Estimated Attenuation Rates Using GPR and TDR in Volcanic Depos

PUBLICATIONS

Journal of Geophysical Research: Planets

RESEARCH ARTICLE Electromagnetic signal penetration in a planetary soil 10.1002/2016JE005192 simulant: Estimated attenuation rates using GPR Key Points: and TDR in volcanic deposits on Mount Etna • GPR methodologies for evaluating the loss tangent of volcanic sediments S. E. Lauro1 , E. Mattei1 , B. Cosciotti1 , F. Di Paolo1 , S. A. Arcone2, M. Viccaro3,4 , • Characterization of electrical 1 properties of a planetary soil simulant and E. Pettinelli • Comparison between GPR and TDR 1 2 measurements Dipartimento di Matematica e Fisica, Università degli Studi Roma TRE, Rome, Italy, US Army ERDC-CRREL, Hanover, New Hampshire, USA, 3Dipartimento di Scienze Biologiche Geologiche e Ambientali, Università degli Studi di Catania, Catania, Italy, 4Osservatorio Etneo, Istituto Nazionale di Geoﬁsica e Vulcanologia, Catania, Italy

Correspondence to: S. E. Lauro, Abstract Ground-penetrating radar (GPR) is a well-established geophysical terrestrial exploration method [email protected] and has recently become one of the most promising for planetary subsurface exploration. Several future landing vehicles like EXOMARS, 2020 NASA ROVER, and Chang’e-4, to mention a few, will host GPR. A GPR Citation: survey has been conducted on volcanic deposits on Mount Etna (Italy), considered a good analogue for Lauro, S. E., E. Mattei, B. Cosciotti, F. Di Paolo, S. A. Arcone, M. Viccaro, and Martian and Lunar volcanic terrains, to test a novel methodology for subsoil dielectric properties estimation. E. Pettinelli (2017), Electromagnetic The stratigraphy of the volcanic deposits was investigated using 500 MHz and 1 GHz antennas in two different signal penetration in a planetary soil configurations: transverse electric and transverse magnetic. Sloping discontinuities have been used to simulant: Estimated attenuation rates using GPR and TDR in volcanic deposits estimate the loss tangents of the upper layer of such deposits by applying the amplitude-decay and on Mount Etna, J. Geophys. Res. Planets, frequency shift methods and approximating the GPR transmitted signal by Gaussian and Ricker wavelets. The 122, 1392–1404, doi:10.1002/ loss tangent values, estimated using these two methodologies, were compared and validated with those 2016JE005192. retrieved from time domain reflectometry measurements acquired along the radar profiles. The results show

Received 7 OCT 2016 that the proposed analysis, together with typical GPR methods for the estimation of the real part of Accepted 11 MAY 2017 permittivity, can be successfully used to characterize the electrical properties of planetary subsurface and to Accepted article online 15 MAY 2017 deﬁne some constraints on its lithology of the subsurface. Published online 3 JUL 2017

