. Early geophysical papers of the Society of Exploration Geophysicists. Petroleum; Prospecting. 4 L. J. PETERS AND J. BARDEEN potential. Any changes of resistivity in the subsurface beds alter this normal potential. Thus measurements of potential on the surface of the earth give an indication of these changes of resistivity. Most prospecting methods differ only in the spacing of the electrodes and in the manner in which the potential is measured. The same mathematical theory thus applies to all of them. The theory is simplified by the fact that problems of steady flow in con- tinuous media are
. Early geophysical papers of the Society of Exploration Geophysicists. Petroleum; Prospecting. 4 L. J. PETERS AND J. BARDEEN potential. Any changes of resistivity in the subsurface beds alter this normal potential. Thus measurements of potential on the surface of the earth give an indication of these changes of resistivity. Most prospecting methods differ only in the spacing of the electrodes and in the manner in which the potential is measured. The same mathematical theory thus applies to all of them. The theory is simplified by the fact that problems of steady flow in con- tinuous media are the same mathematically as similar electrostatic problems. A current / entering an earth of conductivity a at an electrode A may be re- placed by a charge of q = I/l-wa at A. The potential at any point in the earth, due to this electrode is V = I/2irar, where r is the distance from the electrode. If several electrodes An are on the surface of the earth with currents /„ entering the earth, the potential at any point P in the earth is v = ±-?± <» lira rn where r„ is the distance from P to An. It may be noted that algebraic values of the current must be used in this sum. Thus the potential at P in Fig. 1 for the current flow between two electrodes is 27ro-\ri r2/ This additive property of the potentials is general and is not confined to a homogeneous earth. Thus we may simplify the theoretical discussion by con- sidering the potentials due to a single electrode. In order to illustrate the type of departure from normal potential that may be expected, a simple problem will be solved. The earth is of conductivity <Ti, to a depth a and is of conductivity <r2, below this depth. A current / flows. Fig. 2. Coordinate system for two-layer problem. into the earth at the origin of cylindrical coordinates r, z, . (See Fig. 2.) Let the potential in the surface layer be V\ and the potential for z>a be V*. The conditions to be satisfied by the potential are: (1) The differen
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