The use of nonlinear functional expansions in calculation of the terrain effect in airborne and marine gravimetry and gradiometry

The terrain corrections for gravity and gravity gradient data are nonlinear functionals of the surrounding topography. We show how to approximate these corrections by use of Volterra-Wiener functional expansion, which is a sum of linear convolutions using the topography, the square of the topography, etc. The convolution kernels are like Taylor expansion coefficients which depend upon the distance from the source point to the field point. As an example, we compute the field V zz for a two-dimensional ridge by the expansion method and compare the result with the exact result.We then show how the expansion technique can be used to propagate statistical properties through nonlinear functionals. As an example of this, we compute the rms terrain correction for V zz as a function of the flight elevation and terrain relief.