Abstract
The generalized sampling expansion is a method that can be used to combine gravity and gravity gradient data so that the line spacing of a survey can be increased without introducing aliasing into the measured signal. This reduces acquisition costs because the costs of shipborne and airborne gravity and gravity gradient surveys are related to the line spacing of the survey. The generalized sampling expansion combines the Fourier spectra of several undersampled gravity and gravity gradient data sets to produce an unaliased result. To achieve that result, input data are assumed to be noise free, infinite in extent, regularly sampled, and band limited. Deviations from this ideal induce errors, but these can be alleviated to a degree. In theory, the generalized sampling expan-sion can reconstruct an unaliased signal sampled at three times conventional line spacing. Unfortunately, edge effects and the presence of noise limit the practical increase in line spacing to twice normal line spacing. Six methods, each using different gradient components, can be used to achieve this doubling of line spacing. Edge effects introduce short-wavelength errors into several possible applications of the generalized sampling expansion, a problem that can be reduced by filtering the output of an expansion and by trimming away residual errors at its boundary. When applied to a deliberately decimated data set derived from data collected over the Cannington ore deposit in Australia, the generalized sampling expansion method successfully reduced aliasing in the signal and produced a more accurate interpolation than was obtained with a gradient-enhanced Akima spline method.
