Fast reduction of potential fields measured over an uneven surface to a plane surface

The present work is aimed at rapid reduction of the gravity and magnetic fields observed over an uneven surface to a horizontal plane. The approach suggested is to estimate the Fourier transform of the potential field over an imaginary horizontal plane lying entirely above the ground surface and impose boundary conditions; namely, the solution must satisfy the observed field over the ground surface and vanish over an infinite hemisphere. The desired Fourier transform is obtained in an iterating manner. A 2D FFT algorithm can considerably reduce the computational burden. The FFT approach cannot be used unless the discrete data is available on a rectangular grid. If the observations are scattered, interpolation to the nearest grid point will have to be carried out. Interpolation introduces marginal increase in the rms error. The iterating approach is about 10 times faster than the least squares approach