4: Electromagnetic Theory for Geophysical Applications
Section 1 Fundamental Electromagnetism
To comprehend the bases and the interpretational techniques of electrical prospecting methods, requires first a knowledge of the tools of electromagnetic theory. The ability to solve a boundary-value problem in electromagnetic theory then becomes the objective. All electromagnetic phenomena are governed by the empirical Maxwell's equations; we must start with them. Maxwell's equations are uncoupled first-order linear differential equations but can be coupled by the empirical constitutive relations which reduce the number of basic vector field functions from five to two. Care must be taken in selecting the form of the constitutive relations pertinent to the earth. In particular, for most earth problems, we assume isotropy, homogeneity, linearity, and temperature-time-pressure independence of the electrical parameters of local regions of the earth. A more complicated earth model is formed by juxtaposition of several such regions.