Analytical Continuation of a Plane Field

Abstract

Now let us take up one of the most important concepts of the theory of a plane potential field, namely the concept of analytical continuation. As we have implied, in a two-dimensional case a plane field is described unequivocally by complex intensity. Obviously, the problem of analytical continuation of a plane field reduces to the well-known problem of analytical continuation of complex functions. A detailed treatment of this problem is offered in many treatises and monographs on the theory of functions of a complex variable. Those wishing to delve more deeply into this particular topic will no doubt start with the above literature. In this book, however, we will confine ourselves to the basic theorems and principles underlying the theory of analytical continuation, particularly to those needed for geophysical applications.