A least-squares minimisation approach to depth, index parameter, and amplitude coefficient determination from magnetic anomalies due to thin dykes

Abstract

We have developed a least-squares approach to determine, successively, the depth, index parameter, and amplitude coefficient of a buried thin dyke, using moving-average residual anomalies obtained from magnetic data using filters of successive graticule spacings. By defining the moving-average residual anomaly value at the origin on the profile, the problem of depth determination is transformed into the problem of solving a nonlinear equation, f(z) = 0. Knowing the depth and applying the least-squares method, the index parameter is determined by solving a nonlinear equation of the form l(q) = 0. Finally, knowing the depth and the index parameter, the amplitude coefficient is determined in a least-squares sense using a simple linear equation. In this way, the depth, index parameter, and amplitude coefficient are determined individually from all observed magnetic data. We have developed a procedure for automated interpretation of magnetic anomalies attributable to thin dykes. We apply the method to synthetic data with random errors, complicated regionals, and interference from neighbouring magnetic rocks, and we test it on two field examples from Brazil and Canada.