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

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.