A scattered equivalent‐source method for interpolation and gridding of potential‐field data in three dimensions

Abstract

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.