测绘学报

• 学术论文 •    

球冠体积分的重力异常正演方法及其与Tesseroid单元体Taylor级数展开方法的比较

杜劲松,陈超,梁青,王林松,张毅,王秋革   

  1. 中国地质大学(武汉)地球物理与空间信息学院
  • 收稿日期:2011-05-13 修回日期:2011-08-25 出版日期:2012-06-25 发布日期:2012-06-25
  • 通讯作者: 杜劲松

Gravity Anomaly Calculation Based on Volume Integral in Spherical Cap and Comparison with the Tesseroid-Taylor Series Expansion Approach

  • Received:2011-05-13 Revised:2011-08-25 Online:2012-06-25 Published:2012-06-25

摘要: 利用重力资料研究区域乃至全球地质问题时,重力或重力异常正演方法最好从基于直角坐标系向球坐标系方向发展。本文对近似的球冠面积分重力异常正演方法进行改进,使其计算精度和计算效率都得到很大程度地提高;再通过模型试验,分析了Tesseroid单元体基于Taylor级数展开的方法、球冠面积分方法及其改进的球冠体积分方法的计算精度与稳定性,最后指出Tesseroid单元体基于几何中心Taylor级数展开方法的计算精度受级数展开次数、单元体表面大小、厚度、深度、计算点高度与空间地理位置的影响,近似的球冠面积分方法的计算精度受模型重构精度、单元体厚度、深度与计算点高度的影响,而球冠体积分方法只受模型重构精度的影响。Tesseroid单元体基于几何中心Taylor级数展开的方法由于无需坐标系旋转与模型重构,因而适用于重力三维反演,而球冠体积分方法由于其计算精度高适用于局部、区域或者全球的较高精度的重力或重力异常正演。

Abstract: The gravity or gravity anomaly calculating methods must be developed from the rectangular Cartesion coordinate system to the spherical coordinate system when utilizing gravity data to study the regional and global geologic problems. The method of surface integral approximation for gravity anomaly forward in spherical cap is improved so that both calculation accuracy and computing speed are enhanced. By means of the model testing, the calculation accuracy and stability of the methods of gravity anomaly calculation in spherical cap and the Tesseroid-Taylor series expansion are analyzed, and the conclusions are drew that the Tesseroid-Taylor series expansion approach is affected by the expansion order, surface area, thickness, depth and surface position of the Tesseroid, and the height of the calculating point, while the method of surface integral approximation in spherical cap by the thickness and depth of the Tesseroid, and the height of the calculating point and the accuracy of model reconstruction, but the method proposed in this paper only by the model reconstruction. the Tesseroid-Taylor series expansion approach, which does not require coordinate rotation and model reconstruction, is fit for 3-D density imaging by gravity data, but the calculating method in the spherical cap, which has high accuracy and stability, is suite to local, regional and global gravity or gravity anomaly forward modelling.