Using WGM2012 to Compute Gravity Anomaly Corrections of Leveling Observations in China

Gravity Anomaly Correction(GAC)is a very important term in leveling data processing.In most cases,it is troublesome for field surveyors to measure gravity when leveling.In this paper,based on the complete Bouguer Gravity Anomaly(BGA)map of WGM2012,the feasibility of replacing in-situ gravity surveying in China is investigated.For leveling application,that is to evaluate the accuracy of WGM2012 in China.Because WGM2012 is organized with a standard rectangle grid,two interpolation methods,bilinear interpolating and Inverse Distance Weighted(IDW)interpolating,are proposed.Four sample areas in China,i.e.,Hanzhong,Chengdu,Linzhi and Shantou,are selected to evaluate the systems bias and precision of WGM2012.Numerical results show the average system bias of WGM2012 BGA in west China is about-100.1 mGal(1 mGal=10^(-5) m/s^(2))and the standard deviation is about 30.7 mGal.Tests in Shantou indicate the system bias in plain areas is about-130.4 mGal and standard deviation is about 6.8 mGal.All these experiments means the accuracy of WGM2012 is limited in high mountain areas of western China,but in plain areas,such as Shantou,WGM2012 BGA map is quite good for most leveling applications after calibrating the system bias.

A new grid deformation technology with high quality and robustness based on quaternion

Quality and robustness of grid deformation is of the most importance in the field of aircraft design, and grid in high quality is essential for improving the precision of numerical simulation. In order to maintain the orthogonality of deformed grid, the displacement of grid points is divided into rotational and translational parts in this paper, and inverse distance weighted interpolation is used to transfer the changing location from boundary grid to the spatial grid. Moreover, the deformation of rotational part is implemented in combination with the exponential space mapping that improves the certainty and stability of quaternion interpolation. Furthermore, the new grid deformation technique named ‘‘layering blend deformation＇＇ is built based on the basic quaternion technique, which combines the layering arithmetic with transfinite interpolation（TFI） technique. Then the proposed technique is applied in the movement of airfoil, parametric modeling, and the deformation of complex configuration, in which the robustness of grid quality is tested. The results show that the new method has the capacity to deal with the problems with large deformation, and the ‘‘layering blend deformation＇＇ improves the efficiency and quality of the basic quaternion deformation method significantly.