The equivalent data concept applied to the interpolation of potential field data

Abstract

The equivalent layer calculation becomes more efficient by first converting the observed potential data set to a much smaller equivalent data set, thus saving considerable CPU time. This makes the equivalent‐source method of data interpolation very competitive with other traditional gridding techniques that ignore the fact that potential anomalies are harmonic functions. The equivalent data set is obtained by using a least‐squares iterative algorithm at each iteration that solves an underdetermined system fitting all observations selected from previous iterations and the observation with the greatest residual in the preceding iteration. The residuals are obtained by computing a set of “predicted observations” using the estimated parameters at the current iteration and subtracting them from the observations. The use of Cholesky’s decomposition to implement the algorithm leads to an efficient solution update everytime a new datum is processed. In addition, when applied to interpolation problems using equivalent layers, the method is optimized by approximating dot products by the discrete form of an analytic integration that can be evaluated with much less computational effort. Finally, the technique is applied to gravity data in a 2 × 2 degrees area containing 3137 observations, from Equant‐2 marine gravity survey offshore northern Brazil. Only 294 equivalent data are selected and used to interpolate the anomalies, creating a regular grid by using the equivalent‐layer technique. For comparison, the interpolation using the minimum‐curvature method was also obtained, producing equivalent results. The number of equivalent observations is usually one order of magnitude smaller than the total number of observations. As a result, the saving in computer time and memory is at least two orders of magnitude as compared to interpolation by equivalent layer using all observations.