摘要：The knowledge of the behavior of three-dimensional displacements fields is an important requirement in the task of analysis of structures deformations, be them natural or artificial. However, as the geodetic observations are usually accomplished in a finite number of points of the study area, it is necessary to use a mathematical tool of interpolation for the knowledge of such behavior. This way, the aim of this work is to present the concepts involved in the modelling of local displacements fields from three-dimensional displacements obtained by means of the Global Positioning System (GPS). For the attainment of this objective a three-dimensional polynomial model of second degree is used. The coefficients of this model are calculated by a least square adjustment. After this stage, convenient statistical tests are accomplished for the suitable analysis of the quality of the adjusted model, as well as, for the verification of the significance of the estimated coefficients. Later, these concepts werw applied in the three-dimensional displacements detected in the region of Salto Caxias Hydroelectric Power Dam, where it was found out that the results were satisfactory, once the polinomial function modeled was able to determine, also, the deformation parameters in each one of the observation points. Finally, the obtained results and its conclusion will be presented in this paper.
其他摘要：The knowledge of the behavior of three-dimensional displacements fields is animportant requirement in the task of analysis of structures deformations, be themnatural or artificial. However, as the geodetic observations are usually accomplishedin a finite number of points of the study area, it is necessary to use a mathematicaltool of interpolation for the knowledge of such behavior. This way, the aim of thiswork is to present the concepts involved in the modelling of local displacementsfields from three-dimensional displacements obtained by means of the GlobalPositioning System (GPS). For the attainment of this objective a three-dimensionalpolynomial model of second degree is used. The coefficients of this model arecalculated by a least square adjustment. After this stage, convenient statistical testsare accomplished for the suitable analysis of the quality of the adjusted model, aswell as, for the verification of the significance of the estimated coefficients. Later,these concepts werw applied in the three-dimensional displacements detected in theregion of Salto Caxias Hydroelectric Power Dam, where it was found out that theresults were satisfactory, once the polinomial function modeled was able todetermine, also, the deformation parameters in each one of the observation points.Finally, the obtained results and its conclusion will be presented in this paper.
关键词：Deslocamentos tridimensionais;Função polinomial;Movimentos da crosta;Análise estatística;Sistema de Posicionamento Global;Three-dimensional displacements;Polinomial function;Crustal movements;Statistical analysis;Global Positioning System
