geological studies. In some cases, orthogonal and diagonal linear patterns appear on maps of local topographic variables. These patterns may be both portrayals of geological structures and artefacts. Some researchers speculated that possible anisotropy of operators of local topographic variables might be a cause of these artefacts. Using a principle for testing derivative operators in image processing, we gave proof to isotropy (rotation invariability) of operators of a majority of local topographic attributes of the complete system of curvatures (i.e., slope gradient, horizontal curvature, vertical curvature, mean curvature, Gaussian curvature, accumulation curvature, ring curvature, unsphericity curvature, difference curvature, minimum curvature, maximum curvature, horizontal excess curvature, and vertical excess curvature). Rotating an elevation function about z-axis and then applying these operators cannot lead to variations in both values of the topographic variables and patterns in their maps, comparing with results of applying these operators to an unrotated elevation function. This demonstrates that linear artefacts with preferable directions in maps of the topographic attributes specified cannot be caused by intrinsic properties of their operators. Other possible sources for false linear patterns in maps of topographic variables are briefly discussed: (a) errors in the compilation of digital elevation models (DEMs), (b) grid geometry of digital terrain models (DTMs), (c) errors in DEM interpolation, (d) imperfection of algorithms for DTM derivation, and (e) aliasing errors.

Key Words

curvature surface digital terrain modeling derivative lineament artefact 


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  1. Belonin, M. D., and Zhukov, I. M., 1968, Geometrical properties of surfaces of the Alexeevskoye uplift, the Kuibyshev Region, in Romanova, M. A., ed., Problems of mathematical geology: Nauka, Leningrad, p. 194–207 (in Russian).Google Scholar
  2. Brown, D. G., and Bara, T. J., 1994, Recognition and reduction of systematic error in elevation and derivative surfaces from 7.5-minute DEMs: Photogramm. Eng. Remote Sens., v. 60, no. 2, p. 189–194.Google Scholar
  3. Chorowicz, J., Kim, J., Manoussis, S., Rudant, J., Foin, P., and Veillet, I., 1989, A new technique for recognition of geological and geomorphological patterns in digital terrain models: Remote Sens. Environ., v. 29, no. 3, p. 229–239.CrossRefGoogle Scholar
  4. Chorowicz, J., Dhont, D., and Gündoğdu, N., 1999, Neotectonics in the eastern North Anatolian fault region (Turkey) advocates crustal extension: Mapping from SAR ERS imagery and digital elevation model: J. Struct. Geol., v. 21, no. 5, p. 511–532.Google Scholar
  5. Courant, R., and John, F., 1974, Introduction to calculus and analysis, Vol. 2: Wiley, New York, 954 p.Google Scholar
  6. Declercq, F. A. N., 1996, Interpolation methods for scattered sample data: Accuracy, spatial patterns, processing time: Cartogr. Geogr. Inform. Syst., v. 23, no. 3, p. 128–144.Google Scholar
  7. Douglas, R. J. W., 1974, Tectonics, in Fremlin, G., ed., The national atlas of Canada, 4th rev. edn.: Department of Energy, Mines and Resources and Information Canada, Ottawa, p. 29–30.Google Scholar
  8. Fikhtengolts, G. M., 1966, A course in differential and integral calculus, 6th edn., Vol. 1: Nauka, Moscow, 607 p. (in Russian).Google Scholar
  9. Florinsky, I. V., 1993, Analysis of digital elevation models for recognition of linear structures of the land surface: Unpublished Ph.D. Thesis, Institute of Soil Science and Photosynthesis, Russian Academy of Sciences, Pushchino, 133 p. (in Russian).Google Scholar
