THE ANALYSIS AND DESIGN OF TWO‐DIMENSIONAL FILTERS FOR TWO‐DIMENSIONAL DATA *

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Abstract
Some of the methods such as regional removal and second derivative calculations which can be used to outline anomalies on potential data maps can be thought of as a filtering operation. The analysis and design of such two‐dimensional filters by means of direct and inverse two‐dimensional Fourier transforms have been considered.An analysis of several published sets of second derivative coefficient sets indicates that, in general, they are not a good approximation to the theoretical second derivative filter. Alternate methods of designing regional removal and second derivative filters are discussed. The properties of various two‐dimensional filters are further illustrated by means of maps obtained from the convolution of several of these filters with a set of observed field data. These maps show the large changes in anomaly shape which can result from the inclusion or rejection of various wavelength components.