Synthesis of the topside ionograms under the presence of isolated irregularities in the bottomside ionosphere

N. P. Danilkin, V. I. Stasevich, and E. R. Tumanova

Institute of Applied Geophysics, Moscow, Russia

Contents

Abstract

Introduction

As a result of conducting active experiments, disturbances of the electron concentration with characteristic dimensions of kilometers and tens of kilometers and the development time of an hour and longer are created. It is widely known that isolated irregularities of a natural origin with nearly the same parameters were observed [Argo et al., 1992; Calvert and Schmid, 1964; Chidsey, 1965; Fitzgerald et al., 1997]. The ground-based ionospheric sounding is a reliable method of detection of such irregularities [Paul et al., 1968]. However, this method cannot monitor the ionosphere above the F region maximum. It was noted earlier by Danilkin et al. [1987a] that the transionospheric sounding can be used to monitor irregularities in the bottomside ionosphere using the traces in the ionograms of satellite sounding.

The aim of this paper is to demonstrate that the topside sounding itself provides abilities to observe the bottomside ionosphere irregularities because of a presence in the ionograms of the trace of the reflection from the ground.

There are methods of restoration of the vertical profile of the undisturbed electron concentration on the basis of ionograms of vertical, topside, and transionospheric sounding, but currently there is no analogous solution of the inverse problem in the presence in the ionograms of complicated traces formed by the rays, refracted by irregularities. It is reasonable to use the results of numerical solution of the direct problem of the ionogram synthesis and to vary model parameters in order to get maximum agreement with the experimental data.

Formulation of the Problem

The mathematical model of irregularities includes, in the same way as was done by Paul et al. [1968] and Danilkin et al. [1987b], a choice of a continuous function F( r) , which tends to unity at infinity and is superposed on the undisturbed spherically layered distribution of the electron concentration:

where h is the height above sea level; d is the distance at the ground, h₀ and d₀ are the height and distance of the irregularity center, respectively; R is a characteristic dimension of the irregularity, and A is the irregularity magnitude (describes relative depletion of the electron concentration in the ( h₀ , d₀ ) point as compared to the undisturbed ionosphere).

The electron concentration vertical profile with a maximum at an altitude of 300 km and critical frequency of 9.2 MHz typical for middle latitudes was used as a background profile. The height of the satellite orbit used in the calculations was 1000 km.

Methods of Calculations and Numerical Simulation Results

Radio wave propagation in the ionosphere was considered in the geometric optics approximation (GOA). Application of the GOA and the methods of ionogram synthesis in the presence of ionospheric irregularities and of calculation of radio wave trajectories on the basis of integration of a bicharacteristic system of differential equations were described by Danilkin et al. [1987a].

Magnetic field influence leads to a splitting of the radio wave into two components. In that case the system of the bicharacteristic differential equations should be integrated separately for each component; therefore two ionograms would be synthesized, for the ordinary and extraordinary rays. For diagnosis of the ionospheric irregularities it is also reasonable to obtain experimental ionograms for both components, using the polarization separation of the signals [Danilkin, 1987]. To simplify the calculations and make the results more visual, the magnetic field influence was not taken into account in this work. We will call the trace of the reflection of the ordinary wave in the absence of irregularities the main ray. The rays refracted by the irregularities form extra traces with a delay different from that of the main ray. Depending on the irregularity dimension and its position in the ionosphere and in relation to the satellites, several types of ionograms are observed. Figures 1 and 2 show the most characteristic ionograms. The influence of each of the irregularity parameters chosen is considered, the rest of the parameters being fixed.

1. Let us denote as Dd the modulus of the difference between the distances of the satellite and irregularity at the Earth's surface and consider its influence on the topside ionograms, using as an example the irregularity with radius R = 25 km, altitude of the center h₀ = 200 km, and depth A = 1 (which corresponds to a "negative" irregularity with zero electron concentration in the center). Under Dd = 0 km (that is, when the irregularity is situated at the vertical, which passes through the Earth's center and the satellite), all the rays coming to the reception point were refracted by the irregularity. There is no main trace in this case, and the ionogram consists of two curves, forming a "beak" with the sharp part directed to higher frequencies (Figure 1b). The upper curve in Figure 1b is formed by the rays propagating in the direction perpendicular to the Earth. Passing the ionosphere, they cross the region with depleted electron concentration; so their delay is less than the delay of the main ray also propagating perpendicularly to the Earth. Since the lower the radio wave frequency, the stronger they are influenced by the irregularity, the difference in virtual heights of the main (Figure 1a) and the upper (Figure 1b) traces is maximum at a frequency of 9.2 MHz and is equal to 160 km. Under a ray frequency increase the difference gradually decreases and is almost within instrumental errors above 13 MHz. The lower curve is due to the rays emitted from the satellite at a small angle and returned because of refraction by the irregularity.

