NDLI: Statistical inference of the eigenspace components of a two-dimensional, symmetric rank-two random tensor

Content Provider	Springer Nature Link
Author	Cai, J. Grafarend, E.W. Schaffrin, B.
Copyright Year	2004
Abstract	The eigenspace components (i.e. principal components and principal directions) play a key role in the validation of a symmetric rank-two random tensor, e.g. for strain and stress. They classify deformation and stress patterns in earthquake regions, plate tectonics and glacial isostatic adjustment (postglacial rebound). It is assumed that the strain or stress tensor has been directly observed or indirectly determined by other measurements. According to the Measurement Axiom, such a symmetric rank-two tensor is considered random. For its statistical inference, the random tensor is assumed to be tensor-valued Gauss–Laplace normally distributed. The eigenspace synthesis relates the eigenspace elements to the observations by means of a nonlinear vector-valued function, thus establishing a special nonlinear multivariate Gauss–Markov model. For its linearized form, the best linear uniformly unbiased estimation (BLUUE) of the eigenspace elements and the best invariant quadratic uniformly unbiased estimate (BIQUUE) of its variance–covariance matrix have been successfully constructed. The related linear hypothesis test has documented large confidence regions for both eigenvalues and eigendirections based upon real measurement configurations. They lead to a statement of caution when dealing with data concerning extension and contraction, as well as the orientation of principal stresses.
Starting Page	425
Ending Page	436
Page Count	12
File Format	PDF
ISSN	09497714
Journal	Journal of Geodesy
Volume Number	78
Issue Number	7-8
e-ISSN	14321394
Language	English
Publisher	Springer-Verlag
Publisher Date	2004-12-25
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Random tensor Deformation analysis Eigenspace components Multivariate Gauss Markov model Geophysics/Geodesy Math. Applications in Geosciences
Content Type	Text
Resource Type	Article
Subject	Geophysics Geochemistry and Petrology Computers in Earth Sciences

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