Abstract
Methods for the design of spatial filters are discussed in this paper. For a given response of a one‐dimensional filter, the weighting coefficients are calculated by solving a set of simultaneous equations with a simple matrix inversion procedure. In the case of a two‐dimensional filter, the method for obtaining the coefficients of a double Fourier series representing a set of given values is used to design the spatial operator. The problems connected with the length of the operator and the choice of a suitable decay in the high‐frequency response are discussed in detail. In order to show the usefulness of these methods, the paper presents several examples of operators designed for computing the vertical gradient, the second vertical derivative, and downward continuation of potential field data. A two‐dimensional vertical gradient filter is applied to the total field data obtained during a high‐resolution aeromagnetic survey over an area in the Precambrian Shield of Northeastern Ontario. The calculated gradient maps are compared with maps showing measured gradient values. The quality of the calculated maps in defining trends, patterns, and detailed features of anomalies shows the feasibility of obtaining very accurate vertical gradient maps from observed total field data.
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