  10. Florinsky, I. V., 1996, Quantitative topographic method of fault morphology recognition: Geomorphology, v. 16, no. 2, p. 103–119.CrossRefGoogle Scholar
  11. Florinsky, I. V., 1998a, Accuracy of local topographic variables derived from digital elevation models: Int. J. Geogr. Inform. Sci., v. 12, no. 1, p. 47–61.CrossRefGoogle Scholar
  12. Florinsky, I. V., 1998b, Combined analysis of digital terrain models and remotely sensed data in landscape investigations: Prog. Phys. Geogr., v. 22, no. 1, p. 33–60.CrossRefGoogle Scholar
  13. Florinsky, I. V., 1998c, Derivation of topographic variables from a digital elevation model given by a spheroidal trapezoidal grid: Int. J. Geogr. Inform. Sci., v. 12, no. 8, p. 829–852.CrossRefGoogle Scholar
  14. Florinsky, I. V., 2000, Relationships between topographically expressed zones of flow accumulation and sites of fault intersection: Analysis by means of digital terrain modelling: Environ. Modell. Softw., v. 15, no. 1, p. 87–100.Google Scholar
  15. Florinsky, I. V., 2002, Errors of signal processing in digital terrain modelling: Int. J. Geogr. Inform. Sci., v. 16, no. 5, p. 475–501.CrossRefGoogle Scholar
  16. Florinsky, I. V., Grokhlina, T. I., and Mikhailova, N. L., 1995, LANDLORD 2.0: The software for analysis and mapping of geometrical characteristics of relief: Geodesiya Cartogr., no. 5, p. 46–51 (in Russian).Google Scholar
  17. Gesch, D. B., Verdin, K. L., and Greenlee, S. K., 1999, New land surface digital elevation model covers the Earth: Eos, v. 80, no. 6, p. 69–70.Google Scholar
  18. Gosteva, T. S., Patrakova, V. S., and Abramkina, V. A., 1983, Determination of laws controlling spatial distribution of ring structures on the basis of trend-analysis of the topography: Geol. Geophys., no. 8, p. 72–79 (in Russian, with English abstract).Google Scholar
  19. Hunter, G. J., and Goodchild, M. F., 1995, Dealing with error in spatial databases: A simple case study: Photogramm. Eng. Remote Sens., v. 61, no. 5, p. 529–537.Google Scholar
  20. Ioffe, A. I., and Kozhurin, A. I., 1997, Active tectonics and geoecological zoning of Moscow Region: Bull. Moscow Soc. Naturalists, Geol. Ser., v. 72, no. 5, p. 31–35 (in Russian, with English abstract).Google Scholar
  21. Johansson, M., 1999, Analysis of digital elevation data for palaeosurfaces in south-western Sweden: Geomorphology, v. 26, no. 4, p. 279–295.CrossRefGoogle Scholar
  22. Katterfeld, G. N., and Charushin, G. V., 1973, General grid systems of planets: Mod. Geol., v. 4, no. 4, p. 253–287.Google Scholar
  23. Kühni, A., and Pfiffner, O. A., 2001, The relief of the Swiss Alps and adjacent areas and its relation to lithology and structure: Topographic analysis from a 250-m DEM: Geomorphology, v. 41, no. 4, p. 285–307.Google Scholar
  24. Liang, C., and Mackay, D. S., 2000, A general model of watershed extraction and representation using globally optimal flow paths and up-slope contributing areas: Int. J. Geogr. Inform. Sci., v. 14, no. 4, p. 337–358.CrossRefGoogle Scholar
  25. Lisle, R. J., 1994, Detection of zones of abnormal strains in structures using Gaussian curvature analysis: Am. Assoc. Petrol. Geol. Bull., v. 78, no. 12, p. 1811–1819.Google Scholar
  26. McCullagh, M. J., 1988, Terrain and surface modelling systems: Theory and practice: Photogramm. Rec., v. 12, no. 72, p. 747–779.Google Scholar
  27. Moore, I. D., Grayson, R. B., and Ladson, A. R., 1991, Digital terrain modelling: A review of hydrological, geomorphological and biological applications: Hydrol. Process., v. 5, no. 1, p. 3–30.Google Scholar
