On the Possibility of Estimating some Physical Constants of the Earth Crust by the Magnetic Observations on the Surface of it

[摘要] By spherical harmonic analysis it is possible to distinguish between the_??_arts of the earth's magnetic field, at any time, which originate respectively within and above the earth's surface. A. Schuster, S. Chapman and others, applying this method, found that the major parts are of external origin, but that there are also parts produced within the earth so far as the diurnal and the storm-time variations concern. They attributed the parts due to the inner part of the earth to electric currents inducd in the earth by the outer varing field.They considered that the earth is a uniformly conducting sphere, but in reality, there exist oceans and continents of wide extentions over the globe. When we consider the effect of land and ocean the problem becomes too complex to be treated easily, And if we consider the magnetic variation at the middle part of ocean or continent, it will be not so much unreasonable though we do not consider the effects of both, Therefore the present author considered the electromagnetic induction within the earth's crust consisted of many consentric shells, each of which is of uniform nature, putting the ocean and land out of consideration. The earth is considerd to be constructed from m's concentric conducting shells and a non-conducting medium outside the conducting shells. (radius being _??_a)The typical forms of the magnetic potential of the external and internal origins are indicated respectively by (1) and (2) (page. 294) at the earth's surface. While in the core the potential becomes (3). Applying the adequate boundary conditions we have the relations (6) to be fulfilled at the boundaries. Successive application of (6) we have the relation I0/E0as a function of κ electric conductivity, μ magnetic permeability, and ξ depth of conducting shell.If we consider the periodic variation of short period (6) becomes (8) and if the period is sufficiently small we have a functional relation of κ/μ and ξ only. Therefore in the stratum near the earth's surface we can obtain κ/μ and ξ. For the variation of the period little longer than before we should use (9) instead of (10) and then we can obtain κ, μ and ξ separately.On the other hand if we consider the periodic variation of long period we must use (11) instead of (7). Hence in this case if the period is so long to be able to neglect the term L in (11), the resultant expression of I0/E0 contains only μ and ξ. Therefore in this case we can not know κ. Namely as in this case the electromagnetic induction penetrates far deep in the interior of the earth crust, in such a region we can assume the permeability only.The discussions made hitherto are all based on the supposition that the magnetic variation observed on the earth are mainly of external origin and their internal parts should be interpretted as the effect of the electromagnetic induction within the earth. If we have ample data of the magnetic variation of external origin at stations at almost middle part of land or ocean, we can estimate the electric and magnetic states of the upper stratum of the earth from the variation of short period and the magnetic state of the relatively inner core of the earth from the variation of long period. As to the variation of the intermediate period, not so long nor so short, the treatment becomes rather complex.

[学科分类] 大气科学