关键词: 解析延拓, 垂向一阶导数, 导数迭代法, 快速傅里叶变换, 收敛性

Abstract:

We present a new approach for downward continuation of potential fields: a derivative-iteration method in the case of that downward continuation is an unstable problem. From the definition of vertical first-order derivatives, we connect the values of the potential fields of observation planes with the values of the planes of upward continuation in a certain height and downward continuation in the same height. We use also the iterative method to successive approximation. Thus we deduce the recursive formula of the derivativeiteration method for continuation downward of potential fields in space domain. Taking the complexity of achieving upward continuation integral equations in spatial domain into accout, the fast Fourier transform is adopted in the recurrence formula. Then it gets the derivative iteration formula in wavenumber domain. It also proves the convergence of this method.The analysis of model tests and a practical example indicate that,comparing with the immediate FFT method, advantages of the iteration method are strong stability and a great downward continuation depth.

Key words: analytic continuation, vertical first-order derivatives, derivative iteration method, fast Fourier transform, convergence