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The use of surface interpolation methods for landslides monitoring

  • Geotechnical Engineering
  • Published:
KSCE Journal of Civil Engineering Aims and scope

Abstract

The subject of this study is selection of mathematical description (interpolation method) of landslides surface for the purpose of periodic control of terrain movements. Monitoring of landslides, considered in this work, concerns points of periodic GPS or tacheometric measurements carried out in a relatively regular grid. For economic reasons, the grid usually consists of limited group of about several dozen of points that do not allow for an exact description of the terrain surface, nevertheless a general movement of a landslide can be detected (observed). Replacement of discrete set of points to a continuous surface model allows for a better assessment of the phenomenon especially within the scope of its main directions of activity. The choice of best performing interpolation method in order to construct a reliable numerical terrain model was performed through tests carried out on complex model surfaces. These model surfaces encompassed various configurations of terrain relief. In this study four interpolation methods i.e. splines, kriging triangulation with linear interpolation and IDW are compared. Tests on model surfaces distinguished the method of splines as the best performing one as well as the method of kriging which is suitable in some instances. The selected method of splines was then applied to periodically monitored landslide in Milówka in the south of Poland. Interpolation by means of splines allowed for observing progressive movements of the landslide surface with accuracy up to several millimeters. This confirms the usefulness and reliability of this method in landslides monitoring. Specialized field: Surveying & Geo-Spatial Engineering: Deformation Surveying.

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References

  • Aguilar, F. J., Agüera, F., Aguilar, M. A., and Carvajal, F. (2005). “Effects of terrain morphology, sampling density and interpolation methods on grid DEM accuracy.” Photogrammetric Engineering & Remote Sensing, Vol. 71, No. 7, pp. 805–816, DOI: 10.14358/PERS.71.7.805.

    Article  Google Scholar 

  • Dan, J. and Lancheng, W. (2006). “An algorithm of NURBS surface fitting for reverse engineering.” The International Journal of Advanced Manufacturing Technology, Vol. 31, No. 1–2, pp. 92–97, DOI: 10.1007/S00170-005-0161-3.

    Article  Google Scholar 

  • Dewitte, O., Jasselette, J. C., Cornet, Y., Van Den Eecckhaut, M., Collignon, A., Poesen, J., and Demoulin, A. (2008). “Tracking landslide displacements by multi-temporal DTMs: A combined aerial stereophotogrammetric and LIDAR approach in western Belgium.” Engineering Geology, Vol. 99, Nos. 1–2, pp. 11–22, DOI: 10.1016/j.enggeo.2008.02.006.

    Article  Google Scholar 

  • Farin, G. (2002). Curves and surfaces for computer aided geometric design, Academic Morgan Kaufmann Publishers, San Francisco.

    Google Scholar 

  • Fisher, J., Lowther, J., and Ching-Kuang, S. (2004). “If you know bsplines well, you also know NURBS.” ACM SIGCSE Bulletin, Association for Computing Machinery, Vol. 36, No. 1, pp. 343–348, DOI: 10.1145/1028174.971420.

    Article  Google Scholar 

  • Floater, M. S. and Surazhsky, T. (2006). “Parameterization for Curve Interpolation.” Studies in Computational Mathematics, Vol. 12/ 2006, pp. 39–54, DOI: 10.1016/S1570-579X(06)80004-2.

    Article  MathSciNet  Google Scholar 

  • Garnero, G. and Godone D. (2013). “Comparisons between different interpolation techniques.” The Role of Geomatics in Hydrogeological Risk, 27–28 February, Padua, Italy The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. XL-5/W3, pp. 139–144, DOI: 10.5194/isprsarchives-XL-5-W3-139-2013

    Google Scholar 

  • Goovaerts, P. (1997). Geostatistics for natural resources evaluation, Oxford University Press.

    Book  Google Scholar 

  • Hejmanowska, B. (2007). “Analysis of NMT in the form of GRID and TIN on example of data from OKI. Archives of Photogrammetry.” Cartography and Remote Sensing, Vol. 17a, pp. 281–289, DOI: does not exist.

    Google Scholar 

  • Hungr, O. and McDougall, S. (2009). “Two numerical models for landslide dynamic analysis.” Computers & Geosciences, Vol. 35, No. 5, pp. 978–992, DOI: 10.1016/j.cageo.2007.12.003.

    Article  Google Scholar 

  • Lee, J. (1991). “Comparison of existing methods for building triangular irregular network, models of terrain from grid digital elevation models.” International Journal of Geographical Information Systems, Vol. 5, No. 3, pp. 267–285, DOI: 10.1080/02693799108927855.

