Unbiased 3D-Analysis of Earth's Crustal Deformation Using GPS Measurements

3D deformation analysis is a considerable issue in Earth’s crustal deformation studies. In this research، 3D deformation analysis is addressed using isoparametric approach and also developing 2D mode to the 3D one. Since in geodetic networks، some components of the baselines (usually height difference of the points) are smaller than other components، extension of 2D isoparametric method to 3D mode will be a n ill-posed problem which results in unstable solutions. Such this property makes use of regularization approaches inevitable. Use of regularization approaches makes the solution biased. In this regard، in this research for the first time، 3D deformation analysis is formulated such that the discussed problem is switched to a well-posed problem resulting stable solutions. Parameters of such coordinate system are determined through the process of strain tensor components determination. Kenai Peninsula located in south central is selected as the study area. Instability of the 3D deformation analysis has already been proved and demonstrated. Resulted solutions by the extended approach of this research corroborate the fact of maximum compression being in center part of this region emphasized by other researches. Resulted strain tensor is the first unbiased determination of strain tensor in this region computed using a non-element approach. Comparison of resulted solutions to the solutions obtained by 2D deformation analysis (a similar approach) in this region demonstrates that magnitude of vertical deformation effect on horizontal principal strains of the strain tensor is as large as 1. 7 micro strain. This value will be a large amount for the horizontal mentioned components in 2D mode. Hence، disregarding vertical components effects and kinematic investigation of in 2D can lead to a significant bias in the solution. Nevertheless، some overall properties of deformation in region such as maximum compression in center part of this network is observable by 2D deformation analysis. Moreover، studying magnitude of bias due to the regularization demonstrates inappropriate adoption of regularization parameter can cause a significant bias in the obtained results. In this regard، use of already known deformation properties in this research، such as maximum compression in the center part، is not a suitable approach for regularization parameter adoption.