On the Geo-electromagnetic Variations of Shorter Period
Hoshi, T.
Abstract
Assuming that the geo-electro-magnetic variations are produced by a known agency of external origin and that the earth is a homogeneous isotropic medium for the case of short periodic variations of the order less than somo few minutes，the components of the magnetic field and electric field under general consideration are given as follows:
Ｂｒ＝ − １/ｒsinθ・∂/∂θ(sinθ・∂π2/∂θ) −1/ｒsin2θ・∂π2/∂α２
μＣｒ＝−（ １/ｒsinθ・∂/∂θ(sinθ・∂/∂θ)＋1/ｒsin2θ・∂2/∂α２）Ｖ２π2
Ｂθ＝ １/ｒsinθ・∂/∂α(V・２π２) +1/ｒ・∂2(rπ2)/∂r∂θ
μＣθ＝1/r ・∂2/ ∂r∂θ (V・２π２) - １/sinθ・∂/∂α(V・２π２)
Ｂα＝ −∂/∂θ(V・２π１) + 1/ｒsinθ・∂２（ｒπ2）/∂r∂α
μＣα＝1/r sinθ・∂2/ ∂r∂α (rV・２π1) + ∂/∂θ(V・２π２)
where B is magnetic induction , C is total current density composing of conduction current and displacement current and π1, π2 which may have the form πexp(-ipt), are any functions satisfying the condition
V・２π+(4πρμ/ｃ２・ip + εμ/ｃ２・ｐ２）＝０
In a particular case where radial component of the magnetic field is existent, the functional forms are
π1=0, π2=1/(r)1/2 (AnJn+1/2(ξr))+BnJn+1/2(ξr))Pnt(cosθ)exp(-ila),
where An,Bn are constants to be determined form boundary conditions and
ξ=p(εμ)(1/2)((4πρ/εp)2+1)（1/4） exp(t・φ/２)，φ＝arctan(4πρ/εp)
We have applied the above analysis to the variability of vertical component of geomagnetism and related phenomena of the earth-current, and come to the conclusion that the variability and E-W component of the earth-current must behave in a likely mood or the Phase-difference between them is 0 or π, and N-S component is π/2 behind the variability.
Conference to the observational data supports that the analysis holds good, but observation made at Toyohara
Magnetic Observatory contain some difficulties with the another is inclined to attribute to some local anomalies.
