the influence of relief on formation of reflected signals of subsurface sounding radar

ISSN 0038�0946, Solar System Research, 2014, Vol. 48, No. 3, pp. 176–181. © Pleiades Publishing, Inc., 2014.Original Russian Text © V.M. Smirnov, O.V. Yushkova, I.P. Karachevtseva, I.E. Nadezhdina, 2014, published in Astronomicheskii Vestnik, 2014, Vol. 48, No. 3, pp. 192–197.

176

INTRODUCTION

The study of the Moon occupies a special place inspace exploration programs in many countries. Itspractical development could be more efficient if sig�nificant localized water ice deposits were discovered inthe surface layer. One of remote methods for solvingthis problem is subsurface radiolocation.

The radar investigations of the near�surface soillayer of the Moon were performed in 1972 from theApollo�17 spacecraft (SC).

Signals, reflected by subsurface soil boundaries atdepths of 0.9 km, 1.6 km, and 1.4 km (Porcello et al.,1974) were obtained in the measurements.

The possibility of applying specialized orbital sub�surface�sounding radars for determining parametersof the near�surface soil layer was confirmed in Marsstudies. The experiments were performed by MARSIS(Mars Express spacecraft, Mars Advanced Radar forSubsurface and Ionosphere Sounding) and SHARAD(Mars Reconnaissance Orbiter spacecraft) radars.Both devices emitted a linear frequency�modulated(LFM) signal. The MARSIS radar operated in fourmodes with central frequencies of 1.8, 3, 4, and5 MHz; the deviation band of each signal was 1 MHz(Picardi et al., 2005); the frequency range of theSHARAD radar varied from 15 to 25 MHz (Seu et al.,2004; Phillips et al., 2008; Carter et al., 2009).

The experimental data were processed on the Earthby the matching filtering method, which is intended tolocalize (in time) signals, reflected from the surfaceand internal boundaries, and to estimate the delaytime between them. The in situ measurements wererepresented in the form of radargrams, plotted along

the SC ground track. The processed data of the mea�surements, performed above Mars’ North polar cap,are in accord with the geological idea of its structureand visually demonstrate the presence of layered struc�tures. However, this type of processing does not allow oneto determine the depth, thickness, and dielectric param�eters of rocks forming the internal layers.

At present, the performance of radar measure�ments along the flight route of the orbiting spacecraftis planned as part of the Russian Moon–Globe mis�sion. It is assumed that the module will be in a polarorbit at a height of 100–50 km above the surface forone year. The RLK�L low�frequency radar complex isinstalled on board for radar investigations of the sur�face and the near�surface layer of the Moon. One ofthe problems of this experiment is to study dielectricproperties and soil structure in the monostatic loca�tion mode by the LFM signal in a frequency range of17.5–22.5 MHz. The signal duration is selected sothat it should be completely formed in free space, i.e.,

In this case, the Helmholtz approximation is

used in analyzing reflected signals. In the experiment,the duration of the radiated signals is assumed equal to250 µs for a 100�km altitude.

For processing the sounding results, in addition totraditional methods the recovery procedure of thedepth permittivity distribution of the nonhomoge�neous soil will be applied on the basis of the functionalanalysis of parameter changes of the incident andreflected waves, i.e., the frequency dependence of thereflection coefficient (Yushkova, 2010). Since thisinverse recovery problem of the spatial distribution of

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The Influence of Relief on Formation of Reflected Signalsof Subsurface Sounding Radar

V. M. Smirnova, O. V. Yushkovaa, I. P. Karachevtsevab, and I. E. Nadezhdinab

a Kotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences (Fryazino Branch), Moscow oblast, Russia

b Moscow University of Geodesy and Cartography (MIIGAiK), Moscow, RussiaReceived December 3, 2012; in final form, April 18, 2013

Abstract—Radar sounding of the surface and near�surface layer of the Moon by the RLK�L low�frequencyradar complex from the orbiter module is planned for the Moon–Globe Russian mission. To forecast resultsof radar experiments, a simulation procedure of the reflection of the RLK�L radar signal by the Moon’s sur�face is designed. The 3D surface model, based on measurement results of the Lunar Orbiter Laser Altimeter(LOLA) of the Lunar Reconnaissance Orbiter mission was used in the calculations. The simulation resultsshowed that the spectrum shape of the reflected signal depends on the relief type in the experimental area.Therefore, when the depth distribution of the permittivity of the geological media is determined, the topo�graphic information should be taken into account.

