The solutions to the geodetic boundary value problem of predicting geoid undulations from gravity observations are complicated by the non-level observation surface, thus requiring the use of Molodensky’s theory instead of Stokes’ theory. For practical computations, Molodensky’s equations, as well as Stokes’ equation, may be reformulated as convolution integrals that can be efficiently evaluated by Fast Fourier Transform (FFT) techniques. A link between the two approaches, to a first-order approximation, is provided by use of the classical terrain correction, which can also be evaluated by FFT techniques. The terrain correction is also required for terrain reductions, which smooth the gravity data using topographic density assumptions, yielding more reliable gridding of free-air gravity anomalies and smaller and smoother Molodensky corrections. These reductions can be used in a remove-restore fashion as pre- and post-processing steps, analogously to the direct and indirect effects of shifting the topographic masses below the geoid.

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