The Evaluation of the Field of the Currents Induced in the Earth by an External Field Whose Distribution is Known Numerically


  • Attia A. Ashour


The elements of the magnetic field of the currents induced in the earth by an external magnetic field whose distribution is supposed to be known numerically are found in terms of the corresponding elements of the external field. The conductivity of the earth is represented by a uniformly conducting shell of radius qa (q < 1). When the conductivity of the shell is assumed infinite, these relations are Zi(P) = −q3Ze(P″) and Hi(P) = q3He(P″) − (1/qa2) equation imagerHe(r) dr, where Z and H are the vertical and vector horizontal components, P is a point on the earth's surface, P′ is a point on the same radius as P and at distance q2a from the earth's center, and r is the radius vector from the center of the earth. When the conductivity of the shell is taken as finite, a correction to the above formulas is given. The formulas are useful in comparing the observed distribution at the surface of the earth with what is to be expected from an external current system, when the effects of induction in the earth are taken into account.