Résumé
Le problème de la comparison des données obtenues à différentes époques sur un réseau geódésique pour en déduire les déformations subies par ce réseau au cours du temps est discuté, et conduit à proposer un mode de représentation simultané des déformations et des erreurs, utilisant les tenseurs de déformations classiques avec une méthode de Monte Carlo permettant de simuler un grand nombre de séries de mesures.
Abstract
The repetition of geodetic measurements is employed in many cases to monitor ground deformations, and is widely used for civil engineering, geodynamics and slope instabilities studies. Generally the networks used are small and the main problem to solve is how to detect stable zones, i.e. where the signal/noise ratio of the deformation measurements are below unity. This is commonly done using statistical tests. We present here a new tool, the simultaneous display of the deformations and their related errors, using a classical Monte Carlo methodology when computing strain tensors. Such a representation provides to non-specialists in a quit efficient way the significance level of the deformation patterns. Some examples show that even when statistical test show a poor confidence level, this methodology may give anyway in some situations the pattern of the deformation (but—obviously—not its amplitude).
This is a preview of subscription content, log in via an institution to check access.
References
F.K. BRUNNER: On the analysis of geodetic networks for the determination of the incremental strain tensor. Survey Review, 25(192), pp. 56–67, 1979.
F.K. BRUNNER, R. COLEMAN et B. HIRSCH: A comparison of computation methods for crustal strains from geodetic measurements. Tectonophysics, 71, pp. 281–298, 1981.
W. CASPARY et H. BORUTTA: Robust estimation in deformation models. Survey Review, 29 (223), pp. 29–46, 1987.
Y.Q. CHEN: Analysis of deformation surveys - A generalized method. Department of Surveying Engineering, Technical Report 94, University of New Brunswick, Fredericton, N.B., Canada, 1983.
P.A. CROSS, J. HANNAH, L. HRADILEK, R. KELM, J. MAKINEN, C.L. MERRY, L.E. SJOBERG, R.R. STEEVES, P. VANICEK et D.B. ZILKOSKI: Four-dimensional geodetic positioning. Report on the IAG SSG 4.96, Manuscripta Geodaetica, 12 (3), pp. 147–222, 1987.
D. DARBY: The analysis of variance of an underdetermined geodetic displacement problem. Geophys. Res. Lett., 9 (6), pp. 641–644, 1982.
F.C. FRANK: Deduction of Earth strains from survey data. Bull. Seism Soc. Am., 56 (1), pp. 35–42, 1966.
G. GU & W.H. PRESCOTT: Discussion on displacement analysis–Detection of crustal deformation. J. Geophys. Res., 91 (B7), pp. 7439–7446, 1986.
M. KASSER, J.C. RUEGG, P. LESAGE, L. ORTLIEB, J. PAGARETE, N. DUCH, J. GUERRERO & J. ROLDAN: Geodetic measurements of plate motions across the central Gulf of California. Geophys. Res. Lett., 14, pp. 5–8, 1987.
E. LIVIERATOS & D. VLACHOS: The influence of correlations in computing crustal strains from trigonometric network results. Tectonophysics, 77, pp. 323–332, 1981.
E. MIKHAIL: Least squares and observations. University Press of America, Inc., 1976.
J. MOSHMAN: Random number generation. In Mathematical methods for digital computers, ed. by A. Ralston and H.S. Wilf, J. Wiley & Sons Company, U.S.A., Vol. 2, pp. 249–263, 1967.
W.H. PRESCOTT: An extension of Frank's method for obtaining crustal shear strains from survey data. Bull. Seism. Soc. Am., 66 (6), pp. 1847–1853, 1976.
W.H. PRESCOTT: The determination of displacement fields from geodetic data along a strike-slip fault. J. Geophys. Res., 86 (B7), pp. 6067–6072, 1981.
W.H. PRESCOTT, J.C. SAVAGE & W.T. KINOSHITA: Strain accumulation rates in the western United States between 1970 and 1978. J. Geophys. Res., 84 (B10), pp. 5423–5435, 1979.
W.H. PRESS, B.P. FLANNERY, S.A. TEUKOLSKY & W.T. VETTERLING: Numerical recipes–The art of scientific computing. Press Syndicate of the University of Cambridge, 1987.
K.D. SENNE: Machine independent Monte Carlo evaluation of the performance of dynamic stochastic systems. J. of Stochestics, Vol. I, 3, pp. 215–238, 1974.
P. VANI>CEK & E.J. KRAKIWSKY: Geodesy - The concepts. North Holland, 2th ed., Amsterdam, 1986.
J. VAN MIERLO: A testing procedure for analysing geodetic deformation measurements. Proceedings of the II International Symposium of Deformation Measurements by Geodetic Methods, Bonn, 1978.
W. WELSCH: Some techniques for monitoring and analysing deformations and control nets. Lecture, Wuhan College of Geod., Cartogr. and Photogramm., Wuhan, People's Republic of China, 1980.
W. WELSCH: Description of homogeneous horizontal strains and some remarks to their analysis. Proceedings of the International Symposium on Geodetic Networks Computations of the I.A.G., Munich, pp. 188–205, 1981.
W. WELSCH: Finite element analysis of strain patterns from geodetic observations across a plate margin. Tectonophysics, 97, pp. 57–71, 1983.
W. WELSCH: Some aspects of the analysis of geodetic strain observations in kinematic models. Tectonophysics, 130, pp. 437–458, 1986.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pagarete, J., Kasser, M. & Ruegg, J.C. Evaluation et representation des erreurs sur les deformations d'un reseau geodesique: Utilisation de la methode de Monte Carlo. Bull. Geodesique 64, 63–72 (1990). https://doi.org/10.1007/BF02530615
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02530615