Upward continuation of scattered potential field data

Abstract

Numerous methods have been used for upward continuation, but most of them require data on a regular grid. Gridding can introduce errors that affect the continued data in an unpredictable way. To avoid this problem, we design a continuation operator used for the direct continuation of scattered data on a 3-D basis. In this approach a harmonic function, satisfying the constraints imposed by the measured data, is developed. The continuation is written in the form of a linear combination of the measured data, but it depends on the arbitrary choice of the topographic zero level. However, the coefficients of the linear combination depend only on the position of the data points. This allows the zero level to be estimated on the basis of the continuation of synthetic anomalies calculated between the starting and ending surface. An important feature of the method is its local character, which allows the reduction of computation time. Also, the stability of the method for noisy data is reasonably good. The method is applied to both synthetic and real cases. Synthetic examples show how gridding‐related errors may affect the continuation when an irregular distribution of data points and a variable topography are considered.