一种由地心直角坐标到大地坐标的直接转换

                    李延兴 张静华 张俊青 张中伏 杜雪松

                  （中国地震局第一监测中心,天津300180）

摘 要 空间任一点在给定的地心直角坐标系或大地坐标系中,其位置可由地心直角坐标（或大地坐标）唯一的确定,其大地坐标与地心直角坐标的关系也是确定的。在分析大地坐标与地心直角坐标几何关系的基础上,推导建立了地心直角坐标与大地纬度正切的4次方程。由此方程可直接解算大地纬度。本文解算4次方程的算法简单,解算精度和效率优于已有的迭代算法和直接转换方法。给出了一种由地心坐标到大地坐标的近似算法,这种算法非常简单,但它的精度可以满足一般地学研究的需要。

关键词 地心坐标 大地坐标 坐标转换 四次方程 解的唯一性 近似算法

  A DIRECT TRANSFORMATION FROM GEOCENTRIC CARTESIAN TO GEODETIC COORDINATES

          Li Yanxing, Zhang Jinghua, Zhang Junqing, Zhang Zhongfu, Du Xuesong

First Crust Monitoring and Application Center, China Earthquake Administration, Tianjin 30018

Abstract. In a given geocentric or geodetic coordinate system, the location of any point in space can be uniquely determined by with geocentric (or geodetic) coordinates. And the relation between the geodetic and geocentric coordinates of the point is definite. By analyzing the geometric relation between the geodetic and geocentric coordinates, a tangent quartic equation of geodetic latitude is established, by which the geodetic latitude can be solved directly. The algorithm for solving the quartic equation in the paper is simple. The calculated results indicate that the method in the paper is better than the existing iterative methods and the direct transformation method in the calculating accuracy and efficiency. We derived an approximate algorithm from geocentric to geodetic coordinates. The algorithm is very simple, but its accuracy can satisfied general geo-science research.

Key words: geocentric coordinates, Geodetic coordinates, coordinate transformation, Quartic equation, Uniqueness of solution, approximate algorithm

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