Comprhensive Approach to the Analysis of the 3D Kinematics Deformation with appliction to the Kenai Peninsula

The problem of analyzing surface deformation of the Earth's crust in three-dimensions is discussed. The isoparametric and Lagrangian formulations of deformation are extended from 2D to 3D. Analytical and numerical investigation of problem conditioning proves that analyzing the 3D kinematics of deformation can be an ill-posed problem. The required mathematical elements for solving this problem, including sensitivity analysis of the deformation tensor and regularization, are proposed. Regularized deformation tensors were computed using the method of truncated singular value decomposition (TSVD). The optimal regularization parameter was attained by minimizing regularization errors. Regularization errors were assessed using the corresponding 2D results of deformation analysis. The proposed methods were applied to the GPS network in the Kenai Peninsula, south-central Alaska, in order to compute the 3D pattern of postseismic crustal deformation in this area. Computed deformation in the vertical direction is compared to the existing pattern of vertical deformation obtained from the combination of precise leveling, gravity and GPS measurements from other studies on this area.