DOI: 10.1134/S003809461403006X

SOLAR SYSTEM RESEARCH Vol. 48 No. 3 2014

THE INFLUENCE OF RELIEF ON FORMATION OF REFLECTED SIGNALS 177

dielectric parameters of the soil belongs to the class ofincorrectly posed problems, in treatments of measure�ment data and their interpretation, it is necessary totake into account all processes affecting changes of thesignal parameters, and to correct (if possible) theireffect.

In the subsurface sounding, the parameters of thereceived reflected signal depend on characteristics ofthe signal, surface relief, dielectric parameters of thesoil, and their distribution throughout depth.

In spite of the fact that the surface relief is the dom�inating factor affecting the formation of the reflectedsignal, up to now there has been no procedure whichtakes into account topography in processing the resultsof measurements from subsurface sounding radars. Itis known that the delayed pulses, arriving from sidereflectors, incident on the radar antenna during recep�tion, in addition to those vertically reflected, lead toamplitude and phase changes of the signal. The ques�tions arise as to how these factors can be taken intoaccount during data processing, how strong these dis�tortions are, and in what regions it is expedient to per�form radar measurements.

INITIAL DATA FOR THE SIMULATION

To respond to these questions, the signal reflectionprocess of the RLK�L radar from the Moon’s surfacewas simulated.

RLK�L signal. Analytically the LFM signal is spec�ified by the formula:

The envelope of the signal is a constant height rectan�gular function. The LFM signal spectrum does notdepend formally on the frequency range and is also avirtually rectangular function. Figure 1 shows theLFM signal spectrum normalized to unity (curve 1)with deviation = 5 MHz and minimal working fre�quency = 17.5 MHz. If the Moon’s surface wereeven and smooth, the signal reflection would occur atonly one subsatellite point (according to the waveapproximation), in spite of the fact that the antennasof both radars are half�wave vibrators and, hence, havea wide directional pattern. In this case, the spectrumof the signal reflected from the soil, which is uniformthroughout the depth and consists of basalt, is shownin Fig. 1 by curve 2 and that of the signal reflected fromsoft soils is shown by curve 3. The reflected signalspectra differ from the spectrum of the radiated signal

by a factor = where is the soil permittiv�

ity. For regolith = 2.8 and for basalt = 9(Rzhevskii et al., 1976). If there is a subsurface bound�ary between dielectrically nonuniform media, e.g.,

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soil–ice, regolith–basalt, the reflected signal is theinterference of the signal reflected from the upperboundary and the signal reflected from the innerboundary. These signals are shifted relative to oneanother by the time required for propagation of theradio wave of the corresponding frequency from theupper boundary to the lower and back. Since the sig�nals are long, it is very difficult to determine the delaytime between these signals. In the frequency domain,the interference effect is identified more simply, sincethe spectrum acquires an oscillating form. The periodand amplitude of oscillations, the position of localpoints of extremes in the frequency dependence of thespectrum module depend on dielectric characteristicsof rocks and the depth of their horizons. As an exam�ple, Fig. 1 shows the spectrum module of the signal,reflected from a 25�mm�thick regolith layer, lying onbasalt (curve 4).

Surface. The 3D model of the surface of the equa�torial zone of the Moon from 0° to 15° N and from 90°to 105° E (Fig. 2) was used for the simulations. Themodel was constructed from data, obtained in thecourse of the Lunar Reconnaissance Orbiter (LRO)NASA mission by using measurements from the LunarOrbiter Laser Altimeter (LOLA) laser altimeter. Thesurface map is shown in Fig. 2 in geography coordi�nates: the latitude is the vertical line, the longitude is thehorizontal line, and the deviation of the radius–vectorfrom the Moon’s radius taken as equal to 1737.4 km, isshown in the gray color gradation. The permittivity ofthe surface was considered to be constant, corre�sponding to the permittivity of regolith.

Geometry of the problem. When the height of thespacecraft km, the circular orbital velocity is,100H ≈

1

022.517.5

1

2

3

4

f, MHz

Spe

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m m

odul

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Fig. 1. Spectrum module of the signal: (1) radiated, nor�malized to unity; (2) reflected from the soil, consisting ofbasalt; (3) reflected from the soil, consisting of regolith;(4) from the regolith layer, located on basalt, the layerthickness is 25 m.

