614 EXPLORATION GEOPHYSICS 



be explored. The dimensions of the body to be located have a direct 

 bearing on the depth at which they may be detected. As a general rule 

 the conductive body should have at least two dimensions equal to or 

 greater than the depth at which it is located from the coil. For instance, 

 if the coil is held 6 inches above the surface of the ground and the body 

 is buried one foot below the surface, the conducting body should have 

 two dimensions 1^ feet hy ly^ feet. 



Method for Mapping Materials of Anomalous Magnetic Permeability. — Sund- 

 berg t has proposed a method for detecting magnetic materials which utilizes a mag- 

 netic field created by passing direct current through a coil or loop laid on the surface 

 of the ground. This constant field, being vertically polarized, will cause a change in 

 the intensity and direction of the magnetic field normally present in a magnetized 

 subsurface body. By means of a sufficiently sensitive instrument for measuring 

 magnetic field strength, the location and extent of the anomalous magnetic bodies 

 may be determined. 



It will be noted that fundamentally this is not a method of mapping the subsurface 

 distribution of current, but primarily one of mapping materials of greater magnetic 

 permeability than the surrounding earth. 



Methods for Surveying an Area by Determining the Polarization 

 Ellipse. — As indicated previously, the magnetic field at the surface 

 of the earth is the resultant of the primary field due to the energizing coil 

 and the secondary fields due to various induced currents. 



To simplify the mathematical analysis the various secondary fields 

 will be treated as one field. The vector representing this resultant secon- 

 dary field and the vector representing the primary field will generally 

 be displaced in space by some angle, a say, and in time phase by some 

 other angle, for example n + 9. (Compare p. 608.) Hence, the resultant 

 of the primary and secondary fields is of the type known as an elliptically 

 polarized field. The vector representation of an elliptically polarized 

 field is a rotating vector whose tip periodically traces out an ellipse and 

 whose length at any instant is proportional to the magnitude of the 

 field at that instant.* 



The production of a resultant elliptically polarized field by two fields 

 which are out of phase may be shown mathematically as follows : Assume 

 that at a point P the primary field is in the x direction and the secondary 



t K. Sundberg, "Method and Apparatus for Magnetic Prospecting," U. S. Patent 1,748,659, 

 issued Feb. 25, 1930. 



* Consider for example, that the resultant magnetic field at any instant is given 

 by the equation H = Hosin (wt — <p) where Ho, w, and (f> are constants and t denotes 



time. Assign a series of values to t; for example, ? = 0, - — , -r— - — , — , -; — , 



Aw 2iv Aw w Aw 

 '2 y o 



~ — , - — , — and compute the corresponding values of H. Then draw vectors 

 2w Aw w 



whose lengths are proportional to H and whose directions make angles, — 0, (ir/Aw 

 — <^), (ir/2w — 0), etc., with some arbitrary axis. The envelope of the tips of these 

 vectors will be found to be an ellipse. 



