THE FRACTAL DIMENSION OF GRAVITY DATA SETS AND ITS IMPLICATION FOR GRIDDING1

A bstract Gravity survey station locations are, in general, inhomogeneously distributed. This inevitably results in interpolation errors in the computation of a regular grid from the gravity data. The fractal dimension of the station distribution can be used to determine if an interpolated map is aliased at a specific wave‐length and, moreover, it is often possible to determine an optimum gridding interval. Synthetic distributions of gravity station locations have been used for theoretical studies and it is found that for randomly distributed data there is a range of sizes for which the spatial data distribution has a fractal dimension of 2; that is, Euclidean. The minimum length scale at which the distribution ceases to be Euclidean is the optimum interpolation interval obeying Shannon's sampling theorem. For dimensions less than 2, the optimum interpolation interval is the shortest length at which the scaling regime is constant. In this case the gravity field cannot be interpolated without introducing some aliasing. As the fractal dimension characterizes the data distribution globally over the whole study area, the actual gridding interval, in some cases, will be smaller in order to represent short‐wavelength features properly in the more densely sampled sub‐areas, but this may generate spurious anomalies elsewhere. The proposed technique is applied to the station distribution of the Canadian national gravity data base and a series of sub‐areas. A fractal dimension of 1.87 is maintained over a range of sizes from 15 km to over 1600 km. Although aliasing occurs, since the gravity field certainly contains much shorter wavelength anomalies, aliasing errors may be minimized by selecting the proper interpolation interval from the fractal analysis.