NDLI: Surface deformation analysis of dense GPS networks based on intrinsic geometry: deterministic and stochastic aspects

Content Provider	Springer Nature Link
Author	Moghtased Azar, Khosro Grafarend, Erik W.
Copyright Year	2008
Abstract	In this contribution, the regularized Earth’s surface is considered as a graded 2D surface, namely a curved surface, embedded in a Euclidean space $${\mathbb{E}^{3}}$$ . Thus, the deformation of the surface could be completely specified by the change of the metric and curvature tensors, namely strain tensor and tensor of change of curvature (TCC). The curvature tensor, however, is responsible for the detection of vertical displacements on the surface. Dealing with eigenspace components, e.g., principal components and principal directions of 2D symmetric random tensors of second order is of central importance in this study. Namely, we introduce an eigenspace analysis or a principal component analysis of strain tensor and TCC. However, due to the intricate relations between elements of tensors on one side and eigenspace components on other side, we will convert these relations to simple equations, by simultaneous diagonalization. This will provide simple synthesis equations of eigenspace components (e.g., applicable in stochastic aspects). The last part of this research is devoted to stochastic aspects of deformation analysis. In the presence of errors in measuring a random displacement field (under the normal distribution assumption of displacement field), the stochastic behaviors of eigenspace components of strain tensor and TCC are discussed. It is applied by a numerical example with the crustal deformation field, through the Pacific Northwest Geodetic Array permanent solutions in period January 1999 to January 2004, in Cascadia Subduction Zone. Due to the earthquake which occurred on 28 February 2001 in Puget Sound (M w > 6.8), we performed computations in two steps: the coseismic effect and the postseismic effect of this event. A comparison of patterns of eigenspace components of deformation tensors (corresponding the seismic events) reflects that: among the estimated eigenspace components, near the earthquake region, the eigenvalues have significant variations, but eigendirections have insignificant variations.
Starting Page	431
Ending Page	454
Page Count	24
File Format	PDF
ISSN	09497714
Journal	Journal of Geodesy
Volume Number	83
Issue Number	5
e-ISSN	14321394
Language	English
Publisher	Springer-Verlag
Publisher Date	2008-08-19
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Deformation analysis Surface deformation Random tensors Eigenspace components Mathematical Applications in Earth Sciences Geophysics/Geodesy
Content Type	Text
Resource Type	Article
Subject	Geophysics Geochemistry and Petrology Computers in Earth Sciences

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