1. Introduction Ground Penetrating Radar (GPR) has been extensively applied to a large number of terrestrial applications such as glaciology, engineering, archaeology, geology, and environmental and agricultural sciences [Jol, 2008, and references therein]. GPR uses radio waves to image the buried geological structures in a way conceptually similar to seismic reflection methods. The application of GPR to planetary exploration is particu- larly favorable for two main reasons: (1) planetary subsurfaces are generally dry and cold, which minimizes the attenuation and dispersion of the electromagnetic waves; and (2) radar measurements do not require a physical contact between antenna and soil. As a consequence, GPR can be designed to operate either remotely, on board a spacecraft, or on site as part of a payload of a landing vehicle (rover or lander). These different operating modes were first tried during the pioneering electromagnetic experimentation conducted during the Apollo 17 mission: the Surface Electrical Properties (SEP) experiment was hosted on board the Lunar Roving Vehicle [Simmons et al., 1973] and the Apollo Lunar Sounder Experiment (ALSE) on board the Apollo Command and Service Module [Porcello et al., 1974]. In the last 20 years, several orbiting GPR have been proposed, designed, and built (RIME [Bruzzone et al., 2013] and REASON [Phillips and Pappalardo, 2014]) as well as successfully used in various missions (MARSIS [Plaut et al., 2007], SHARAD [Phillips et al., 2008], Kaguya Lunar Radar Sounder (LRS) [Ono et al., 2010], CONSERT [Kofman et al., 2015], and Chang’E-3 Lunar Penetrating Radar (LPR) [Fang et al., 2014]). Furthermore, several landing missions to Mars and the Moon will rely on GPR to investigate geological structures at shallow depth (RIMFAX [Hamran et al., 2015] and China’s Mars 2020 mission [Zhou et al., 2016]) and/or to guide drilling for subsurface soil sampling (WISDOM [Dorizon et al., 2016]). The Chinese lunar mission CHANG’E-3 has already attempted dual-frequency GPR [Fang et al., 2014]. Radar data can provide qualitative and quantitative information that can be integrated to reconstruct the geological struc- fi ©2017. American Geophysical Union. ture of the subsurface. Quantitative information is more dif cult to retrieve because it requires the imple- All Rights Reserved. mentation of inverse algorithms [e.g., Zhang et al., 2008; Lauro et al., 2017]. Nevertheless, the extraction of

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the complete set of dielectric parameters, that is, the real part of permittivity, the polarization term, and the conductivity strongly improves the interpretation of the composition of the planetary subsurface. The potentials of this approach can be seen in the detailed reconstruction of the Moon shallow subsurface structure, which is well constrained by the variation of permittivity and loss tangent with depth [Strangway et al., 1977]. The present work is dedicated to improve our capability to retrieve quantitative information on the electrical nature of a planetary subsurface and discuss some of the problems encountered in data analysis and interpretation when using a high-frequency GPR in proximity of the planetary surface [Vannaroni et al., 2004; Fang et al., 2014], that is, when the radar is on board a rover or a lander. As is well known, GPR data are not self-consistent. For example, in a radar cross section the positions of different subsurface interfaces (or of the single scatterers) are ranged in time delay (specifically two-way travel time) and aspect (look angle), and electromagnetic wave velocity is needed to convert time into depth. Therefore, detailed and accurate data interpretation requires additional information regarding the media velocity and attenuation (which depend on the real and imaginary parts of permittivity), especially if the final goal is the identification of the subsurface lithology, as any single velocity or attenuation value can be associated with more than one type of rock (or soil). On the Earth the electromagnetic parameters can be independently measured on site using complementary techniques (e.g., time or frequency domain techniques), whereas in a planetary mission some ad hoc procedure must be developed. Several methods have been proposed to estimate the electromagnetic pulse velocity: (i) hyperbola calibration [Annan, 2004]; (ii) surface reflectivity (in case of noncontact antennas) [e.g., Lambot et al., 2004]; (iii) early-time attribute (for ground coupled antennas) [Pettinelli et al., 2014]; and (iv) multioffset antenna configuration [Jol, 2008; Annan, 2004; Huisman et al., 2003]. However, among these, only the hyperbola calibration method appears suitable for planetary exploration because it can be applied to a single offset antenna configuration (fixed position of the Tx-Rx antennas) and does not require any calibration. On the other hand, in GPR studies, the attenuation factor is commonly evaluated using spectral ratio [Harbi and McMechan, 2012], frequency shift [Liu et al., 1998; Bradford, 1999], or amplitude-decay [Tonn, 1991; Grimm et al., 2006]; in principle, almost all seismic reflection methods [Tonn, 1991] could be implemented for GPR. The only drawback associated with such techniques is the need for a buried sloping horizon. In this work we focus on estimating the loss tangent (attenuation) from GPR data acquired on volcanic deposits we consider good petrological analogues of various terrains present in all terrestrial planets [Wilson and Head, 1994; Pettinelli et al., 2003] and even on comets [Brouet et al., 2014]. The survey was performed using a commercial GPR equipped with soil coupling antennas. The work is strictly methodological, as the survey could have been performed at any other site of interest for planetary exploration and the proposed analysis can be extended to other types of radar systems equipped with suspended (uncoupled) antennas. The data were collected on two different volcanic deposits which were fairly homogeneous at the scale of the radar wavelength. Under the assumption that such deposits were low loss and weakly dispersive, we estimated the loss tangent by applying two different methods, the amplitude decay and the frequency shift in the portion of radar cross sections where dipping reflectors were well detectable. The results were validated using time domain reflectometry (TDR) measurements collected at various depths along the GPR profiles and compared with radar data collected on the Moon and Mars to highlight the potentials of the proposed approach.

