Multivariate statistical analysis of deformation tensors: independent vs. correlated tensor observations
详细信息 查看全文
- 作者：Khosro Moghtased-Azar (1)
Erik W. grafarend (2)
Farokh Tavakoli (3)
Hamid R. Nankali (3) - 关键词：random tensor ; principal components ; (co)variance component estimation
- 刊名：Studia Geophysica et Geodaetica
- 出版年：2012
- 出版时间：October 2012
- 年：2012
- 卷：56
- 期：4
- 页码：977-992
- 参考文献：1. Amiri-Simkooei A.R., 2007. / Least-Squares Variance Component Estimation: Theory and GPS Applications. Ph.D. Thesis, Technical University Delft, Delft, The Netherlands.
2. 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. Geodesy, 78, 425鈥?36. CrossRef
3. Crocetto N., Gatti M. and Russo P., 2000. Simplified formulae for the BIQUE estimation of variance components in disjunctive observation groups. / J. Geodesy, 74, 447鈥?57. CrossRef
4. DeMets C., Gordon R.G., Argus D.F. and Stein S., 1994. Effect of recent revisions to the geomagnetic reversal time scale on estimates of current plate motions. / Geophys. Res. Lett., 21, 2191鈥?194. CrossRef
5. Eshagh M. and Sj枚berg L.E., 2008. The modified best quadratic unbiased non-negative estimator (MBQUNE) of variance components. / Stud. Geophys. Geod., 52, 305鈥?20. CrossRef
6. Grafarend E., 1984. Variance-covariance-component estimation of Helmert type in the Gau脽-Helmert model. / Z. Geod. Geoinf. Landmanagement, 109, 34鈥?4.
7. Grafarend E., Kleusberg A. and Schaffrin B., 1980. An introduction to the variance-covariancecomponent estimation of Helmert type. / Z. Geod. Geoinf. Landmanagement, 105, 161鈥?80.
8. Grafarend E.W. and Voosoghi B., 2003. Intrinsic deformation analysis of the Earth鈥檚 surfacebased ondisplacement fields derived from space geodetic measurements, case studies: present-day deformation patterns of Europe and of the Mediterranean area (ITRF data sets). / J. Geodesy, 77, 303鈥?26. CrossRef
9. Helmert F., 1907. / Die Ausgleichungsrechnung nach der Methode der kleinsten Quadrate. 2nd Edition. Teubner, Leipzig, Germany (in German).
10. Jackson J. and McKenzie D., 1984. Active tectonics of the alpine-himalayan belt between western turkey and pakistan. / Geophys. J. R. Astr. Soc., 77, 185鈥?64. CrossRef
11. Malley J.D., 1986. / Optimal Unbiased Estimation of Variance Components. Springer-Verlag, Berlin, Germany. CrossRef
12. Moghtased-Azar K., 2007. / Surface Deformation Analysis of Dense GPS Networks Based on Intrinsic Geometry: Deterministc and Stochastic Aspects. Ph.D. Thesis. Bayerische Akademie der Wissenschaften, Reihe C (Deutsche Geodatische Kommission), Dissertationen, Heft Nr. 612, M眉nchen, Germany.
13. Moghtased-Azar K. and Grafarend E., 2009. Surface deformation analysis of dense GPS networks based on intrinsic geometry: deterministic and stochastic aspects. / J. Geodesy, 83, 431鈥?54. CrossRef
14. Nilforoushan F., Masson F., Vernant P., Vigny C., Martinod J., Abbassi M., Nankali H., Hatzfeld D., Bayer R., Tavakoli F., Ashtiani A., Doerflinger E., Daignires M., Collard P. and Chery J., 2003. GPS network monitors the Arabia-Eurasia collisiondeformation in Iran. / J. Geodesy, 77, 411鈥?22. CrossRef
15. Rao C. and Kleffe J., 1988. / Estimation of Variance Components and Applications. North-Holland, Amsterdam, The Netherlands.
16. Satirapod C., Wang J. and Rizos C., 2001. A new stochastic modelling procedure for precise static GPS positioning. / Z. Geod. Geoinf. Landmanagement, 126, 365鈥?73.
17. Sella G.F., Dixon T.H. and Mao A., 2002. REVEL: A model for recent plate velocities from spacegeodesy. / J. Geophys. Res., 107(B4), 2081, DOI: 10.1029/2000JB000033. CrossRef
18. Sepehr M. and Cosgrove J.W., 2005. Role of the Kazerun Fault Zone in the formation and deformation of the Zagros Fold-Thrust Belt, Iran. / Tectonics, 24, TC5005, DOI: 10.1029/2004TC001725. CrossRef
19. Shaffrin B., 1983. / Varianz-Kovarianz-Komponenten-Sch盲tzung bei der Ausgleichung heterogener Wiederholungsmessungen. Ph.D. Thesis. Bayerische Akademie der Wissenschaften, Reihe C (Deutsche Geodatische Kommission), Dissertationen, Heft Nr. 282, M眉nchen, Germany (in German).