Let us increase Dd , that is, change the irregularity position horizontally in relation to the satellite. The "beak" then becomes narrower, and under Dd 100 km both curves almost merge (the difference in the virtual height is comparable to the instrumental errors) and the ionogram looks undisturbed.

Further increase of Dd leads to an increase of the difference in altitudes of the main and extra traces by the same value at any sounding frequency, and so the traces in the ionogram in the frequency intervals, where the extra trace exists, are similar (Figure 1a).

The trace's beginning and ending frequencies (Figure 1a) also are characteristic of an extra trace. The synthesis results have demonstrated that with an increase of Dd from 100 km and higher, the length of the extra trace shortens: its beginning frequency increases and its ending frequency decreases. For example, for Dd = 200 km, these values are 9.4 MHz and 14.5 MHz.

2. To study the influence of the irregularity height above the ground, ionograms for several values of this parameter were calculated. The irregularity below 180 km does not influence radio wave propagation, and no extra traces are seen in the ionograms. Under the irregularity center height at 200 km, two extra short traces parallel to the main trace appear at frequencies from 10.2 to 10.7 MHz and from 11.5 to 12 MHz. It may be assumed that there are extra traces corresponding to the frequencies between the end of the first trace and the beginning of the second one, and their absence in the ionogram is due to incompleteness of the algorithm used for a search of rays returned to the reception point. On the basis of the ray trajectories, one can conclude that the "low-frequency" and "high-frequency" extra traces are formed by different types of rays. In the former case the descent and ascent (after reflection from the ground) branches of the ray lay at opposite sides from the irregularity center; in the latter case they lay at the same side.

When the height of the irregularity center is from 250 km to 300 km (the height of the electron concentration maximum), two extra traces are well pronounced in the 10.5- to 15-MHz interval, one of the traces being similar to the main trace and the other being located so that it adjoins the main trace by its high-frequency end and the first extra trace by its low-frequency end. The topside ionogram and the ray trajectories, which lead to the traces of such type, are presented in Figure 2a.

3. Let us discuss now the influence of irregularity parameters such as radius and depth on the synthesized ionograms. It can be seen from the above considered ionograms for disturbed electron concentration that the extra traces in them are formed mainly by two types of rays: first, the rays that crossed the region situated within a characteristic volume of the irregularity, and, second the rays that which were refracted at the irregularity outer boundary. These two types of rays should be manifested in the ionogram by two extra traces. However, if the residual of the virtual heights of these two traces is small (within instrumental error), actually only one extra trace would be seen in the ionogram. For example, at altitudes of h₀ = 200 km (Figure 1a), both rays refracted by the irregularity and returned to the reception point have traces with almost the same virtual heights. We will call the trace of the rays that crossed the irregularity the first extra trace, and we will call the trace of the rays refracted by the irregularity boundary the second extra trace. The ionograms in Figures 1a, 1b and 2a were synthesized for an irregularity with a characteristic dimension of R = 25 km. The ray trajectories are significantly different for the irregularities with smaller or larger dimensions. Under the irregularity dimension from 10 km to 50 km the position of the second extra trace is slightly changed owing to a small change of the ray path. However, the first extra trace is subjected to the stronger influence of the irregularity dimensions: its virtual height would be lower if the rays pass through the negative irregularity of larger dimensions with depleted concentration (the trace is situated higher in the ionogram) and would be higher if the irregularity dimensions are smaller. It is found that the difference between the virtual heights of the first and second extra traces at the 10.5-MHz frequency is about 10 km for the irregularity with R = 15 km. If R = 25 km and 30 km and the other parameters are the same, the height difference increases to 20 km and 30 km, respectively. The traces merge at a frequency of about 12 MHz. The irregularities with the characteristic dimension of 50 km influence the rays passing through them so strongly that the reduced height of the extra trace becomes lower than that of the main trace (Figure 2b).

Considered above were ionograms synthesized for irregularities with depth A = 1 , that is, with zero electron concentration in its center. The synthesis results show that the higher the A parameter, the more high-frequency rays are influenced by the irregularity. For example, the extra trace of the irregularity in Figure 1a under A = 1 stops at a frequency of 14 MHz, under A = 0.7 it stops at 12 MHz, and under A = 0.3 it stops at 9.8 MHz.

Conclusions

Principal possibilities for diagnosing irregularities of the bottomside ionosphere mainly of artificial origin on the basis of characteristic features of the topside sounding signals reflected from the ground are demonstrated. Solution of the corresponding direct problem and comparison of the experimental data with synthesized ionograms may provide determination of irregularity location, dimensions, and depth.

References

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