2. Theoretical Background 2.1. Wave Propagation Parameters The propagation of GPR signals depends on the constitutive parameters of the medium. For nonmagnetic

material, they can be expressed in terms of soil complex permittivity εs [Pozar, 2009] as σ ε ε0 ε″ ε0 ε″ ; s ¼ s i s ¼ s i p i (1) ωε0 ε00 ε ″ σ where the imaginary part s is given by the contribution of both polarization ( p ) and conduction ( ) 12 processes, ω =2πν (ν is the frequency) and ε0 = 8.85 × 10 F/m is the dielectric permittivity of a vacuum. ε00 ε 0 δ The ratio of s to s gives the loss tangent tan :

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ε00 δ s δ δ tan ¼ 0 ¼ tan p þ tan σ (2) εs ″ 0 where we define the partial loss tangent due to polarization absorption tanδp = εp /εs and that due to the 0 conductive losses tanδσ = σ/ωε0εs . We can also define the attenuation factor A(ν, z), which depends on the electromagnetic losses of the material. For a plane wave propagating along the direction z, A can be written as ffiffiffi pffiffiffi p Imfgεs 2πν Imfgεs 2πν ffiffiffi τ 2z pε AðÞ¼ν; z e c ¼ e Refgs ; (3) ÈÉ ÈÉ 0 ″ pffiffiffiffi pffiffiffiffi where c is the velocity of light in a vacuum. For low loss materials (i.e., ε ≫ ε ), Im ε = Re ε ⋍ tanδ=2, A ÈÉpffiffiffiffi s s s s (ν, z) can be expressed as a function of τ ¼ 2z=cRe εs (the two-way travel time) and loss tangent tanδ: σ τπv tanδpτ πv tanδτ ε ε0 AvðÞ; τ ≃e ¼ e 2 0 s (4)

According to Turner and Siggins [1994], the attenuation factor A(ν, τ) can be expressed as

πv πv α τ τ τ; AvðÞ; τ ≃e 0 Q ¼ e Q (5) where Q* is a generalization of the quality factor Q = 1/ tan δ and can include other losses like scattering. 0 * Comparing equation (4) with equation (5), we find α0 = σ/2ε0εs and Q = 1/ tan δp. 2.2. Spectral Analysis The presence of an electromagnetic discontinuity in the subsurface (i.e., an interface between two different layers) is recorded at the radar position x as an echo signal r(t, x) the features of which depend on the dielectric contrast between the two adjacent layers and the electromagnetic properties along the propagation path. The reflected echo r(t, x) is given by the inverse Fourier transform of its spectrum R(ν, x, z): ; ∫þ∞ ; ; i2πvt ; rtðÞ¼x ∞RvðÞx z e dv (6) with pffiffiffi pffiffiffi pffiffiffi iω ε 2zxðÞ iω Re ε 2zxðÞ ω Im ε 2zxðÞ; RðÞ¼ν; x; z YðÞν; x ΓðÞx e c s ¼ YðÞν; x ΓðÞx e c fgs e c fgs (7)

and z(x) is the depth of the reflector, Y(ν, x) is the spectrum of the transmitted signal, and Γ(x) is the reflection coefficient at the interface between the two adjacent layers at the radar position x. In equation (7) the expo- nential function has been divided into two terms: one that accounts for the phase delay and one that accounts for the attenuation (equation (3)). Hereafter, we assume that the medium is homogeneous, the subsurface electromagnetic features do not depend on the radar position x (i.e., Γ(x)=Γ, Y(ν, x)=Y(ν)), and the subsurface interface depth z = z(x) can vary. Assuming low losses, R(ν, x, z) can be expressed as a function of frequency ν and the time delay, τ, such that

