Magnetic Potential Spectrum Analysis and Calculating Method of Magnetic Anomaly Derivatives Based on Discrete Cosine Transform

Abstract

AbstractA method of magnetic potential spectrum analysis based on the cosine transform is proposed in order to improve the calculating accuracy of magnetic anomaly derivatives. According to the Poisson equation of gravity‐magnetic potential, we derive the relation of cosine transform spectrum between magnetic potential and magnetic field constituent and deduce the cosine transform spectrum formula of n degree derivatives using the cosine transform. The horizontal and vertical first derivatives of magnetic anomalies of an infinite cylinder are calculated by the cosine transform method, in which the maximum errors are –0.28 nT/m and 0.47nT/m, respectively and the percent errors are generally within –3.57%~3.27% and –1.94%~1.88%, respectively except several data of the boundary and part are bigger because of remains of Gibbus effect. The calculating curve and theoretical curve are approximately coincident, and there is no influence by effective magnetic dip angle in computing. But the errors with the Fourier transform method are –10.62nT/m and 14.42nT/m, there is large departure between the calculating curve and theoretical curve and evident influence by effective magnetic dip angle in computing. It indicates that the calculating accuracy of magnetic anomaly derivatives calculated by cosine transform is higher than that by Fourier transform, and the computing stability is excellent.