解析延拓高阶解的推导方法与比较分析

利用迭代求导法、直接求导法推导了解析延拓高阶解公式,并与经典递推方法进行了比较分析。利用迭代求导法得到了重力异常径向导数在球近似下的通用递推公式,该公式表明,解析延拓的经典递推求解方法实际上是忽略小项的近似,在忽略小项后,迭代求导法与递推法的形式是一样的。虽然直接求导法可以提高计算速度,但利用5°×5°实验区的重力数据进行解析延拓实验的结果表明,直接求导法获得的犵2项数值较其他方法偏小0.1～0.4mGal,这种差异的产生主要由于计算误差引起的。

Solution and Comparison of High Order Term of Analytical Continuation

In order to improve the accuracy of earth gravity field measurements，a high order term for analytical continuation must be considered in practical applications. The high order term for analytical continuation solution was derived using the direct derivative method and iterative derivative method，which were compared with the traditional recursion method. The general recursion formula is obtained using the iterative derivative method. The formula shows that the classical recursion method has the same form as iterative derivative method after ignoring the little quantity term. An analysis also showsthat ananalytical continuation solution can be induced into the solution of different order derivatives for gravity anomalies along the plumb direction. This analytical continuation experiment was applied to the 50×50 area. and a n，term，and n2 term were calculated in this experiment. The reason for this difference may stem from computation error in the integral operation.