A Comprehensive Study of Subsurface Propagation from Horizontal Electric Dipoles

Abstract

The general exact integrals for the electromagnetic field of an electric dipole in the earth near its boundary with the air are evaluated numerically over the full range of conductivities and permittivities that characterize different parts of the earth's surface. The following ranges are included: permittivities from 2 to 80, conductivities from 4 x 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> to 4 S/m, frequencies from 10 to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">9</sup> Hz, radial distances from 0.1 to 100 km, and depths of the source and point of observation from 0.15 to 15 m. The generally useful component of the electric field E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> is represented in graphs and contour diagrams that display the characteristics of propagation in their dependence on the frequency, the radial distance, the depth, and the electrical parameters of the earth. They are interpreted in terms of approximate formulas of Banos which are evidences of the lateral-wave nature of the field.