The Influence of Relief on Formation of Reflected Signals of Subsurface Sounding Radar. V. M. Smirnova, O. V. Yushkovaa, I. P. Karachevtsevab, and I. E. ...
ISSN 00380946, 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.
The Influence of Relief on Formation of Reflected Signals of 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, Russia Received December 3, 2012; in final form, April 18, 2013
Abstract—Radar sounding of the surface and nearsurface layer of the Moon by the RLKL lowfrequency radar complex from the orbiter module is planned for the Moon–Globe Russian mission. To forecast results of radar experiments, a simulation procedure of the reflection of the RLKL 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 results showed 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
INTRODUCTION The study of the Moon occupies a special place in space exploration programs in many countries. Its practical development could be more efficient if sig nificant localized water ice deposits were discovered in the surface layer. One of remote methods for solving this problem is subsurface radiolocation. The radar investigations of the nearsurface soil layer of the Moon were performed in 1972 from the Apollo17 spacecraft (SC). Signals, reflected by subsurface soil boundaries at depths 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 surfacesounding radars for determining parameters of the nearsurface soil layer was confirmed in Mars studies. The experiments were performed by MARSIS (Mars Express spacecraft, Mars Advanced Radar for Subsurface and Ionosphere Sounding) and SHARAD (Mars Reconnaissance Orbiter spacecraft) radars. Both devices emitted a linear frequencymodulated (LFM) signal. The MARSIS radar operated in four modes with central frequencies of 1.8, 3, 4, and 5 MHz; the deviation band of each signal was 1 MHz (Picardi et al., 2005); the frequency range of the SHARAD 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 Earth by the matching filtering method, which is intended to localize (in time) signals, reflected from the surface and internal boundaries, and to estimate the delay time between them. The in situ measurements were represented 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 structure and visually demonstrate the presence of layered struc tures. However, this type of processing does not allow one to 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 spacecraft is planned as part of the Russian Moon–Globe mis sion. It is assumed that the module will be in a polar orbit at a height of 100–50 km above the surface for one year. The RLKL lowfrequency radar complex is installed on board for radar investigations of the sur face and the nearsurface layer of the Moon. One of the problems of this experiment is to study dielectric properties and soil structure in the monostatic loca tion mode by the LFM signal in a frequency range of 17.5–22.5 MHz. The signal duration is selected so that it should be completely formed in free space, i.e., T < H . In this case, the Helmholtz approximation is c used in analyzing reflected signals. In the experiment, the duration of the radiated signals is assumed equal to 250 µs for a 100km altitude. For processing the sounding results, in addition to traditional methods the recovery procedure of the depth permittivity distribution of the nonhomoge neous soil will be applied on the basis of the functional analysis of parameter changes of the incident and reflected waves, i.e., the frequency dependence of the reflection coefficient (Yushkova, 2010). Since this inverse recovery problem of the spatial distribution of
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INITIAL DATA FOR THE SIMULATION To respond to these questions, the signal reflection process of the RLKL radar from the Moon’s surface was simulated. RLKL signal. Analytically the LFM signal is spec ified by the formula:
( (
))
⎧sin 2π f + Δ f t t , t ≤ T ⎪ min U (t ) = ⎨ . T ⎪⎩0, t > T The envelope of the signal is a constant height rectan gular function. The LFM signal spectrum does not depend formally on the frequency range and is also a virtually rectangular function. Figure 1 shows the LFM signal spectrum normalized to unity (curve 1) with deviation Δ f = 5 MHz and minimal working fre quency f min = 17.5 MHz. If the Moon’s surface were even and smooth, the signal reflection would occur at only one subsatellite point (according to the wave approximation), in spite of the fact that the antennas of both radars are halfwave vibrators and, hence, have a wide directional pattern. In this case, the spectrum of the signal reflected from the soil, which is uniform throughout the depth and consists of basalt, is shown in Fig. 1 by curve 2 and that of the signal reflected from soft soils is shown by curve 3. The reflected signal spectra differ from the spectrum of the radiated signal
by a factor r01 = 1 − ε1 , where ε1 is the soil permittiv 1 + ε1 ity. For regolith Re ε1 = 2.8 and for basalt Re ε1 = 9 (Rzhevskii et al., 1976). If there is a subsurface bound ary between dielectrically nonuniform media, e.g., SOLAR SYSTEM RESEARCH