178


SMIRNOV et al.

approximately, v = ≈ 1.6 km/s, wherethe mean radius of the Moon = 1738 km, the accel�eration due to gravity of the gravitational field on theMoon’s surface = 1.63 m/s2. The time from thestart of the signal radiation to the end of reception ofthe reflected signal ≈ 0.9 µs. During thistime the orbiter moves 1–2 m. This allows one to con�sider that the radar receives the reflected signal at thesame point where it was emitted. The radiation andreception starts are spaced at the time equal to (the spacecraft height H is defined more exactly beforethe radiation). The recording time of the reflected sig�nal corresponds to Trec = 350 µs, ensuring the reflec�tion of longest wave of the working range of the devicefrom the layer, the thickness of which is about 30 km.According to the results of analysis of the gravity map,compiled from the Gravity Recovery and InteriorLaboratory (GRAIL) spacecraft data (NASA), thepower of the lunar crust is evaluated namely by thisvalue (Zuber et al., 2013).

After the signal reception, the RLK�L switches offthe low�frequency radar and turns on the other radarfor performing the next experiment at higher frequen�cies. The switching between the radars is intended to

( )R g R H+L L L

RL

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avoid recording in the 1current session the re�reflectedsignals of the previous measurements.

When the reflected signal is recorded, not onlyvertically reflected signals but signals from sidereflectors, located at any point of the surface in thespot with radius D = Rarccos([8R2 + 8RH –

, fall on the antenna sys�tem. When the height of the spacecraft H = 100 kmabove the Moon’s surface and Trec = 350 µs, D does notexceed 120 km. If the reception time would be equal tothe radiation time, i.e., 250 µs, the spot radius wouldcorrespond to 90 km.

Received signal. The modified facet surface repre�sentation model was selected for calculations of thereflected signal. The surface is considered as a set ofreflecting elements, for each obeying the Lambert lawin combination with the law of mirror reflection withthe vertical radio wave incidence. The reflecting ele�ment is the part of the square between map nodes. Thesoil permittivity was considered constant within eachsurface element.

The reflected signal was calculated as a sum of par�tial signals, and each signal was shifted by the timerequired for the propagation of the signal from thespacecraft to the center of the corresponding reflecting

rec rec2 24 ] [2 ( )])HT c T c R R H− +

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95° 100° 105°

5°

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15°

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2

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Fig. 2. Map of region of the Moon equatorial zone from 0° to 15° N and from 90° to 105° E.



element and back with consideration for the tilt of thearea. It is considered that this representation about theideally rough surface of the reflecting element is a fullyacceptable approximation for evaluating the reflectionfrom many types of surfaces at moderate angles ofincidence of radio waves (Skolnik, 1976).

RESULTS OF THE SIMULATION

In the simulation the element was consideredreflecting if the angle between its normal and the direc�tion to the spacecraft did not exceed 30°. Figure 3 showsthe spectrum modules of the LFM signals, reflectedfrom the plane section, corresponding to the configu�ration and the area of one reflecting element, equal to

( = 15 m is the wavelength of the central fre�quency of the signal), located directly under thespacecraft. Curve 1 corresponds to the zero anglebetween the normal and direction to the spacecraft,and curve 2 corresponds to the angle, equal to 30°. It isseen in the graph that the spectrum module of the sig�nal even with collection from the small but tilted areais subject to transformation at high frequencies. Thesame tendency can be seen in the spectrum module ofthe signal (curve 3), reflected from the comparativelyuniform surface of region 1, marked in Fig. 2 by a cir�cles with a 120�km radius.

The signal with the spectrum, shown by curve 4,was collected from the area confined by the circle withthe center at the same point but with a 90�km radius,corresponding to a signal recording time equal to theradiation time (250 µs). Both spectra are qualitativelysimilar, namely, they have a triangular form and, inaddition, their low�frequency section is subject to lessdestruction. The localization of the signal (as the spec�trum) at low frequencies and the separation of its lead�

20λ 0λ

ing edge significantly facilitates determination of thedelay time between the signals reflected from differentboundaries of the medium in the analysis of measure�ments in the time domain.

If the soil in the considered region 1 were to have atwo�layer structure, the oscillating component (curve 1and curve 2 in Fig. 4) would appear in the spectrum ofthe reflected signal, the period of oscillations of whichdepend on the dielectric parameters and soil structure.In addition, the period and position of local extremalpoints in the graph will depend on corresponding ele�ments of the spectrum of the signal, reflected onlyfrom a single subsatellite element (curve 3, Fig. 4).

The presence of reflections from internal bound�aries in the area with a relatively even relief is confi�dently diagnosed from the shape of the signal spec�trum module by spectral analysis methods, even byvisual inspection.