ωτ RvðÞ; τ ≃YvðÞΓei AvðÞ; τ ; (8)

where A(ν, τ) is the attenuation factor and it is given by equation (4). In general, for GPR antennas close to the surface, the source waveform (or the transmitted spectrum Y(ν)) is not known a priori because it depends on the coupling of the antenna system with the shallow part of the soil [Jol, 2008]; in fact, the central frequency of transmitted spectrum [Padaratz and Forde, 1995], as well as the bandwidth and the amplitude, depends on the permittivity of the surface. In this paper, we consider two possible types of source wavelets, a modulated Gaussian pulse and a Ricker function [Economou and Kritikakis, 2016]. The ﬁrst allows simple equations that relate the amplitude and the central frequency of the spectrum to the partial loss tangents as a function of time delay. In the second case, only the central frequency information of the spectrum can be analytically related to the partial loss tangent due to polarization.

2 2 ðÞνν0 =2σν For a Gaussian modulated pulse, i.e., YðÞ¼ν Y0e equation (8) becomes (see equation (4))

2 δ ðÞvv0 ω tan pτ σ τ 0 2σ2 iωτ 2 2ε ε RvðÞ¼; τ R0e v e e 0 s ; (9)

where R0 = Γ Y0, Y0 is the amplitude, ν0 is the central frequency, and σν is the bandwidth of the transmitted pulse. The reﬂected spectrum (equation (9)) can still assume the shape of the transmitted signal (i.e., a

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Gaussian function) if the losses due to polarization phenomena (i.e., tanδp) are frequency independent in the speciﬁc GPR frequency range (a reliable assumption for dry granular basaltic materials [i.e., Grimm et al., 2006; Mattei et al., 2014]). In fact, in this scenario, the spectrum amplitude |R(ν, τ)| can be rewritten as follows:

0 2 vv ðÞ0 ; σ2 jjRvðÞ; τ ≃Rτe 2 v (10) with

0 πσ2 δ τ; v ¼ v0 v tan p (11) and

σ2 2 v 2 2 πv0 tanδ0τþπ tan δpτ Rτ ¼ jjR0 e 2 ; (12)

where tan δ0 is the total loss tangent calculated at ν = ν0. According to equations (10)–(12), the echo spectrum ν0 ν is a Gaussian function centered at a new central frequency, 0, shifted with respect to the transmitted one, 0 [Quan and Harris, 1997]. Such a shift exhibits a linear trend with time delay and only depends on the partial

loss tangent tanδp (equation (11)). On the other hand, the amplitude of the spectrum (equation (12)) does not depend on frequency and the exponent exhibits a quadratic dependence with time delay. The linear term of

the exponent is caused by the total loss tangent tanδ0, whereas its quadratic term is caused only by the polarization component tanδp. 2 ν 2 ν ν 0 In the case of a Ricker wavelet, i.e., YðÞ¼ν Y0 e , the spectrum of the reﬂected signal R(ν, τ) ν0 (equation (8)) at τ > 0 cannot be analytically written as a Ricker function. However, we can still determine the central frequency of the spectrum as a function of time delay, τ:

0 1 π tanδpτ sinh ðÞv0 8 : v0 ¼ v0e (13)

This equation represents the explicit form given by Bradford [2007] and Zhang and Ulrych [2002]. It shows a

spectral frequency shift caused by the partial loss tangent tanδp, as in the case of Gaussian input waveform (equation (11)). A comparison between the two equations shows that equation (13) contains only two

unknown parameters (ν0 and tanδp), in contrast with equation (11) which contains also σν. Moreover, we note 0 2 that if πν tan δ τ/8 ≪ 1, then equation (13) can be written in the approximated form ν ⋍ν0 πν0 =8 tanδp τ, 0 p pffiffiffi 0 which becomes equal to equation (11) assuming σν ¼ ν0 2=4.

