Correction of systematic error in magnetic surveys: An application of ridge regression and sparse matrix theory

Abstract

Foster, Jines, and van der Weg showed that systematic error in potential field surveys could be corrected by simultaneously adjusting all survey lines so that the root‐mean‐square mis‐tie at survey intersections was minimized. Their somewhat restrictive method is extended here for maximum flexibility, thereby allowing for irregular survey shapes, diagonal lines, constrained lines, varying degrees of adjustment for different lines, and weighting of intersections. By casting the adjustment as a large, sparse, linear least‐squares problem, the survey corrections may be efficiently computed using a block orthogonal decomposition scheme. This method is based on recent work in numerical linear algebra by Golub and Plemmons, Heath, and others. Foster et al. showed that the computed adjustments are not unique; for our extension we show the adjustments are also likely unstable. This nonuniqueness and instability of adjustments may be effectively handled by the use of ridge regression.