Interpretation of the secondary electromagnetic field by analytic continuation

Abstract

Given the values of a component of secondary magnetic
field on the plane surface of the earth, an attempt has been made to approach
the sources by finding the values of the component on a plane at
a depth h below the surface, the plane being above the sources.
To this end a Green's Function for the wave equation, appropriate
for a semi — infinite space was determined. The integral obtained was
expanded into series suitable for numerical calculations.
The average values of the component on the earth plane were assumed
to satisfy a double series and the coefficients were determined by the least
square method.
Formulae were ultimately developed to calculate the values on a plane
at a depth h, in terms of average values on six concentric circles around
each point.