A SCATTERED EQUIVALENT-SOURCE METHOD FOR INTERPOLATION AND GRIDDING OF POTENTIAL-FIELD DATA IN 3 DIMENSIONS

Potential-field geophysical data observed at scattered discrete points in three dimensions can be interpolated (gridded, for example, onto a level surface) by relating the point data to a continuous function of equivalent discrete point sources. The function used here is the inverse-distance Newtonian potential. The sources, located beneath some of the data points at a depth proportional to distance to the nearest neighboring data point, are determined iteratively. Areas of no data are filled by minimum curvature. For two-dimensional (2-D) data (all data points at the same elevation), grids calculated by minimum curvature and by equivalent sources are similar, but the equivalent-source method can be tuned to reduce aliasing. Gravity data in an area of high topographic relief in southwest U.S.A. were gridded by minimum curvature (a 2-D algorithm) and also by equivalent sources (3-D). The minimum-curvature grid shows strong correlation with topography, as expected, because variation in gravity effect due to variation in observation-point elevation (topography) is ignored. However, the data gridded and reduced to a level surface at the mean observation-point elevation, by means of the equivalent-source method. also show strong correlation with topography even though variation in observation-point elevation is accounted for. This can be attributed mostly to the inadequacy of constant-density terrain correction or to data error. Three-dimensional treatment in this example is required as a means of calculating the data onto a level surface, above regions where data and geologic sources overlap, as a necessary first step for making geologic correction, variable-density terrain correction, and evaluating data error. Better spectral estimates are obtained by direct calculation of the Fourier transform of the equivalent-source function than by the discrete fast Fourier transform computer algorithm.