ULF-Sounding of Magnetosphere and Earth - Hydromagnetic Waves in the Magnetosphere and the Ionosphere - page 319

of the resonant peak by applying the extreme values of the phase difference
( D )toget

cot ∆ψ ∗
2

.

δ = ∆x
2

However, the developed method can be applied only if both observation points
are located in the same geoelectrical conditions. The lateral geoelectrical in-
homogeneity, especially when the condition of a strong skin effect is violated,
may substantially distort a resonant structure of pulsations. The disturbing
influence of geoelectrical cross-section would be mainly seen in the behavior
of the magnetic component oriented across the structure's extension. Above a
rock with higher conductivity, an pulsation magnetic H -component increases
by ∆H . An additional phase shift ∆ψ (0) > 0 , as compared with the incident
field, appears that can reach values of ∆ψ (0) (180 /π ) ∆H/H .

A theoretical modification of the gradient method of MHD-diagnostics for
the case of a crust geoelectrical inhomogeneity requires numerical calculations
of a complicated self-consistent problem. To eliminate the geological influence,
it is possible to use the following simple phenomenological method. Suppose
that the influence of a geoelectrical inhomogeneity can be expressed as some
coecient M , which the ratio G is multiplied by; and an additional phase
shift ∆ψ (0) , which is added to the phase difference ∆ψ = ψ (1)

∼

ψ (2) . Then
the experimentally measured functions G and ∆ψ will be presented in the
form: G = MG and ∆ψ = ∆ψ + ∆ψ (0) . Hereafter we neglect a weak depen-
dence of the unknown coecients M ( f )and ∆ψ (0) ( f ) on the frequency in a
bounded frequency band near the resonant frequency, as compared with G ( f )
and ∆ψ ( f ) (11.4), (11.5). The coecient M can be found experimentally from
the following set of simple relationships resulting from the properties ( C )of
function G ( f ):

−

G + = MG + , G −

= MG − , G − G + =1 . (11.6)

The correction coecient for amplitude ratio can be estimated as
M = G − G + .

As a rough estimate of ∆ψ (0) , the constant level of phase shift away from
resonant phase excursion can be taken. So, the amplitude ratio (11.4) and
phase difference (11.5)

will be shifted to the new levels M and ∆ψ (0)

(see

Fig.11.1).
A meridional gradient of the Alfven frequency can be estimated from the
data of gradient measurements as

∂f
∂x

f + − f − 2 ∆f

[ δ 2 +( ∆x/ 2) 2 ] 1 / 2 .

= (11.7)

x + − x −

The gradient method can even be used to restore a smooth f r ( L ) profile
in a limited interval of latitudes. The properties ( A, B, C )of G provide a way