Filtering using variable order vertical derivatives

Abstract

Vertical derivatives of aeromagnetic and gravity datasets are routinely used as an aid to the interpretation process because they enhance detail and sharpen geophysical anomalies. Since they are a form of high-pass filter they also have the undesirable property of enhancing noise. Traditionally, the second order vertical derivative of a dataset would be calculated, and if this proved too noisy then the first-order derivative map would be used. Recently, much interest has been shown in the use of derivatives of fractional order to achieve a derivative map that contains the correct balance between the enhancement of signal and noise. If the data set being processed has a frequency content which does not vary spatially by a great amount this process can be effective. However, if this is not the situation then the result is a map where some portions are too noisy for convenient interpretation, whereas other portions are too smooth and show little detail. The use of derivatives whose order varies across the dataset in a manner based on the local standard deviation of the data proved effective in resolving this problem. The method is demonstrated on aeromagnetic data from Botswana and on elevation data from South Africa.