20. Talebian M. and Jackson J., 2002. Offset on the Main Recent Fault of NW Iran and implications for the late Cenozoic tectonics of the Arabia-Eurasia collision zone. / Geophys. J. Int., 150, 403鈥?10. CrossRef
21. Talebian M. and Jackson J., 2004. A reappraisal of earthquake focal mechanisms and active shortening in the Zagros mountains of Iran. / Geophys. J. Int., 156, 506鈥?26. CrossRef
22. Tavakoli F., A, A.W., Authemayou C., Nankali H., Hatzfeld D., Tatar M., Djamour Y., Nilforoushan F. and Cotte N., 2008. Distribution of the right-lateral strikeslip motion from the Main Recent Fault to the Kazerun Fault System (Zagros, Iran): Evidence from present-day GPS velocities. / Earth Planet. Sci. Lett., 257, 342鈥?47. CrossRef
23. Xu P., 1999. Spectral theory of constrained second-rank symmetric random tensors. / Geophys. J. Int., 138, 1鈥?4. CrossRef
24. Xu P., 2009. Iterative generalized cross-validation for fusing heteroscedastic data of inverse illposed problems. / Geophys. J. Int., 179, 182鈥?00. CrossRef
25. Xu P., Liu Y., Shen Y. and Fukuda Y., 2007. Estimability analysis of variance covariance components. / J. Geodesy, 81, 593鈥?02. CrossRef
26. Xu P., Shen Y., Fukuda Y. and Liu Y., 2006. Variance component estimation in linear inverse illposed models. / J. Geodesy, 80, 69鈥?1. CrossRef
27. Xu P.L. and Grafarend E.W., 1996a. Probability distribution of eigenspectra and eigendirections of a two-dimensional, symmetric rank two random tensor. / J. Geodesy, 70, 419鈥?30. CrossRef
28. Xu P.L. and Grafarend E.W., 1996b. Statistics and geometry of the eigenspectra of threedimensional second-rank symmetric random tensor. / Geophys. J. Int., 127, 744鈥?56. CrossRef - 作者单位：Khosro Moghtased-Azar (1)
Erik W. grafarend (2)
Farokh Tavakoli (3)
Hamid R. Nankali (3)
1. Department of Surveying Engineering, Faculty of Civil Engineering, University of Tabriz, 29 Bahman Boulevard, P.O. Box, 51666-16471, Tabriz, Iran
2. Institute of Geodesy, Geschwister-Scholl-Str. 24D, P.O. Box D-70174, Stuttgart, Germany
3. National Cartographic Centre (NCC) of Iran, Meraj Ave., Azadi Sq., P.O. Box 13185, 1684, Tehran, Iran - ISSN：1573-1626
文摘
In the presence of errors in measuring a random displacement field (under the normal distribution assumption of displacement field), stochastic behaviors of principal components of deformation tensors (strain tensor and tensor of change of curvature (TCC)), based on the intrinsic assumption of geometrical modeling of surface deformation analysis, are discussed. We divided the contents into two parts: In the first, we considered independent random vectors of repeated tensor measurements. In the second step, we considered correlations among repeated measurements. Then, covariance components between tensor elements by Helmert estimator, based on prior information of variance components, are estimated. As a case study, both assumptions are applied to the estimation of principal components of deformation rate tensor observations in Zagros region (Western Iran). The results of numerical analysis showed that greatest shortening is accommodated in oblique orientation (NS) with respect to the Main Recent Fault (MRF), northwest part of North Zagros, Central Iran block and MRF, respectively. Most of the extensions occurred in the east part of the belt. The pattern of eigenspace components of TCC shows highest positive values across the NW region, nearly in orthogonal direction to the MRF and Main Zagros Fault (MZF). The pattern has insignificant values in the Central Zagros. It takes the significant negative values across the SW part, especially along the SPF and Persian Gulf shore. The effect of non-independent observations on the estimation of eigenspace components of deformation tensors (strain tensor and TCC) shows that the estimation of covariance components has influence on the confidence intervals of eigenspace components, especially in seismically active regions of the belt (along the Persian Gulf shore, NW of the belt and region between the Central Iran block and MRF). The results demonstrate the importance of considering the correlation structure among the observations on statistical behavior of principal components of deformation tensors in seismically active regions.