Statistical Properties of Strain and Rotation Tensors in Geodetic Network

Abstract

This article deals with the characteristics of deformation of a body or a figure represented by discrete points of geodetic network. In each point of geodetic network kinematic quantities are considered: normal strain, shear strain and rotation. They are computed from strain and rotation tensors represented by displacement gradient matrix on the basis of known point displacement vector. Deformation analysis requires the appropriate treatment of kinematic quantities. Thus statistical properties of each quantity in a single point of geodetic network have to be known. Empirical results have shown that statistical properties are strongly related to the orientation in single point and local geometry of the geodetic network. Based on the known probability distribution of kinematic quantities the confidence areas for each quantity in certain point can be defined. Based on this we can carry out appropriate statistical testing and decide whether the deformation of network in each point is statistically significant or not. On the other hand, we are able to ascertain the quality of the geometry of the geodetic network. Known characteristics of the probability distributions of two strain parameters and rotation in each point can serve us as useful tool in the procedures of optimizing the geometry of the geodetic networks.

Extensão Do Método De Análise De Robustez Para Múltiplos Outliers

“…Caso desejado, pode-se adotar uma estratégia de ponderação para os elementos do vetor de deslocamentos (u), introduzindo uma matriz peso na Equação (5) em função das distâncias entre os diferentes pontos considerados (ver, por exemplo, VANÍČEK et al, 1996;MARJETIČ et al, 2010).…”

“…A análise de robustez vem sendo largamente investigada desde o trabalho pioneiro de Vaníček et al (1991), podendo-se citar os estudos de Vaníček et al (1996) em redes geodésicas de grande extensão, Seemkooei (2001aSeemkooei ( , 2001b na etapa de planejamento, Vaníček et al (2001) e Hsu e Li (2004) em redes geodésicas horizontais, Berber (2006) no campo de deslocamentos dos vértices, Hsu et al (2008) e Vaníček et al (2008) em redes tridimensionais, Marjetič et al (2010) sobre as propriedades estatísticas dos tensores, no caso de observações correlacionadas, e no âmbito nacional, Klein et al (2013) sobre a acurácia de redes horizontais e Cavalheri e Chaves (2014) sobre a robustez das estações da rede GNSS-SP.…”

Datum dependency of strains and rotations in geodetic network

“…Ugotavljamo statistično značilnost deformacij in rotacij. Osnovni pogoj za to je seveda poznavanje porazdelitev posameznih parametrov (Marjetič et al, 2010).…”

A preliminary catalogue of Hikurangi, New Zealand, Slow Slip Earthquakes, from January 2000 to February 2014

“…Uncertainties for strains and rotations shown in Appendix 12 were empirically derived by Monte Carlo simulation [Cox and Siebert, 2006;Papadopoulis and Yeung, 2001]. Marjetič et al [2010] have shown that this is an appropriate method for determining the statistical properties of strain and rotation tensors in a geodetic network, but it should be noted that this method only applies to the specific combination of sites used in each region, and, as observed above, changes in the selection of sites can have much greater effects on the results than these uncertainty values imply.…”

“…For small regional areas, over which it appears that displacement fields are relatively uniform, we might consider the average displacement field D to comprise a tensor of small strains and small rotations. This tensor can then be decomposed into the symmetric (strain) and the asymmetric (rotation) components [Marjetič et al, 2010]: Also shown in Appendix 12 is an analysis for the combination of the northeast coast and Mahia-Gisborne regions. This illustrates that the strain rate magnitudes and rotation rates are very sensitive to the number of sites selected.…”