PRINCIPLES OF THE MAGNETIC METHODS IN GEOPHYSICS

Magnetic methods are widely used in exploration, engineering, borehole, and global geophysics and the subjects of this monograph are the physical and mathematical principles of these methods regardless of the area of application. The first chapter is devoted entirely to the magnetic field caused solely by conduction currents. Beginning with Ampere’s law we analyze the force of interaction between currents and then introduce the concept of the magnetic field and discuss its fundamental features. In order to simplify a study of magnetic field the vector potential is introduced. Special attention is paid to the system of equations of the magnetic field at regular points and at places where surface density of currents differs from zero. We also consider several examples of the field behavior because of its relationship to the application of magnetic methods in geophysics. The second chapter describes in detail the theory of the magnetic field in the presence of magnetic medium. There is a section where we study distribution of magnetization currents and association between these currents and the vectors of the inductive and remanent magnetization. The systems of equations for the magnetic field and fictitious field H are derived and we illustrate a difference between these fields considering several examples. The behavior of magnetic field in the presence of magnetic medium is described in the next chapter, where at the beginning we consider questions such as a solution of the boundary-value problems and theorem of uniqueness. Then behavior of the magnetic field and the vector of magnetization are analyzed in the presence of different magnetic bodies. In order to describe the theory of the vertical magnetometer we study several topics related to this subject,

among them are the force acting on magnet, moment of rotation, interaction between two magnets, and the relationship between Ampere’s and Coulomb’s laws. The main magnetic field of the earth is described in Chapter 4. We begin with an introduction to the central characteristics of this field and briefly describe the history of its study. Then we consider the spherical harmonic analysis of the earth’s field that is naturally preceded by information on Legendre’s functions. In Chapter

5 we focus on a solution of the inverse problems in the magnetic method and describe uniqueness and nonuniqueness, ill- and well-posed problems, stable and unstable parameters, regularization, as well as different methods of solution to the forward problem. The main purpose of Chapter 6 is to describe diamagnetic, paramagnetic, and ferromagnetic substances proceeding from the atomic physics. Following the Feynman lectures, we introduce concepts of the angular momentum and magnetic moment of atom, derive an expression for the frequency of precession, and describe energy states of atomic systems.

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