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dielectric parameters of the soil belongs to the class of incorrectly posed problems, in treatments of measure ment data and their interpretation, it is necessary to take into account all processes affecting changes of the signal parameters, and to correct (if possible) their effect. In the subsurface sounding, the parameters of the received reflected signal depend on characteristics of the signal, surface relief, dielectric parameters of the soil, and their distribution throughout depth. In spite of the fact that the surface relief is the dom inating factor affecting the formation of the reflected signal, up to now there has been no procedure which takes into account topography in processing the results of measurements from subsurface sounding radars. It is known that the delayed pulses, arriving from side reflectors, incident on the radar antenna during recep tion, in addition to those vertically reflected, lead to amplitude and phase changes of the signal. The ques tions arise as to how these factors can be taken into account during data processing, how strong these dis tortions are, and in what regions it is expedient to per form radar measurements.
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Fig. 1. Spectrum module of the signal: (1) radiated, nor malized to unity; (2) reflected from the soil, consisting of basalt; (3) reflected from the soil, consisting of regolith; (4) from the regolith layer, located on basalt, the layer thickness is 25 m.
soil–ice, regolith–basalt, the reflected signal is the interference of the signal reflected from the upper boundary and the signal reflected from the inner boundary. These signals are shifted relative to one another by the time required for propagation of the radio wave of the corresponding frequency from the upper boundary to the lower and back. Since the sig nals are long, it is very difficult to determine the delay time between these signals. In the frequency domain, the interference effect is identified more simply, since the spectrum acquires an oscillating form. The period and amplitude of oscillations, the position of local points of extremes in the frequency dependence of the spectrum module depend on dielectric characteristics of rocks and the depth of their horizons. As an exam ple, Fig. 1 shows the spectrum module of the signal, reflected from a 25mmthick regolith layer, lying on basalt (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. The model was constructed from data, obtained in the course of the Lunar Reconnaissance Orbiter (LRO) NASA mission by using measurements from the Lunar Orbiter Laser Altimeter (LOLA) laser altimeter. The surface map is shown in Fig. 2 in geography coordi nates: the latitude is the vertical line, the longitude is the horizontal line, and the deviation of the radius–vector from the Moon’s radius taken as equal to 1737.4 km, is shown in the gray color gradation. The permittivity of the surface was considered to be constant, corre sponding to the permittivity of regolith. Geometry of the problem. When the height of the spacecraft H ≈ 100 km, the circular orbital velocity is,
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N
15° 2600
1
100
10° 3
–2400 5° 2 –4900
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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.
approximately, v = RL g L (RL + H ) ≈ 1.6 km/s, where the mean radius of the Moon RL = 1738 km, the accel eration due to gravity of the gravitational field on the Moon’s surface g L = 1.63 m/s2. The time from the start of the signal radiation to the end of reception of the reflected signal 2H c + T ≈ 0.9 µs. During this time the orbiter moves 1–2 m. This allows one to con sider that the radar receives the reflected signal at the same point where it was emitted. The radiation and reception starts are spaced at the time equal to 2H c (the spacecraft height H is defined more exactly before the 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 device from 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 Interior Laboratory (GRAIL) spacecraft data (NASA), the power of the lunar crust is evaluated namely by this value (Zuber et al., 2013). After the signal reception, the RLKL switches off the lowfrequency radar and turns on the other radar for performing the next experiment at higher frequen cies. The switching between the radars is intended to
1
avoid recording in the current session the rereflected signals of the previous measurements. When the reflected signal is recorded, not only vertically reflected signals but signals from side reflectors, located at any point of the surface in the spot with radius D = R arccos([8R2 + 8RH – 2 2 4HTrecc − Trec c ] [2R(R + H )]) , fall on the antenna sys tem. When the height of the spacecraft H = 100 km above the Moon’s surface and Trec = 350 µs, D does not exceed 120 km. If the reception time would be equal to the radiation time, i.e., 250 µs, the spot radius would correspond to 90 km. Received signal. The modified facet surface repre sentation model was selected for calculations of the reflected signal. The surface is considered as a set of reflecting elements, for each obeying the Lambert law in combination with the law of mirror reflection with the vertical radio wave incidence. The reflecting ele ment is the part of the square between map nodes. The soil permittivity was considered constant within each surface element. The reflected signal was calculated as a sum of par tial signals, and each signal was shifted by the time required for the propagation of the signal from the spacecraft to the center of the corresponding reflecting SOLAR SYSTEM RESEARCH
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0 17.5
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f, MHz 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 120km radius; (4) from the spot with a 90km radius.