  28. Morris, K., 1991, Using knowledge-base rules to map the three-dimensional nature of geological features: Photogramm. Eng. Remote Sens., v. 57, no. 9, p. 1209–1216.Google Scholar
  29. Natural Resources Canada, 1997, Canadian Digital Elevation Data: Standards and Specifications: Centre for Topographic Information, Sherbrooke, 11 p.Google Scholar
  30. NOAA, 1988, Digital Relief of the Surface of the Earth: NOAA, National Geophysical Data Center, Boulder, Data Announcement 88-MGG-02.Google Scholar
  31. Pike, R. J., 2000, Geomorphometry—diversity in quantitative surface analysis: Prog. Phys. Geogr., v. 24, no. 1, p. 1–20.CrossRefGoogle Scholar
  32. Riazanoff, S., Cervelle, B., and Chorowicz, J., 1988, Ridge and valley line extraction from digital terrain models: Int. J. Remote Sens., v. 9, no. 6, p. 1175–1183.Google Scholar
  33. Robinson, J. E., Charlesworth, H. A. K., and Ellis, M. J., 1969, Structural analysis using spatial filtering in Interior Plains of south-central Alberta: Am. Assoc. Petrol. Geologists Bull., v. 53, no. 11, p. 2341–2367.Google Scholar
  34. Rosenfeld, A., and Kak, A. C., 1982, Digital picture processing, 2nd edn., Vol. 1: Academic Press, New York, 435 p.Google Scholar
  35. Samson, P. P., and Mallet, J. L., 1997, Curvature analysis of triangulated surfaces in structural geology: Math. Geol., v. 29, no. 3, p. 391–412.Google Scholar
  36. Shary, P. A., 1995, Land surface in gravity points classification by complete system of curvatures: Math. Geol., v. 27, no. 3, p. 373–390.Google Scholar
  37. Shary, P. A., Sharaya, L. S., and Mitusov, A. V., 2002, Fundamental quantitative methods of land surface analysis: Geoderma, v. 107, no. 1–2, p. 1–32.CrossRefGoogle Scholar
  38. Sheridan, R. E., 1989, The Atlantic passive margin, in Bally, A. W., and Palmer, A. R., eds., The geology of North America—an overview: Geological Society of America, Boulder, p. 81–96.Google Scholar
  39. Smith, D. E., Zuber, M. T., Solomon, S. C., Phillips, R. J., Head, J. W., Garvin, J. B., Banerdt, W. B., Muhleman, D. O., Pettengill, G. H., Neumann, G. A., Lemoine, F. G., Abshire, J. B., Aharonson, O., Brown, C. D., Hauck, S. A., Ivanov, A. B., Mcgovern, P. J., Zwally, H. J., and Duxbury, T. C., 1999, The global topography of Mars and implications for surface evolution: Science, v. 284, no. 5419, p. 1495–1503.CrossRefPubMedGoogle Scholar
  40. Vigil, J. F., Pike, R. J., and Howell, D. G., 2000, A Tapestry of Time and Terrain, USGS Geologic Investigations Series Map I-2720, scale 1:3 500 000: US Geological Survey.Google Scholar
  41. Wladis, D., 1999, Automatic lineament detection using digital elevation models with second derivative filters: Photogramm. Eng. Remote Sens., v. 65, no. 4, p. 453–458.Google Scholar
  42. Wood, J. D., and Fisher, P. F., 1993, Assessing interpolation accuracy in elevation models: IEEE Comp. Graph. Applic., v. 13, no. 2, p. 48–56.CrossRefGoogle Scholar
  43. Zamani, A., and Hashemi, N., 2000, A comparison between seismicity, topographic relief, and gravity anomalies of the Iranian Plateau: Tectonophysics, v. 327, no. 1–2, p. 25–36.CrossRefGoogle Scholar

Copyright information

© International Association for Mathematical Geology 2005

Authors and Affiliations

  • Igor V. Florinsky
    • 1
    • 2
    • 3
  1. 1.DTM LabWinnipegCanada
  2. 2.Institute of Mathematical Problems of BiologyRussian Academy of SciencesPushchinoRussia
  3. 3.KievUkraine

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