对迭代法位场向下延拓方法的剖析

Analysis of the Potential Field Downward Continuation Iteration Method

位场向下延拓迭代法的实质内容是"向上延拓而不是向下延拓"和以"迭代的结果趋近于观测值"为标准的操作过程。根据数据操作流程剖析了位场向下延拓迭代法的运行机制,得到了迭代数据在空间域的变化规律,即用迭代法将观测高度的位场向下延拓一个深度h。这实际上是通过不同高度的向上延拓来实现的。也就是说,迭代次数增加一次,涉及的上延平面就增大一个h的高度。一般地,迭代次数n与上延高度h的关系为n^(n+1)h。在空间域中,初值、上延结果、差以及每一次校正后的结果都能用满足莱布尼兹定理的交错级数表示,从而得出了迭代法能够收敛的结论;或者,以"观测高度上的实测值与计算值的差值小到可以忽略"为标准,从数学上也能证明迭代法能够收敛。数学推论和模型试验结果说明了迭代的位场初值可以任意给定。在实际操作中,迭代误差标准的影响和由于迭代误差标准不恰当可能出现不能达到迭代标准的情况,需引起注意,也值得进一步研究。

The substance of the potential field downward continuation iteration method is an operating process of＂upward continuation rather than downward continuation＂based on the criterion of＂iteration result tend to be the observation data＂.We have analyzed the operational mechanism of the method by chasing its operation routine,and obtained the dynamic rule of the data flow in spatial domain.It turned out that the iteration method for a downward continuation leads to an upward continuation of the potential field on the individual levels.The relationship between the iteration period nand the height hof the upward continuation is n^（n＋1）h.Shown in an alternating serie of satisfying Leibniz theorem to each iteration result in spatial domain,the convergence of this method is obtained.The convergence can also be verified by using the criterion of minimizing the difference between measured value and calculated data.The mathematical reasoning and numerical computation results show that an initial value of the iteration method can be arbitrary.Also,we have studied the effect of the iteration tolerance criterion,and pointed out the possibility that a tolerance might never be satisfiedin practice if the criterion is not fitted.