Abstract
A kinematic deformation analysis (KDA) model is mostly preferred to estimate the displacement, velocity, and acceleration parameters in deformation analysis. Different models, such as linear and quadratic, are used in KDA. The displacement, velocity, and acceleration parameters are generally determined by the least-squares estimation (LSE) method. The LSE method smears the effects of the displaced points to the other nondisplaced points. Therefore, it should be noted that although the point is flagged as displaced from the KDA, it may not actually be displaced. Additionally, this may result in incorrect estimation of the velocity or acceleration. In this article, the reliability of the results of different models estimated by the KDA is discussed. To investigate the reliability of the models, different deformation scenarios were simulated in the Global Navigation Satellite Systems (GNSS) network. Different velocity and acceleration parameters were taken into account in these scenarios. The reliability of the KDA models was measured by the mean success rate (MSR). Different approaches for linear and quadratic models—namely, deduction, induction, and quadratic—were considered. According to the results, the solutions of the quadratic model are more successful when the acceleration is considered as zero and nonzero. Also, the MSRs of the induction and deduction models are very similar when the loaded acceleration is considered as zero.
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Acknowledgments
The authors are thankful to the Scripps Orbit and Permanent Array Center (SOPAC), International GNSS Service (IGS), and Center for Orbit Determination in Europe (CODE) for the GNSS data, IGS precise orbits, and global ionosphere maps. The authors are also grateful to anonymous reviewers and the editor for their helpful comments on the manuscript.
References
Acar, M., Ozludemir, M. T., Erol, S., Celik, R. N., and Ayan, T. (2008). “Kinematic landslide monitoring with Kalman filtering.” Nat. Hazards Earth Syst. Sci., 8(2), 213–221.
Bernese 5.2 [Computer software]. Astronomical Institute Univ. of Bern, Bern, Switzerland.
Betti, B., Biagi, L., Crespi, M., and Riguzzi, F. (1999). “GPS sensitivity analysis applied to permanent deformation control networks.” J. Geod., 73(3), 158–167.
Cai, J., Wang, J., Wu, J., Hu, C., Grafarend, E., and Chen, J. (2008). “Horizontal deformation rate analysis based on multiepoch GPS measurements in Shanghai.” J. Surv. Eng., 132–137.
Caspary, W. (1988). “A robust approach to estimating deformation parameters.” Proc., 5th Canadian Symp. on Mining Surveying and Rock Deformation Measurements, Dept. of Surveying Engineering Univ. of New Brunswick, Fredericton, New Brunswick, Canada, 124–135.
Caspary, W. F., Haen, W., and Borutta, H. (1990). “Deformation analysis by statistical methods.” Technometrics, 32(1), 49–57.
Cooper, M. A. R. (1987). Control surveys in civil engineering, Nichols, New York.
Duchnowski, R., and Wiśniewski, Z. (2014). “Comparison of two unconventional methods of estimation applied to determine network point displacement.” Surv. Rev., 46(339), 401–405.
Durdag, U. M., Hekimoglu, S., and Erdoğan, B. (2016). “Outlier detection by using fault detection and isolation techniques in geodetic networks.” Surv. Rev., 48(351), 400–408.
Erdoğan, B. (2014). “An outlier detection method in geodetic networks based on the original observations.” Bol. Ciênc. Geod., 20(3), 578–589.
Erdoğan, B., and Hekimoglu, S. (2014). “Effect of subnetwork configuration design on deformation analysis.” Survey Review, 46(335), 142–148.
Erdoğan, B., Hekimoglu, S., and Durdağ, U. M. (2017). “Theoretical and empirical minimum detectable displacements for deformation networks.” FIG Working Week 2017 Surveying the world of tomorrow – From digitalisation to augmented reality, Helsinki, Finland, May 29–June 2 2017.
Ghitau, D. (1970). “Modellbildung und Rechenpraxis bei der nivellitischen Bestimmung siikularer Landerhebungen.” Ph.D. dissertation, Bonn, Germany.
Hekimoglu, S., and Erenoglu, R. C. (2007). “Effect of heteroscedasticity and heterogeneousness on outlier detection for geodetic networks.” J. Geod., 81(2), 137–148.
Hekimoglu, S., Erdogan, B., and Butterworth, S. (2010). “Increasing the efficacy of the conventional deformation analysis methods: Alternative strategy.” J. Surv. Eng., 53–62.
Hekimoglu, S., Erdogan, B., and Erenoglu, R. C. (2015). “A new outlier detection method considering outliers as model errors.” Exp. Tech., 39(1), 57–68.
Hekimoglu, S., Erdogan, B., Soycan, M., and Durdag, U. M. (2014). “Univariate approach for detecting outliers in geodetic networks.” J. Surv. Eng., 04014006.
Hekimoglu, S., and Koch, K. R. (1999). “How can reliability of the robust methods be measured?” Proc., 3rd Turkish-German Joint Geodetic Days, Vol. 1, Istanbul Technical Univ., Istanbul, Turkey, 179–196.
Hekimoglu, S., and Koch, K. R. (2000). “How can reliability of tests for outliers be measured?” AVN, 107(7), 247–254.
Heunecke, O. (1995). Zur identification und verifikation von deformationsprozessen mittels adaptiver Kalman-filterung, wissen. Arbet. Der fahricht. Vermess, Der Universitat Hannover, Hannover, Germany.
