Reference: Abstr. for the 8th Scientific Assembly of IAGA with ICMA and STP Symposia (Sveden, Uppsala, August 1997). Editors: Rolf Bostrom, Tobia Carozzi, Inger Arlefjard, Ann-Sofi Wahlberg, P O Dovner. P. 178.

DIAGNOSTICS OF IONOSPHERIC IRREGULARITY SPECTRUM USING MEASUREMENTS OF RADIO WAVE ANOMALOUS ATTENUATION UNDER VERTICAL SOUNDING

(poster paper #28 full text)

A G Bronin, N A Zabotin, G A Zhbankov

(Rostov State University, Rostov-on-Don, 344090, Russia)

I B Egorov, A L Karpenko, V V Koltsov, E V Kuznetsov

(IZMIRAN, Troitsk, Moscow Reg., 142092, Russia)

Under radio wave ionospheric propagation the multiple scattering on small-scale (500 m - 5 km) field-aligned irregularities takes place. The shape of irregularities is the reason for the ionospheric scattering strong anisotropy. Both under oblique and vertical sounding the basic energy flow in a reflected signal may not coincide with a direction determined by geometrical optics laws.

One of the multiple scattering effects consists in anomalous attenuation of a wave reflected from the ionosphere which is registered on the Earth' surface in a vicinity of sounding station and in its site. Attenuation of a vertical sounding signal depends on frequency what allows one to solve an inverse problem - to find parameters of irregularities from the measured wave attenuation. In this report the results of the first experimental realization of this approach are stated.

The measurements were carried out at Troitsk on the digital ionosond "Parus". The selected experimental data are characterized by a high average level of attenuation of a signal of vertical sounding (10 dB and above), which cannot be caused by collisional absorption of radio waves (practically absent in a dark time of day) and, hence, being a consequence of scattering on random irregularities. The algorithm of solving of the inverse problem was based on the Levenberg-Marquardt nonlinear optimization method. The attenuation dependencies for ordinary and extraordinary waves at the same frequency bands are close. It is necessary to note the good qualitative and quantitative agreement between altitude dependencies of the irregularity level obtained from the data on attenuation of ordinary and extraordinary waves. In some sessions the change of irregularity level altitude dependence character at heights about 200 km is observed. It can be caused by distinction of mechanisms of formation of irregular structure at different heights in ionosphere.

SPATIAL SPECTRUM OF THE IRREGULARITIES

The basic model of ionospheric irregularities spectrum is

where ; are the outer and the inner scales of spectrun for j-th coordinate axis.

Versions of the anisotropic spectrum:

or

The sectrum is normed with respect to value of irregularities structural function in given scale R.

Poeverlein's construction

It is convenient to display graphically the electromagnetic wave propagation in a plane-stratified plasma layer with the aid of the Poeverlein construction (see fig. 1). Convenience of this construction (in fact, this is an example of coordinate system in space of wave vectors ) is become evident when drawing the wave trajectory: it is represented by a straight line, parallel to the axis . This is a consequence of the generalized Snell law, which also requires of equality of the incident angle and outgoing angle from a layer (), and constantness of the wave vector azimuth angle (). The crossing point of a wave trajectory with the refractive index surface under given value of determines current direction of the wave vector in a layer (it is anti-parallel to a radius-vector) and current direction of the group speed vector (it coincides with the normal to the refractive index surface). The projection of a wave trajectory onto the plane is a point which radius-vector has module and its angle with relation to axis equals to . Thus, the coordinates define completely the whole ray path shape in a plane layer and outside of it and are, in this sense, invariant on this ray path.

Radiation of an arbitrary point source of electromagnetic waves within the solid angle ; corresponds to the energy flux in the -space inside of a cylindrical ray tube parallel to axis with cross section . In case of regular (without random irregularities) plasma layer this energy flux is conserved and completely determined by the source directivity diagram:

(1)

where P is energy flux density in the direction determined by angles through the point on some base plane situated outside of the layer parallel to it (in the ionosphere case it is convenient to choose the Earth' surface as the base plane), is distance from the base plane (height in the ionosphere case).

