Interpolation of potential‐field data by equivalent layer and minimum curvature: A comparative analysis

Abstract

Interpolation using only the observations at discrete points is an ill‐posed problem because it admits infinite solutions. Usually, to reduce ambiguity, a priori information about the sample function is introduced. Current interpolation methods in mineral exploration introduce only the constraints of continuity and smoothness of the interpolating function. In interpolating potential‐field anomalies, the constraint that the sampled function is harmonic may be introduced by the equivalent‐layer method (ELM). We compare the performance of the ELM and the minimum curvature method (MCM) in interpolating potential‐field anomalies by applying these methods to synthetic magnetic data simulating an aeromagnetic survey. In the case the anomaly flanks and peak are undersampled, the ELM performs better than the MCM in recovering the anomaly gradients and peak. In the case of elongated linear anomalies, the ELM recovers the exact linear pattern, but the MCM introduces spurious oscillations in the linear pattern. Also, the ELM is able to reduce the data from a survey flown at different heights to a common level. In contrast, the MCM, being a 2-D interpolation method, cannot account for variations in the vertical coordinates of the observation points.