3. TDR Relevant Equations The frequency response of a TDR is conveniently formulated by using the scatter function S(ν), which allows estimation of the electromagnetic properties of the material embedded in the TDR probe. The transfer function can be computed in the frequency domain assuming a linear regime as follows:

V0ðÞ¼v VvðÞSvðÞ; (14)

where Vo(ν) and Vi(ν) are the fast Fourier transform (FFT) of the output and input signal, respectively. For the TDR step function input, it is useful to work with the derivative of the input and output function; in fact, using the property of the FFT derivatives, equation (14) can be rewritten as

0 V ðÞν SðÞ¼ν o (15) 0 ν Vi ðÞ 0 ν 0 ν where VoðÞand Vi ðÞare the FFTs of the derivatives of the output and input response, respectively. Equation (15) allows S(ν) to be derived from the experimental data, assuming that the input function Vi(ν), can be derived from the signal reﬂected from the open end of the coaxial cable when it is disconnected from the TDR probe [Mattei et al., 2006]. The scatter function S(ν), is related to the input admittance of a transmis- sion line as follows [Ramo et al., 2008]:

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1 1 SvðÞ i pffiffiffiffi YinðÞ¼v ¼ εS tanðÞkL ; (16) Zcl 1 þ SvðÞ Zc0 where L is the probe length, Z is the impedance of the coaxial cable, Z is the characteristic impedance of pclffiffiffiffi c0 the probe in air, and k ¼ 2πν εs=c. The real part of the input admittance Yin(ν) exhibits local maxima at the frequencies νm for which the real part of the tangent argument in equation (16) is equal to odd multiples of π/2. These frequencies correspond to the resonances of the probe when its length equals a quarter wavelength:

ðÞ2m þ 1 c ν ≃ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; m 0; 1; 2…: (17) m 0 ¼ 4L εs ðÞνm

At such frequencies, the real and imaginary part of permittivity can be evaluated from equation (16) as follows: () hi 2 π 2 2 ’ c 1 Zc0 4vmL εS ðÞ¼vm ðÞ2m þ 1 coth RefgYinðÞvm 2πvmL 2 2m þ 1 c (18) 2 ’’ c 1 Zc0 4vmL εS ðÞ¼vm πðÞ2m þ 1 coth RefgYinðÞvm 2πvmL 2m þ 1 c

4. GPR and TDR Data Collections GPR and TDR data were collected at two sites on Mount Etna volcano (Sicily, Italy) (Figure 1a). The first site is at the base of the southwestern flank of the pyroclastic cone of the 1669 A.D. eruption (Mount Rossi), near the village of Nicolosi (Figure 1b). The second site is at 1800 m above sea level on the southern flank of Mount Etna, close to Rifugio Sapienza (Figure 1c). The shallowest part of the deposit is chiefly tephra fallout in both sites, although some minor differences in terms of chemical and physical characteristics occur (e.g., bulk composition and grain size). The deposit of site 1 is primarily vesiculated lapilli and ashes, whose petrographic characteristics have evidenced the presence of 67 ± 3 vol . % plagioclase, 15 ± 3 vol . % augitic clinopyroxene, 15 ± 2 vol . % olivine, 3 ± 2 vol . % titaniferous-magnetite, and very minor amounts of glass. Volcanic products at site 2 are mainly unwelded ashes from explosive eruptions of Mount Etna (namely, the 2001 A.D. and 2002–03 A.D. eruptions; cf. Ferlito et al. [2012]). Ashes of site 2 slightly differ from products of the site 1 for what concerns the dimension of the grain size (which is lower than site 1) and the relative abundance of some of the mineralogical components, being constituted by 60 ± 13 vol . % plagioclase, 27 ± 8 vol . % augitic clinopyroxene, 11 ± 4 vol . % olivine, 2 ± 1 vol . % titaniferous-magnetite, and appreciable amounts of sideromelane glass (<10 vol %). Despite the presence of titaniferous-magnetite, the investigated soil is not magnetic [Mattei et al., 2014]. The minor compositional and textural differences observed at the two sites do not influence the porosity, which is rather similar for both the deposits and can be considered the same at the scale of the GPR wavelength. GPR measurements were performed in reflection mode (single offset) using a PulseEKKO Pro™ bistatic system (Sensors & Software, Inc.) operating at 500 MHz and 1 GHz and equipped with an odometer. Traces were acquired every 0.02 m, using a time resolution of 0.1 ns at 500 MHz and 0.05 ns at 1 GHz, and a time window of 100 ns. For each frequency, measurements were performed in two antenna configurations: transverse electric (TE) and transverse magnetic (TM) acquisition modes [Jol, 2008]. On site 1, the GPR profile was acquired on a natural scarp (Figure 1a) parallel to the edge of the slope but sufficiently far from it to avoid lateral reflec- tions. On site 2, GPR data were collected along a hillside (Figure 1b). TDR measurements were acquired using a Tektronix 1502C cable tester (Tektronix Inc. Beaverton, Oregon) connected to a three-pronged probe by a 50 Ω coaxial cable. At both sites, TDR data were randomly collected along the radar profiles using probes with different lengths L (0.080 ± 0.002, 0.100 ± 0.002 and