Radiation energy balance equation:

When scattering is present the radiation energy redistributes over angular variables and in space what is described by variable . The value of satisfies in this case to the equation of radiation energy balance:

where , ,

is cosine of a ray trajectory inclination angle corresponding to the invariant angles and ; is Jacobean of transition from angular coordinates to the wave vector polar and azimuth angles and in the "magnetic" coordinate system (which axis is parallel to the magnetic field); is scattering differential cross section describing intensity of the scattered wave with wave vector coordinates , in magnetic coordinate system (corresponding invariant coordinates are and ) which arises at interaction of the wave with wave vector coordinates , (invariant coordinates and ) with irregularities. Vector function represents the displacement of the point of arrival onto the base plane of a ray which has angular coordinates and after scattering at level with relation to the point of arrival of an incident ray with angular coordinates .

Let us suppose that scattering causes a small change in invariant angles a ray path: (it also means that ). Note that in this approximation the angle of scattering may be large. For example, near the turning point small change in inariant angles correspond to large chage of wave vector direction.

We search for the solution of a kind:

, and .

For basic energetic term we obtain:

or ,

where .

Numerical estimation of the solution for reflection from the isotropic plasma layer:

where .

The solution describes three basic observable effects:

- Attenuation of a vertical sounding signal (up to 1020 dB in the location and in vicinities of the sounding station)

- Change of angles of arrival

- Angular spectrum broadening (~1 2 )

Fig. 2 represents the results of numeric calculations of effect of attenuation of vertical sounding signal in the vicinity of sounding station (in dB) for the following parameters of irregularities spectrum:

The frequency dependance of attenuation is represented on Fig. 3. The frequency dependance is different for spectra with different parameters what gives the principle opportunity to determine this parameters from attenuation measurements data.

The sequence of the solution of an inverse problem:

Ю) division of initial data into similar frequency intervals;

1. Approximation of high-altitude dependence of irregularities level on each high-altitude interval by linear function

;

c) realization of leasts quares algorithm on the base of repeated solution of a direct problem;

d) determination of the best set of parameters of high-altitude dependence of a irregularities level for each interval;

1. synthesis of obtained results in a uniform structure .

The results of solution of inverse problem are reprsented at Fig.5 and Fig. 6.

Results of account of frequent dependence of absorption for optimum parameters of high-altitude dependence of a irregularities level

Electron Density Random Irregularities and

Decameter Radio Wave Anomalous Attenuation

at the Mid-Latitude Ionosphere

A G Bronin, P F Denisenko, N A Zabotin,

G A Zhbankov, V I Vodolazkin

(Rostov State University, Rostov-on-Don, 344090, Russia)

It has been stated lately that natural random electron density irregularities of the ionospheric plasma play an essential role in energy redistribution of decameter radio waves radiated from a point source located on the Earth surface. In particular, under vertical sounding the multiple scattering takes place that results in the collisionless attenuation of waves. The attenuation in the

ionospheric F region, being measured by the A1 method, reaches of 10 - 15 dB. The attenuation value depends on the irregularity spatial spectrum and, therefore, it can be used for determination of their parameters.

The present paper describes the results of irregularity diagnostics in the mid-latitude ionospheric F region. Frequency dependencies of o- and x-wave attenuation obtained by the A1 method were used as initial data. The measurements were carried out at point Rostov in the 1989 winter season (high solar activity period) at night time. Estimation of the irregularity spectrum parameters was obtained by means of the inverse problem solution based on the Levenberg-Markvardt nonlinear optimization numerical algorithm. The method of calculations is described in poster # 28 "Diagnostics of ionospheric irregularity spectrum using measurements of radio wave anomalous attenuation under vertical sounding"(A G Bronin, N A Zabotin, G A Zhbankov I B Egorov, A L Karpenko, V V Koltsov, E V Kuznetsov). For calculations there were chosen experimental data from 4 sounding sessions carried out at January 23, 25 and 28 and February 2. The results of calculations are represented on Fig.1 - Fig.8. On Fig.1 - Fig. 4 are shown the the best fits to experimental data for each session. On each figure plot "a" corresponds to ordinary wave and plot "b" corresponds to extraordinary wave. The obtained high-altitude profiles of irregularities level for each session are show on Fig.5 - Fig.8. It was assumed in calculations that the irregularity spectrum has power-law shape with index 2.5. For the irregularity level in a scale length of 1 km values in the range were obtained. This value has the tendency to decrease with growth of height in the ionospheric layer both for ordinary wave data and for extraordinary wave data.

a) b)

Fig. 1

1. b)

a) b)

a) b)

Results of synthesis of high-altitude dependence of irregularities level:

Fig. 5 Fig.6

Fig. 7 Fig.8