Potential field data interpolation by Taylor series expansion

Data interpolation is critical in the analysis of geophysical data when some data are missing or inarci-ssible. We interpolate irregular or missing potential field data using the relation between adjacent data points inspired by the Taylor series expansion (TSE). The TSE method first finds the derivatives of a given point near the query point using data from neighboring points and then uses the Taylor series to obtain the value at the query point. The TSE method works by extracting local features represented as derivatives from the original data for interpolation in the area of data vacancy. Compared with other interpolation methods, the TSE provides a complete description of potential field data. Specifically, the remainder in TSE can measure local fitting errors and help obtain accurate results. Implementation of the TSE method involves two critical parameters - the order of the Taylor series and the number of neighbors used in the calculation of derivatives. We find that the fast parameter must be carefully chosen to balance between the accuracy and numerical stability when data contain noise. The second parameter can help us build an over-determined system for improved robustness against noise. Methods of selecting neighbors around the given point using an azimuthally uniform distribution or the nearest-distance principle are also presented. Our approach is first illustrated by a synthetic gravity data set from a single survey line, and then it is generalized to the case over a survey grid. In both numerical experiments, the TSE method demonstrates an improved interpolation accuracy in comparison with the minimum curvature method. Finally, we apply the TSE method to a ground gravity data set from the Abitibi Greenstone Belt, Canada, and an airborne gravity gradient data set from the Vinton Dome. Louisiana. USA.