0.210 ± 0.002 m) and characteristic impedances Zc0 (233 ± 2, 221 ± 2 and 113 ± 2 Ω). Furthermore, at spe- ciﬁc locations along the GPR proﬁle several measurements at different depths were acquired (reaching a maximum 70 cm), to check the homogeneity of the shallow portion of the deposit.

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Figure 1. a) Satellite image of the area that locates the two sites; (b) site 1, which contains vesiculated lapilli, at the base of the southwestern ﬂank of Mount Rossi, the pyroclastic cones formed during the 1669 A.D. eruption of Mount Etna; (c) site 2, which mainly contains recently erupted ashes, on the upper southern ﬂank of Mount Etna.

5. Analysis and Results 5.1. GPR Figure 2 shows the GPR cross-sectional proﬁles acquired at both sites using 500 MHz antenna. In particular, Figures 2a and 2b are data collected in TE and TM modes at site 1, whereas Figures 2c and 2d are data collected in TE and TM modes at site 2. The radar cross sections acquired at site 1 (Figures 2a and 2b) show

Figure 2. GPR cross sections for (a and b) site 1 and (c and d) site 2 acquired using 500 MHz antennas in TE and TM con- ﬁgurations. The gray scale values represent the signal amplitude measured by the instrument in arbitrary units.

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Figure 3. (a) Subsurface reﬂector, (b) signal amplitude, and (c) central frequency extracted from site 1 using the 1 GHz TE data set. The results of the ﬁtting procedures are the solid lines.

an inclined, strong continuous reflector located between 12 ns and 45 ns, while Figures 2c and 2d show a more complex structure with several subsurface weak reflectors and a basal, stronger continuous reflector that extends along the whole profile. The direction of the antenna with respect to the profile (TE or TM) does not introduce any appreciable difference in the cross sections, confirming the assumption of homogeneity. Furthermore, the sections clearly show the absence of any large subsurface scatterer. The radar sections acquired in the two sites with the 1 GHz antenna are quite similar (see, for example, Figure 3) although, as expected, the higher frequency provides a better image resolution. We took advantage of the dipping nature of the strongest basal reflectors detected at both sites (Figure 2) to apply our procedure and estimate the loss tangent of the material overlaying such reflectors. The loss tangent fl ν0 was computed using the re ected signal spectral attributes (i.e., amplitude Rτ, central frequency 0, and bandwidth σν) as a function of the reflector time delay, τ, by applying the following procedure: (i) to estimate τ, the subsurface reflector was picked as a function of radar position x through a cross-correlation method [Turin, 1960; Lauro et al., 2013]; (ii) the r(τ, x) echo signal was extracted using a box window centered at τ and having

a time width equal to 2.4/ν0n, where ν0n is the nominal frequency of the antenna; (iii) the relevant spectrum R (ν, τ) was obtained by applying the FFT algorithm; and (iv) the analysis was split (according to section 2.2) to account for the two different source wavelets. We ﬁtted |R(ν, τ)| with a Gaussian function to retrieve the ν0 σ central frequency 0, the maximum amplitude Rτ and the bandwidth ν, whereas, in the Ricker analysis, we ν0 computed the central frequency 0 at the peak of the maximum of the spectrum. Finally, (v) we computed tanδp, tanδ0 , and ν0 applying a polynomial regression to the logarithm of the maximum amplitudes Rτ ν0 ﬁ (see equation (12)), whereas the 0 values were tted using equations (11) and (13), for the Gaussian and Ricker analysis, respectively. Note that in equations (11) and (12) σν is the average of all the estimated values.