In radiophysics there exists a valuation of a reduc�tion in the spectrum amplitude of the signal, reflectedfrom the statistically nonuniform surface of the signal

in the high�frequency range according to (Bass, 1972), where δ is the dispersion of heights ofinhomogeneities in the reflection signal zone, and λ isthe radio wavelength. In spite of the fact that theamplitude of the spectrum really decreases in accor�dance with the exponential law and depends on thesquare of the corresponding wavelength, we failed toconnect the second factor in the index with the disper�sion of the relief heights of region 1.

However, the simulation procedure should be con�sidered adequate (Smirnov, 2012), since the results,obtained by the numerical analysis, are qualitativelyconfirmed by the in situ measurement data, obtainedby the MARSIS (Mars�Express spacecraft, ESA) sub�

2exp( )−δ λ

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2

3

4

f, MHz

Spe

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Fig. 3. Module of the signal spectrum normalized to unity:(1) reflected to nadir from the soil consisting of regolith;(2) from reflecting element; (3) from the spot with a 120�kmradius; (4) from the spot with a 90�km radius.

1

022.517.5

1

2

3

f, MHz

Spe

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m m

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Fig. 4. Spectrum module of the signal, normalized tounity: (1) reflected from the soil, consisting of the regolithlayer, lying on the uniform basalt, the radius of the spot is120 km; (2) radius of the spot is 120 km, the soil is uniform;(3) reflected to the nadir from the layer on basalt.

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SMIRNOV et al.

surface radar. Figure 5 shows the spectrum module ofthe reflected signal for measurements no. 783. Thisexperiment was performed with a minimum iono�sphere density on pass 1855, which passed above theMartian north polar cap. According to data of theMOLA (Mars Global Surveyor spacecraft, NASA)altimeter, the relief of this region is sufficiently uni�form. The subsurface boundary between the ice–basegeological media ensures internal reflection.

As in the case of the numerical simulation, spec�trum oscillations are related to the delay time of thesignal reflected from the surface and the signalreflected from the internal boundary, the relief rough�ness leads to destruction of the high�frequency spec�trum domain. We did not find works which theoreti�cally evaluate what occurs with the spectrum moduleof the wideband signal on reflection from the regionwith a more complex relief, but, as result of a set ofnumerical experiments, concluded that extreme spec�trum frequencies are subject to destruction. The typi�cal form of the spectrum is shown in Fig. 6. This is thespectrum of the signal reflected from the spot on thesurface with a radius of 120 km. In Fig. 2 this region isdesignated by circle 2. The subsurface reflection istaken into account in the represented spectrum. Inthis case, it is possible to diagnose and study propertiesof the soil from results of the joint analysis in the fre�quency and time domains.

At this time, to diagnose the subsurface reflectionin the signals reflected from the more complex relief,e.g., such as a region, limited on the map by the circle 3(Fig. 2), practically no methods have been developed.The spectrum module of the signal, reflected from thisregion, is shown in Fig. 7. Low frequencies are sub�jected to the heavy destruction in this signal. The radarmeasurements, performed in regions with a high sur�face roughness, are inconclusive in respect of the sub�

surface location but interesting for classical radiophys�ics as a part of the experiment studying interactions oflong waves with a nonuniform surface.

Thus, the simulation results showed that:

(1) the shape of the spectrum module of thereflected signal depends on the nature of the relief inthe area of the experiment;

(2) in solving problems of subsurface sounding, theprocessing of RLK�L measurements should beginfrom data obtained in regions with the most uniformsurface, and only after systematization and analyzingthe cumulative experience proceed to processing themeasurements obtained in more complex regions;

(3) it is expedient to use a 3D model of the Moon’ssurface to simulate full�scale experiment results.

25

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f, MHz

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arb

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20

15

10

5

Fig. 5. Module of the spectrum of the reflected signal,recorded by the MARSIS device, route 1855, measurementno. 783.

1

022.517.5

f, MHz

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Fig. 6. Spectrum module of the signal, normalized to unity,reflected from the surface, within circle 2 (Fig. 2).

1

022.517.5

f, MHz

Spe

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m m

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Fig. 7. Spectrum module of the signal, normalized to unity,reflected from the surface, within circle 3 (Fig. 2).



ACKNOWLEDGMENTS

This work was partially supported by Programno. 22 of the Fundamental Studies of the Presidium ofthe Russian Academy of Sciences “FundamentalProblems of Studies and Solar System Development”and a grant of the Ministry of Education and Scienceof the Russian Federation, project no. 11.G34.31.0021dated 30.11.2010.

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Translated by N. Pakhomova

the influence of relief on formation of reflected signals of subsurface sounding radar

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