New Formulas for HED (Horizontal Electric Dipole), HMD (Horizontal Magnetic Dipole), VED (Vertical Electric Dipole), and VMD (Vertical Magnetic Dipole) Subsurface-to-Subsurface Propagation

New formulas for the electric and magnetic fields produced by the four elementary dipole antennas have been developed for the subsurface-to- subsurface, subsurface-to-surface, surface-to-subsurface, and surface-to-surface propagation cases. These formulas are of rather simple, but useful, form and are completely general (i.e., the air can easily be replaced by the sea bottom). They are valid at any frequency and at any range beyond a certain minimum distance for the flat-earth case. The main restrictions on these formulas are that the square of the index of refraction is >or= 10 and that the horizontal separation is >or= 3 times the sum of the depths of burial of the transmitting and receiving point sources. With these new formulas, computer evaluation can be reduced to fractions of a minute, compared with hours for the complete numerical evaluation of the exact Sommerfeld integrals. There also will be an interference pattern set up under certain close-range conditions because the three waves (direct, modified mirror image, and lateral may interfere, either constructively or destructively, with each other.