Analysis of Error Caused by Replacing Spherical Shell with an Elastic Plate Model in Studying Bending Deformation of the Lithosphere

To study the bending deformation of the lithosphere, the simplification of replacing a spherical shell by a plate model is usually made. Based on the differential equations for the bending of plates and shallow spherical shells, an expression for the error caused by such a simplification is derived in this paper. The effect of model sizes on the error is discussed. It is proved that if we replace the shallow spherical shell by a plate model to solve the bending deformation of lithospheric plate, a large error will be caused. In contrast, if we use a plate on an elastic foundation instead, an approximate solution closer to that of spherical shell can be obtained. In such a way, the error can be reduced effectively and the actual geological condition can be modeled more closely.

Transformation Method of Exterior Orientation Angular Elements Obtained via Position and Orientation System Under Gauss-Kruger Projection Coordinate System

Data obtained via airborne position and orientation system （POS） is in WGS 84 global geocentric reference frame, while the national coordinate reference system for topographic mapping in China is generally Gauss-Kruger projection coordinate system. Therefore, data obtained via a POS must be transformed to national coordinate system. Owing to the effects of earth curvature and me- ridian deviation, there are some errors in the process of angle transformation from roll, pitch, and heading （φ,θ,ψ） obtained directly via a POS to the attitude angles of images （φ,ω,κ） needed in photogrammetry. On the basis of effect theories of earth curvature and meridian deviation on exterior orientation angular elements of images, a method using a compensation matrix to correct the transformation errors from attitude angles obtained via the POS to exterior orientation angular elements of images is proposed in this paper. Moreover, the rigorous formula of the compensation matrix is deduced. Two sets of actual data obtained via a POS AV 510, which are different in scale and terrain, are selected and used to perform experiments. The empirical results not only indicate that the compensation matrix proposed in this paper is correct and practical but also show that transformation accuracy of exterior orientation angular elements obtained via the POS based on compensation matrix is relevant to the selection of vertical axis （a projection of central meridian） of Gauss-Kruger projection coordinate system; the proper vertical axis should be the Gauss-Kruger projection of the central meridian of projection zone in which the survey area locates. However, the transformation accuracy of exterior orientation angular elements is irrelevant to the choice of origin of coordinate system; it is appropriate that the origin of coordinate system locates at the center point of the survey area. Moreover, transformation accuracy of exterior orientation angular elements achieved based on the compensa- tion matrix deduced in this paper is higher than that obtained via the existing POS processing software.