Although 1D and 2D fast Fourier transforms (FFTs) have long been used for the filtering, interpretation, and modeling of potential-field data, 3D FFTs have not enjoyed similar popularity. This may change with the recent discovery (Caratori Tontini et al., in press, JGR) that simple 3D FFT filters can be used to transform distributions of density (or magnetization) within a box-shaped 3D volume into gravity (or magnetic) fields within the same volume. For example, the continuous 3D Fourier transform of the vertical gravity anomaly ∆gz(x,y,z) in a volume is related to the 3D Fourier transform of the density ρ(x,y,z) in the volume by F[∆gz] = i4πG(kz/ | k |^2)F[ρ]; |k| ≠0, (1) where G is the gravitational constant, kx, ky, kz are wavenumbers, and | k |^2 = kx2+ ky2+ kz2. (2) Translating (1) into a digital FFT filtering operation requires careful consideration of the periodicity of the density distribution and the gravity field. Nevertheless, (1) provides a highly efficient way to calculate the vertical gravity anomaly of a 3D density distribution within a few minutes. The calculated gravity anomaly can be sampled at random points or on an arbitrary surface using tri-linear interpolation.
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