The FOURPOT program is made for frequency domain processing and analysis of two-dimensional (2D) potential field arising, in particular, from geophysical gravity and magnetic field measurements. The data can be irregularly or regularly sampled. The frequency domain operations include frequency filtering, reduction to (magnetic) pole or equator, 1.st and 2.nd degree xyz gradients, horizontal, total and tilt gradients, gravity and magnetic potentials and pseudo fields as well as sun shading and general derivative filtering.
FOURPOT computes the discrete 2D Fourier transform using the fast Fourier transform (FFT) algorithm. The Fourier transform represents a sum of sine and cosine terms with different spatial frequencies (Kx and Ky) that are defined by data coverage (Dx= max(x)-min(x)) and sampling (dx=Dx/N and dy=Dy/M) in x and y directions. The highest spatial frequency is the so-called Nyquist frequency (e.g., max(Kx)= 0.5/dx). The lowest frequency is based on the data coverage (e.g., min(Kx)= 0.5/Dx). Considering that the inverse of the spatial frequency represents wave length (Lx = 1/Kx), zero frequency means infinite wave length, i.e., constant level of data. Because of the properties of the Fourier transform (symmetry, linearity, shift and derivate properties) several computational operations can be performed in Fourier transformed frequency (kx,ky) domain more efficiently than in the spatial (x, y) domain. For more detailed information about Fourier transform methods in potential field analysis, please, see Blakely (1995), for example.