Integral equation method in three dimensions

We shall use these formulae (9.34) and (9.36) in electromagnetic inversion. 9.1.5 Integral equation method in three dimensions 

Wc can apply an approach, similar to the one used in the 2-D case, to derive the electromagnetic integral equations in three dimensions. Electromagnetic Green s tensors, introduced in the previous chapter, make it possible to determine the electromagnetic field of an arbitrary current distribution j (r) within a medium with background conductivity (Ti,  

Maxwell s equations (9.2) can be rewritten for the background medium with excess current j =A(tE  

Substituting the expression for the excess current (9.4) into (9.39), we finally obtain the well-known representation for electromagnetic field as an integral over the excess currents in the inhomogeneous domain D (Raiche, 1974 Hohmann, 1975 Weidelt, 1975a)  

Using integral formulae (9.44) and (9.45), one can calculate the electromagnetic field in any point r, if the electric field is known within the inhomogeneity. Expression 

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