Integral equation method in two dimensions

For such geoelectrical models, the electric field has but a single component, Ey, which can be represented as the sum of a background (normal) part and an anomalous part  

It should be clear that the total field, Ey, satisfies the equation 

Subtracting the last equation from the one before it, we find an equation for the anomalous field  

An important role is played in the integral equation method by the Green s function for the background (normal) model of the earth. The Green s function, Gft(r lr), depends on the positions of two points, M(r) and M (r ), and is determined by a solution of the equation  

In this last equation, 6 is the two dimensional Dirac delta-function which is defined as follows  

---