起伏地形位场快速延拓新方法

将起伏地形上的测点垂直投影至水平面上，并将地形上的位场u放在水平面的对应点上，这样就有一个平面上的假想位场u。用快速傅立叶变换（FFT）计算平面位场的垂向导数δu/δn，将这个垂向导数移至地形的对应点上，近似作为地形上的位的垂向导数δu/δn。根据Green公式，从地形上的位u和位的法向导数δu/δn，用积分的方法可计算地形上部任一点的位。在计算出地形上部一个平面上的位后，可用FFT迅速计算其它平面的位，包括与地形相交的平面上的位。在通常的位场延拓方法中，如用等效源法解一个线形代数方程组要需用很大内存量，要耗去大量计算时间。本方法的主要特点是省略了解线形代数方程组的步骤，从而大大节约计算时间。模型计算表明，本方法的计算精度是令人满意的。用本方法对航磁实际资料进行延拓，取得较好的效果。

A New Fast Method for Continuation of Potential Field on an Undulate Terrain

Vertically projecting the observation point at a undulate terrain onto a horizontal plane and copying the potential at the terrain to the corresponding point at the horizontal plane,we get a fictitious potential field on a horizontal plane.An FFT is then can applied to calculate the outward normal derivativ a u／ n of the potential u on the horizontal plane.The calculated derivativeis u／ n is used approximately as the outward normal derivative of u／ n of the potential on the terrain.Based on the potential u and the normal derivativeon the terrain,Green’s formula is used to calculate the potential u at an arbitrary point above the terain.When the potential u at a level above the terrain is obtained,an FFT is used again to calculate the potential u at other level above the sources of the potentia1.The other method of continuation of potential field,e.g.,the equivalent source method, requires solving a large set of linear algebraic equations that take a hefty amount of computer memory and expends considerably the computation time.This method does not require solving algebraic equations and is of a high computation speed.The model tests demonstrated that the accuracy of this method is satisfactory.Using this method to continue the practical aeromagnetic anomaly shows a good result.