Proceeding of the Joint International Symposium on Deformatuon Monitoring. 2-4 November, 2011. Hong Kong. China. Report. In this contribution, the procedure of estimation of principal components of deformation tensors in the presence of both independent and correlated tensor observations of displacement field is presented. This approach is based upon the intrinsic method which assumed the Earth as two-dimensional Riemmannian manifold ( M2) embedded in the ambient space (three-dimensional Euclidean space E3) at various time instants. The context is divided into two parts: In the first, we considered independent random vectors and in the second step we considered correlations between repeated measurements. Then, the covariance components between tensor elements are estimated by Helmert estimator, based on prior information of variance components. As a case study, both assumption, are applied to the estimation of principal components of deformation rate tensor observations in Zagros region. The latest available continuous GPS data around the region, when this research is undertaken, was from January 2006 through January 2009. Due to the sparsity of the data between the January 2006 through January 2007, which could effect the construction of the Earths surface as regularized and graded M2 at continuous time instants, we have chose the daily solutions between January 2007 through January 2009. In this region, the invariants of deformation rates tensors within 95matrix and, (b) after estimation of covariance matrix. The related linear hypothesis test has documented larger confidence regions for the active areas, after estimation of (Co)variance components. They lead to a statement of caution when dealing with data concerning extension and contraction, as well as the orientation of principal stresses. Further detailed analysis of the results is also performed with respect to geodynamical and statistical aspects.