位场向下延拓的波数域迭代法及其收敛性

Wave number domain iteration method for downward continuation of potential fields and its convergence

提出了位场向下延拓的波数域迭代法.对水平面上的位场观测值进行Fourier变换,得到其波谱.根据第一类Fredholm积分方程的空间域迭代解法,推导出计算向下延拓水平面上位场波谱的波数域迭代公式.在波数域中进行迭代,一直进行到相继两次迭代近似解的差值最大绝对值小于给定的精度,或迭代达到给定的最大迭代次数.对这种迭代近似解进行Fourier逆变换,得到向下延拓的位场.数值计算结果表明:与空间域迭代法比较,这种波数域迭代法简单、快速,并有同样好的向下延拓效果.本文还证明了这种迭代法是收敛的,并给出了它的收敛特性和滤波特性.

The wave number domain iteration method is proposed for downward continuation of potential fields. The values of a potential field measured on a horizontal plane are transformed by the Fourier transform, so the wave spectrum of the potential field is gained. According to the space domain iteration method of the Fredholm integral equation of the first kind, the wave number domain iteration formula is deduced for calculating the wave spectrum of the potential field on a lower horizontal plane. The procedure of the wave number domain iteration is repeated until the maximum absolute value of difference of two successive iterative approximate solutions in the wave number domain is smaller than a given threshold, or a given maximum iteration number is reached. The downward continuation potential field is computed by the inverse Fourier transform of the iterative approximate solution. Numerical computation results show that the wave number domain iteration method is simpler and faster than the space domain iteration method, and possesses the same good effects for downward continuation. Convergence of this method is proved, and its convergence characteristics and filter characteristics are studied.