element and back with consideration for the tilt of the area. It is considered that this representation about the ideally rough surface of the reflecting element is a fully acceptable approximation for evaluating the reflection from many types of surfaces at moderate angles of incidence of radio waves (Skolnik, 1976). RESULTS OF THE SIMULATION In the simulation the element was considered reflecting if the angle between its normal and the direc tion to the spacecraft did not exceed 30°. Figure 3 shows the spectrum modules of the LFM signals, reflected from the plane section, corresponding to the configu ration and the area of one reflecting element, equal to λ 20 (λ 0 = 15 m is the wavelength of the central fre quency of the signal), located directly under the spacecraft. Curve 1 corresponds to the zero angle between the normal and direction to the spacecraft, and curve 2 corresponds to the angle, equal to 30°. It is seen in the graph that the spectrum module of the sig nal even with collection from the small but tilted area is subject to transformation at high frequencies. The same tendency can be seen in the spectrum module of the signal (curve 3), reflected from the comparatively uniform surface of region 1, marked in Fig. 2 by a cir cles with a 120km radius. The signal with the spectrum, shown by curve 4, was collected from the area confined by the circle with the center at the same point but with a 90km radius, corresponding to a signal recording time equal to the radiation time (250 µs). Both spectra are qualitatively similar, namely, they have a triangular form and, in addition, their lowfrequency section is subject to less destruction. The localization of the signal (as the spec trum) at low frequencies and the separation of its lead SOLAR SYSTEM RESEARCH
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Fig. 4. Spectrum module of the signal, normalized to unity: (1) reflected from the soil, consisting of the regolith layer, lying on the uniform basalt, the radius of the spot is 120 km; (2) radius of the spot is 120 km, the soil is uniform; (3) reflected to the nadir from the layer on basalt.
ing edge significantly facilitates determination of the delay time between the signals reflected from different boundaries of the medium in the analysis of measure ments in the time domain. If the soil in the considered region 1 were to have a twolayer structure, the oscillating component (curve 1 and curve 2 in Fig. 4) would appear in the spectrum of the reflected signal, the period of oscillations of which depend on the dielectric parameters and soil structure. In addition, the period and position of local extremal points in the graph will depend on corresponding ele ments of the spectrum of the signal, reflected only from 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 by visual inspection. In radiophysics there exists a valuation of a reduc tion in the spectrum amplitude of the signal, reflected from the statistically nonuniform surface of the signal in the highfrequency range according to exp(−δ λ 2 ) (Bass, 1972), where δ is the dispersion of heights of inhomogeneities in the reflection signal zone, and λ is the radio wavelength. In spite of the fact that the amplitude of the spectrum really decreases in accor dance with the exponential law and depends on the square of the corresponding wavelength, we failed to connect 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 qualitatively confirmed by the in situ measurement data, obtained by the MARSIS (MarsExpress spacecraft, ESA) sub
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20 Spectrum module
Amplitude, arb. units
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Fig. 5. Module of the spectrum of the reflected signal, recorded by the MARSIS device, route 1855, measurement no. 783.
