Reflection of VLF radio waves from an inhomogeneous ionosphere. Part II. Perturbed exponential model

Abstract

Th e obli que refl ection of radio waves from a continuously stratified ionized medium is cons id ered . In this p ap er t he m ed iu m is assumed to be isotrop ic. T he h eight profile of the effect ive cond uctivity is a Gaussian curve superimposed on th e (u nd istu rbed ) exponentia l form. The refl ection coefficient is shown to be influenced by the vertical location of the Ga uss ian perturbation . In some cases the magnitude of the reflection coefficient is increased while, in other situations, it is d ecrea cd. In nearly all cases, insofa r as p hase is concerned, t he pre ence of t he p ert ur bation correspon ds to a lowering of the refl ection h eig ht .

Characteristics of the earth-ionosphere waveguide for VLF radio waves

“…The location of this plane is the reference surface which is referred to as z = in the previous section. As indicated in the previous section and from earlier work [Wait, 1962a;Wait and Walters, 1963], the reflection coefficient R for a rather broad class of inhomogeneous media may be written in the form…”

“…Nevertheless, it is not unreasonable to suggest that a suitable analytical model for the lower ionosphere is described by an effective conductivity which varies exponentially with height. It would then seem fruitful to regard more realistic models as a perturbation about the exponential form such as investigated analytically by Wait and Walters [1963]. It might also be mentioned that heavy ions will contribute to the effective value of W , In fact, provided the frequency CO is much less than v. (the collision frequency for the ions), the lower ionosphere may still be represented by an effective conductivity which is numerically equal to e CO (e. g. , see chapter VII in Wait, 1962a…”

“…for grazing modes. For example, it was shown before [Wait and Walters, 1963] that the oblique reflection of plane waves from a planar exponentially stratified medium could always be characterized in terms of an equivalent free -space problem. This equivalent situation could be imagined as a reflecting plane with a specified impedance boundary condition.…”

“…However, these levels (i. e. , heights less than 70 km) do not materially influence the reflection of VLF radio waves although they have a significant effect for LF radio waves at oblique incidence. This latter statement is borne out by a theoretical study of perturbed exponential N profiles [Wait and Walters, 1963].…”

“…Fortunately, there is some leeway in choosing this reference level. Variations by as much as ±5 km do not materially influence the final results, provided the appropriate value of the normal surface impedance is used.From a study of the reflection process for an isotropic exponentially stratified ionosphere[Wait and Walters, 1963], it is determined that a satisfactory choice for the reference level at VLF is where CO has the value 2. 5 X 10 sec .…”