THE EQUIVALENT DATA CONCEPT APPLIED TO THE INTERPOLATION OF POTENTIAL-FIELD DATA

The equivalent layer calculation becomes more efficient by first conve rting the observed potential data set to a much smaller equivalent dat a set, thus saving considerable CPU time. This makes the equivalent-so urce method of data interpolation very competitive with other traditio nal 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 un derdetermined system fitting all observations selected from previous i terations and the observation with the greatest residual in the preced ing iteration. The residuals are obtained by computing a set of ''pred icted observations'' using the estimated parameters at the current ite ration and subtracting them from the observations. The use of Cholesky 's decomposition to implement the algorithm leads to an efficient solu tion update everytime a new datum is processed. In addition, when appl ied to interpolation problems using equivalent layers, the method is o ptimized by approximating dot products by the discrete form of an anal ytic integration that can be evaluated with much less computational ef fort. Finally, the technique is applied to gravity data in a 2 x 2 deg rees area containing 3137 observations, from Equant-2 marine gravity s urvey offshore northern Brazil. Only 294 equivalent data are selected and used to interpolate the anomalies, creating a regular grid by usin g the equivalent-layer technique. For comparison, the interpolation us ing the minimum-curvature method was also obtained, producing equivale nt results. The number of equivalent observations is usually one order of magnitude smaller than the total number of observations. As a resu lt, the saving in computer time and memory is at least two orders of m agnitude as compared to interpolation by equivalent layer using all ob servations.