| In the interpretation of magnetic anomalies, the determination of the magnetic remanent magnetization strength and direction is very important. This problem can be solved by two ways. Firstly, the analytic signal of the magnetic field which, for 2D structures, is independent of the induction and the magnetization direction can be used. However, its shape is not totally independent of the induction and magnetization directions for 3D structures. The second method is based on the assumption that the remanent magnetization does not significantly alter the total magnetization direction. Nevertheless, in many applications, remanent magnetization is often strong and cannot be disregarded.;In order to implement the joint inversion of the total magnetic field and its analytic signal, I have developed the analytic derivatives of the body parameters. These derivatives are used to compute the Jacobian matrix used in the inversion. A new formula for the relationship between the remanent magnetization and the induced magnetization is also introduced. The inversion of analytic signal gives better results of geometry than total magnetic field inversion. In the situation where the remanent magnetization is not known, the analytic signal is best choice to be inversed for the geometry of the magnetic body.;Finally, the joint inversion of total magnetic field and its analytic signal was implemented successfully. The joint inversion has better precision and stability than the separate inversion of the magnetic anomaly or its analytic signal. Firstly, it performs better for high inclinations. Secondly, it has the best stability and precision when the initial values of the inversion are far from the true values. Thirdly, it has the best stability and the precision in the presence of noise.;The major objective of this study is to develop an algorithm for the joint inversion of the magnetic anomaly due to a vertical right circular cylinder with arbitrary polarization and its analytic signal. The main advantage of a joint inversion is that the information from two different data sets is used to reduce the non-uniqueness inherent in the inversion. The proposed joint inversion gives more robust and accurate results than the separate inversions of these two data sets. Moreover, it is possible to determine the direction of the remanent magnetization vector as well as its strength. |