    Article  Google Scholar 

  • Neaupane, K. M. and Piantanakulchai, M. (2006). “Analytic network process model for landslide hazard zonation.” Engineering Geology, Vol. 85, Nos. 3–4, pp. 281–294, DOI: 10.1016/j.enggeo.2006.02.003.

    Article  Google Scholar 

  • Noferini, L., Pieraccini, M., Mecatti, D., Macaluso, G., Atzeni, C., Mantovani, M., Marcato, G., Pasuto, A., Silvano, S., and Tagliavini, F. (2007). “Using GB-SAR technique to monitor slow moving landslide.” Engineering Geology, Vol. 95, pp. 88–98, DOI: 10.1016/j.enggeo.2007.09.002.

    Article  Google Scholar 

  • Olea, R. A. (1997). Geostatistics for engineers and earth scientists. Kluwer Academic Publishers.

    Google Scholar 

  • Pieraccini, M., Noferini, L., Mecatti, D., Luzi, G., and Atzeni, C. (2006). “Long term landslide monitoring by Ground Based SAR Interferometry.” International Journal of Remote Sensing, Vol. 27, No. 10, pp. 1893–1905, DOI: 10.1080/01431160500353908.

    Article  Google Scholar 

  • Razak, K. A., Santangelo, M., Van Westen, C., Straatsma, M., and De Jong, S. (2013). “Generating an optimal DTM from airborne laser scanning data for landslide mapping in a tropical forest environment.” Geomorphology, Vol. 190, pp. 112–125, DOI: 10.1016/j.geomorph.2013.02.021.

    Article  Google Scholar 

  • Ries, L. (1993). “Areas of influence for IDW-interpolation with isotropic environmental data.” Catena, Vol. 20, Nos. 1–2, pp. 199–205, DOI: 10.1016/0341-8162(93)90039-R.

    Article  Google Scholar 

  • Santini, M., Grimaldi, S., Nardi, F., Petroselli, A., and Rulli, M. C. (2009). “Pre-processing algorithms and landslide modelling on remotely sensed DEMs.” Geomorphology, Vol. 113, Nos. 1–2, pp. 110–125, DOI: 10.1016/j.geomorph.2009.03.023.

    Article  Google Scholar 

  • Shewchuk, J. R. (2002). “Delaunay refinement algorithms for triangular mesh generation.” Computational Geometry, Vol. 22, Nos. 1–3, pp. 21–74, DOI: 10.1016/S0925-7721(01)00047-5.

    Article  MathSciNet  Google Scholar 

  • Teza, G., Pesci, A., Genevoisa, R., and Galgaroa, A. (2008). “Characterization of landslide ground surface kinematics from terrestrial laser scanning and strain field computation.” Geomorphology, Vol. 97, Nos. 3–4, pp. 424–437, DOI: 10.1016/j.geomorph.2007.09.003.

    Article  Google Scholar 

  • Lukaszyk, S. (2004). “A new concept of probability metric and its applications in approximation of scattered data sets.” Computational Mechanics, Vol. 33, No. 4, pp. 299–304, DOI: 10.1007/s00466-003-0532-2.

    Article  MathSciNet  Google Scholar 

  • Vorpahl, P., Elsenbeer, H., Märker, M., and Schröder, B. (2012). “ How can statistical models help to determine driving factors of landslides?.” Ecological Modelling, Vol. 239, pp. 27–39, DOI: 10.1016/j.ecolmodel.2011.12.007.

    Article  Google Scholar 

  • Yin, K., Chen L., Zhang G. (2007). “Regional Landslide Hazard Warning and Risk Assessment.” Earth Science Frontiers, Vol. 14, No. 6, pp. 85–93, DOI: 10.1016/S1872-5791(08)60005-6.

    Article  Google Scholar 

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Authors and Affiliations

  1. AGH University of Science and Technology, Faculty of Mining Surveying and Environmental Engineering, Cracow, Mickiewicza, 30, Poland

    Grzegorz Lenda, Marcin Ligas, Paulina Lewińska & Anna Szafarczyk

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  1. Grzegorz Lenda
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  2. Marcin Ligas
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  3. Paulina Lewińska
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  4. Anna Szafarczyk
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Correspondence to Grzegorz Lenda.

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Lenda, G., Ligas, M., Lewińska, P. et al. The use of surface interpolation methods for landslides monitoring. KSCE J Civ Eng 20, 188–196 (2016). https://doi.org/10.1007/s12205-015-0038-4

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  • DOI: https://doi.org/10.1007/s12205-015-0038-4

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