科研之友
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摘要
The computation of gravitational vector field of variable-density bodies has been attracting much attention in high precision gravity investigation. In forward and inverse gravity modeling, a 3-D rectangular prism, as a simple building block, is commonly used to approximate 3-D variable-density bodies with irregular shape. In this paper, we first model the density of a rectangular prism using an arbitrary-order polynomial function of depth, and derive the closed-form expressions for computing the vertical and horizontal components of the gravitational vector field of a 3-D rectangular prism with the polynomial density variation. Then, we extend the polynomial density function of depth to a linear combination of three arbitrary-order polynomial functions in x-, y- and z-directions, and derive the analytical expressions of the gravitational vector field of a 3-D rectangular prism with such more general density function. The analytic expressions are numerically validated and compared with other existing methods. It is shown that the new expressions are far superior to the common method based on the stack of a collection of uniform subprisms in computational efficiency. In addition, the numerical error of the expressions is analysed and the results show that the expressions are available for practical applications.
- 出版日期2017-8
- 单位中国海洋大学
