Sensitivity Analysis for the Principal Strain Parameters of a Deformation Monitoring Network
Publication: Journal of Surveying Engineering
Volume 138, Issue 3
Abstract
Strain tensor analysis plays an essential role in geophysics and engineering applications, because it provides a numerical measure on the relative deformation behavior of the object under investigation. A strain tensor can be estimated by observing the positional coordinates of the deforming network at different epochs. Consequently, the quality of a strain analysis is highly dependent on the accuracy of position measurement and network configuration. In this study, a strain sensitivity index, namely the minimum detectable principal strain parameter, has been developed based on the concept of the invariant function and statistical theory. A simulation test and a real case study have both been carried out to demonstrate the feasibility of the proposed approach. Based on the numerical results from the case study on the first-order global positioning system network in Taiwan, it has been revealed that the coastal areas in Taiwan have a lower capability in detecting surface strains because of poor network configuration. On the other hand, it has also been illustrated that, by incorporating the network optimization guidelines developed in this study, the strain sensitivity index can be substantially improved in these areas.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The authors thank the three anonymous reviewers for their constructive comments, which significantly improved the quality of the original manuscript. The funding support by the National Science Council in Taiwan (under Contract No. NSC 9100-2221-E-002-217) is also gratefully acknowledged.
References
Aydin, C. (2011). “Power of global test in deformation analysis.” J. Surv. Eng.JSUED2, 138(2), 51–56.
Baarda, W. (1968). “A testing procedure for use in geodetic networks.” Publications on geodesy, new series, 2(5), Netherlands Geodetic Commission, Delft, Netherlands.
Berber, M., Dare, P., and Vaníček, P. (2006). “Robustness analysis of two-dimensional networks.” J. Surv. Eng., 132(4), 168–175.JSUED2
Betti, B., Biagi, L., Crespi, M., and Riguzzi, F. (1999). “GPS sensitivity analysis applied to non-permanent deformation control networks.” J. Geodes.JOGEF8, 73(3), 158–167.
Billington, E. W., and Tate, A. (1981). The physics of deformation and flow. McGraw-Hill, New York.
Cai, J., Grafarend, E. W., and Schaffrin, B. (2005). “Statistical inference of the eigenspace components of a two-dimensional, symmetric rank-two random tensor.” J. Geodes.JOGEF8, 78(7–8), 425–436.
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., 134(4), 132–137.JSUED2
Calais, E., Han, J. Y., DeMets, C., and Nocquet, J. M. (2006). “Deformation of the North American plate interior from a decade of continuous GPS measurements.” J. Geophys. Res., 111, B06402.JGREA2
DeMets, C., Gordon, R. G., Argus, D. F., and Stein, S. (1990). “Current plate motions.” Geophys. J. Int., 101(2), 425–478.GJINEA
Eringen, A. C. (1962). Nonlinear theory of continuous media, McGraw-Hill, New York.
Even-Tzur, G. (2002). “GPS vector configuration design for monitoring deformation networks.” J. Geodes.JOGEF8, 76(8), 455–461.
Grafarend, E. W., and Schaffrin, B. (1993). Ausgleichungsrechnung in linearen modellen, BI Wissenschaftsverlag, Mannheim, Germany (in German).
Han, J. Y., van Gelder, B. H. W., and Lin, S. L. (2010). “Rotation- and translation—free estimations of symmetric, rank-two tensors with a case study in LIDAR surveying.” J. Surv. Eng., 136(1), 23–28.JSUED2
Han, J. Y., van Gelder, B. H. W., and Soler, T. (2007). “On covariance propagation of eigenparameters of symmetric n-D tensors.” Geophys. J. Int., 170(2), 503–510.GJINEA
Holzapfel, G. A. (2000). Nonlinear solid mechanics: A continuum approach for engineering, Wiley, New York.
Hsu, R., and Hsiao, K. (2002). “Pre-computing the sensitivity of a GPS station for crustal deformation monitoring.” J. Chin. Inst. Eng., 25(6), 715–722.CKCKDZ
Hsu, R., Lee, H. C., and Kao, S. P. (2008). “Three-dimensional networks are horizontally superior in robustness: a mathematical reasoning.” J. Surv. Eng., 134(2), 61–65.JSUED2
Koch, K. R. (1988). “Bayesian statistics for variance components with informative and noninformative priors.” Manuscr. Geod., 13(8), 370–373.MANGEH
Kutterer, H. (1998). “Quality aspects of a GPS reference network in Antarctica-a simulation study.” J. Geodes.JOGEF8, 72(2), 51–63.
Marjetič, A., Ambrožič, T., Turk, G., Sterle, O., and Stopar, B. (2010). “Statistical properties of strain and rotation tensors in geodetic network.” J. Surv. Eng., 136(3), 102–110.JSUED2
Soler, T., and van Gelder, B. H. W. (1991). “On covariances of eigenvalues and eigenvectors of second rank symmetric tensors.” Geophys. J. Int., 105(2), 537–546.GJINEA
Soler, T., and van Gelder, B. H. W. (2006). “Corrigendum: On covariances of eigenvalues and eigenvectors of second-rank symmetric tensors (vol. 105, 537–546, 1991).” Geophys. J. Int., 165(1), 382.GJINEA
Vaníček, P., Craymer, M. R., and Krakiwsky, E. J. (2001). “Robustness analysis of geodetic horizontal networks.” J. Geodes.JOGEF8, 75(4), 199–209.
Vaníček, P., Krakiwsky, E. J., Craymer, M. R., Gao, Y., and Ong, P. (1990). “Robustness analysis.” Geodetic Survey Division Contract Rep. 91-002, Geomatics Canada, Ottawa, Canada.
Wegener, A. (1912). “Die Entstehung der Kontinente.” Geologische RundschauGERUA3, 3(4), 276–292 (in German).
Xu, P. (2004). “Determination of regional stress tensors from fault-slip data.” Geophys. J. Int., 157(3), 1316–1330.GJINEA
Xu, P., and Grafarend, E. (1996). “Probability distribution of eigenspectra and eigendirections of a twodimensional, symmetric rank two random tensor.” J. Geodes.JOGEF8, 70(7), 419–430.
Xu, P., Shimada, S., Fujii, Y., and Tanaka, T. (2000). “Invariant geodynamical information in geometric geodetic measurements.” Geophys. J. Int., 142(2), 586–602.GJINEA
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 138 • Issue 3 • August 2012
Pages: 109 - 116
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Aug 21, 2011
Accepted: Nov 30, 2011
Published online: Dec 2, 2011
Published in print: Aug 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.