OPTIMUM SECOND‐DERIVATIVE AND DOWNWARD‐CONTINUATION FILTERS

Abstract

Second‐derivative and downward‐continuation filtering are often employed to enhance gravity and magnetic maps. Noise due to aliasing, measurement errors, and near‐surface sources can be greatly amplified and lead to erratic filter outputs which produce spurious anomalies. To prevent this undesirable occurrence, it is often necessary to smooth the data, or equivalently, to modify the response of the applied filter. By means of the Wiener filter theory it is possible to derive optimum second‐derivative and downward‐continuation filters in either the wavenumber or space domain. Application of the theory involves separating the power spectrum into signal and noise components. A white noise assumption is realistic if the noise is due to small random near‐surface sources, random measurement errors, and random errors in corrections for terrain and elevation. As a striking demonstration of the superiority of optimum filters, the effects of optimum and “ideal” filters on a synthetic gravity map are compared.