Holdahl, S. R. (1975). “Models and strategies for computing vertical crustal movements in the United States.” Proc., Int. Symp. on Recent Crustal Movements, International Union of Geodesy and Geophysics, Grenoble, France.
Kenner, S. J., and Segall, P. (2000). “Postseismic deformation following the 1906 San Francisco earthquake.” J. Geophysical Res., 105(B6), 13195–13209.
Koch, K. R. (1985). “Ein statistisches auswerteverfahren für deformationsmessungen.” Allgemeine Vermessung-Nachrichten, 92(3), 97–108.
Koch, K. R. (1999). Parameter estimation and hypothesis testing in linear models, 2nd Ed. Springer, New York.
Liu, Q. (1998). “Time-dependent models of vertical crustal deformation from GPS-leveling data.” Surv. Land Inf. Syst., 58, 5–12.
Mälzer, H., Hein, G., and Zippelt, K. (1983). “Height changes in the Rhenish massif: Determination and analysis” Plateau uplift: The Rhenish Shield—A case history, K. Fuchs, K. von Gehlen, H. Mälzer, H. Murawski, and A. Semmel, eds., Springer, New York, 164–176.
Mälzer, H., Schmitt, G., and Zippelt, K. (1979). “Recent vertical movements and their determination in the Rhenish massif.” Tectonophys., 52(1-4), 167–176.
MATLAB [Computer software]. MathWorks, Natick, MA.
Moon, P., and Spencer, D. E. (1988). Field theory handbook: Including coordinate systems, differential equations, and their solutions, Springer, New York.
Niemeier, W. (1985). “Deformations analyis.” Geodetic networks in land surveying and engineering II: Preliminary study of contact study February 1985 in Hannover, H. Pelzer, ed., Wittwer, Stuttgart, Baden Wurttemberg, Germany, 559–623.
Nowel, K. (2016). “Investigating efficacy of robust M estimation of deformation from observation differences.” Surv. Rev., 48(346), 21–30.
Nowel, K., and Kamiński, W. (2014). “Robust estimation of deformation from observation differences for free control networks.” J. Geod., 88(8), 749–764.
Pelzer, H. (1971). Zur analyse geodätischer deformationsmessungen, Deutsche Geodätische Kommission, Munich, Germany.
Pelzer, H. (1985). Statische, kinematische und dynamische punktfelder in: Pelzer (hrsg.): Geodätische netze in landes-und ingenieurvermessung II, Wittwer, Stuttgart, Baden Wurttemberg, Germany, 225–262.
Pelzer, H. (1986). “Application of Kalman and Wiener filtering on the determination of vertical movements.” Proc., Recent Vertical Crustal Movements in Western Europe, Dümmler, Bonn, Germany, 529–555.
Pelzer, H. (1987). “Deformationsuntersuchungen auf der Basis Kinematischer Bewegungsmodelle.” AVN, 94(2), 49–62.
Schaffrin, B. (1986). “New estimation/prediction techniques for the determination of crustal deformations in the presence of prior geophysical information.” Tectonophys., 130(1–4), 361–367.
Schaffrin, B., and Bock, Y. (1994). “Geodetic deformation analysis based on robust inverse theory.” Manuscripta Geod., 19, 31–44.
Shahar, L., and Even-Tzur, G. (2014). “Definition of dynamic datum for deformation monitoring: Carmel fault environs as a case study.” J Surv. Eng., 04014002.
Snow, K., and Schaffrin, B. (2007). “GPS-network analysis with BLIMPBE: An alternative to least-squares adjustment for better bias control.” J. Surv. Eng., 114–122.
Velsink, H. (2015). “On the deformation analysis of point fields.” J. Geod., 89(11), 1071–1087.
Welsch, W. M., and Heunecke, O. (2001). “Models and terminology for the analysis of geodetic monitoring observations.” Final Rep. FIG Publication No. 25, International Federation of Surveyors, Copenhagen, Denmark, 390–412.
Wolf, H. (1975). Ausgleichugsrechnung; Formeln zur praktischen anwendung, Dümmler, Bonn, Germany.
Wolf, P. R., and Ghilani, C. D. (1997). Adjustment Computation: Statistics and Least Squares in Surveying and GIS, 2nd Ed. John Wiley and Sons, Inc., New York.
Yalçinkaya, M., and Bayrak, T. (2005). “Comparison of static, kinematic and dynamic geodetic deformation models for Kutlugün landslide in northeastern Turkey.” Nat. Hazards, 34(1), 91–110.
Yu, E., and Segall, P. (1996). “Slip in the 1868 Hayward earthquake from the analysis of historical triangulation data.” J. Geophys. Rec., 101(B7), 16101–16118.
Zienkiewicz, M. H., Hejbudzka, K., and Dumalski, A. (2017). “Multi split functional model of geodetic observations in deformation analyses of the Olsztyn castle.” Acta Geodyn. Geomater., 14(2), 195–204.
Zippelt, K. (1986). “Recent vertical movements in the Testnet Pfungstadt conception, application and results of the Karlsruhe approach.” Proc., Recent Vertical Crustal Movements in Western Europe, Dümmler, Bonn, Germany, 599–617.
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Received: Sep 13, 2017
Accepted: Feb 7, 2018
Published online: Apr 23, 2018
Published in print: Aug 1, 2018
Discussion open until: Sep 23, 2018
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