As in the case of the numerical simulation, spec trum oscillations are related to the delay time of the signal reflected from the surface and the signal reflected from the internal boundary, the relief rough ness leads to destruction of the highfrequency spec trum domain. We did not find works which theoreti cally evaluate what occurs with the spectrum module of the wideband signal on reflection from the region with a more complex relief, but, as result of a set of numerical 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 the spectrum of the signal reflected from the spot on the surface with a radius of 120 km. In Fig. 2 this region is designated by circle 2. The subsurface reflection is taken into account in the represented spectrum. In this case, it is possible to diagnose and study properties of the soil from results of the joint analysis in the fre quency and time domains. At this time, to diagnose the subsurface reflection in 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 this region, is shown in Fig. 7. Low frequencies are sub jected to the heavy destruction in this signal. The radar measurements, performed in regions with a high sur face roughness, are inconclusive in respect of the sub
Fig. 6. Spectrum module of the signal, normalized to unity, reflected from the surface, within circle 2 (Fig. 2).
surface location but interesting for classical radiophys ics as a part of the experiment studying interactions of long waves with a nonuniform surface. Thus, the simulation results showed that: (1) the shape of the spectrum module of the reflected signal depends on the nature of the relief in the area of the experiment; (2) in solving problems of subsurface sounding, the processing of RLKL measurements should begin from data obtained in regions with the most uniform surface, and only after systematization and analyzing the cumulative experience proceed to processing the measurements obtained in more complex regions; (3) it is expedient to use a 3D model of the Moon’s surface to simulate fullscale experiment results. 1
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surface radar. Figure 5 shows the spectrum module of the reflected signal for measurements no. 783. This experiment was performed with a minimum iono sphere density on pass 1855, which passed above the Martian north polar cap. According to data of the MOLA (Mars Global Surveyor spacecraft, NASA) altimeter, the relief of this region is sufficiently uni form. The subsurface boundary between the ice–base geological media ensures internal reflection.
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Fig. 7. Spectrum module of the signal, normalized to unity, reflected from the surface, within circle 3 (Fig. 2). SOLAR SYSTEM RESEARCH
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ACKNOWLEDGMENTS This work was partially supported by Program no. 22 of the Fundamental Studies of the Presidium of the Russian Academy of Sciences “Fundamental Problems of Studies and Solar System Development” and a grant of the Ministry of Education and Science of the Russian Federation, project no. 11.G34.31.0021 dated 30.11.2010. REFERENCES Bass, F.G. and Fuks, I.M., Rasseyanie voln na statisticheski nerovnoi poverkhnosti (Waves Scattering by Statistically Rough Surface), Moscow: Nauka, 1972. Carter, L.M., Campbell, B.A., Watters, T.R., Phillips, R.J., Putzig, N.E., Safaeinili, A., Plaut, J.J., Okubo, C.H., Egan, A.F., Seu, R., Biccari, D., and Orosei, R., Shal low radar (SHARAD) sounding observations of the Medusae Fossae Formation Mars, Icarus, 2009, vol. 199, pp. 295–302. Picardi, G., Plaut, J.J., Biccari, D., Bombaci, O., Cala brese, D., Cartacci, M., Cicchetti, A., Clifford, S.M., Edenhofer, P., Farrell, W.M., Federico, C., Frigeri, A., Gurnett, D.A., Hagfors, T., Heggy, E., Herique, A., Huff, R.L., Ivanov, A.V., Johnson, W.T.K., Jordan, R.L., Kirchner, D.L., Kofman, W., Leuschen, C.J., Nielsen, E., Orosei, R., Pettinelli, E., Phillips, R.J., Plettemeier, D., Safaeinili, A., Seu, R., Stofan, E.R., Vannaroni, G., Watters, T.R., and Zampolini, E., Radar sounding of the surface of Mars, Science, 2005, vol. 310, pp. 1925–1928.
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