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Table 1. Central Frequency and Loss Tangent Estimated at Sites 1 and 2 Gaussian Analysis Ricker Analysis

Linear Fit Equation (11) Linear Fit Equation (12) Linear Fit Equation (13)

ν0 (GHz) tanδp tanδ0 ν0 (GHz) tanδp Site 1 TE 500 MHz 0.44 ± 0.01 0.039 ± 0.009 0.052 ± 0.002 0.45 ± 0.01 0.034 ± 0.007 TM 500 MHz 0.45 ± 0.01 0.038 ± 0.008 0.053 ± 0.002 0.44 ± 0.01 0.030 ± 0.005 TE 1 GHz 0.91 ± 0.02 0.033 ± 0.007 0.039 ± 0.002 0.87 ± 0.02 0.028 ± 0.004 TM 1 GHz 0.90 ± 0.02 0.029 ± 0.006 0.038 ± 0.002 0.84 ± 0.03 0.025 ± 0.003 Site 2 TE 500 MHz 0.48 ± 0.02 0.021 ± 0.009 0.071 ± 0.004 0.53 ± 0.01 0.035 ± 0.005 TM 500 MHz 0.51 ± 0.02 0.029 ± 0.012 0.068 ± 0.004 0.54 ± 0.01 0.038 ± 0.005 TE 1 GHz 0.93 ± 0.05 0.023 ± 0.009 0.040 ± 0.004 0.96 ± 0.06 0.041 ± 0.008 TM 1 GHz 0.95 ± 0.04 0.028 ± 0.009 0.046 ± 0.003 1.00 ± 0.05 0.042 ± 0.006

Figure 3 shows an example of the results obtained with the 1 GHz data acquired at site 1 in TE mode. The red circles in Figure 3a identify the subsurface reflector and its relevant time delay, τ. The maximum of the echo ν0 spectrum amplitude Rτ, is shown in Figure 3b, and the central frequency 0 retrieved after applying a Gaussian fit (black circles) and peaking the maximum of the spectrum (red circles), is plotted in Figure 3c. These results ν0 show that the retrieved data (Rτ and 0 ) are scattered and that the amplitude values do not follow the parabolic trend expected by equation (12); rather they exhibit a linear trend. This behavior can be explained considering that the quadratic term in equation (12) cannot be appreciated if the time delay is much smaller ν δ “ ” τ 2 0 tan 0 than a characteristic time c ¼ 2 2 , which is the time at which the linear and the quadratic terms in the πσν tan δp exponent of equation (12) are comparable. A practical wayÀÁ to demonstrate that the time delay in our data fi τmin satis es this condition is to compute a lower limit c of the characteristic time approximating tanδ0 ≅ tan δp and using the estimated quantities σν, ν0, and tanδp fitted through equations (10)–(11); this lower limit is then compared with the maximum time delay. For example, in the data presented in Figure 3, the time delay associated with the deepest portion of the reflector (τ = 37ns) is an order of magnitude lower τmin ν =πσ2 δ δ σ ν fi than c ¼ 2 0 ν tan p ¼ 279ns (tan p = 0.023, ν = 0.3 GHz and 0 = 0.91 GHz). This condition is ful lled for the whole data set (i.e., different frequency, polarization, and measuring site), thus justifying the use of the linearization of the polynomial fit. The results of the analysis computed for both sites with different antenna frequencies and different polariza- tions are summarized in Table 1. The associated uncertainties have been estimated from the covariance matrix after applying, when needed, the uncertainty propagation formula [Kirkup and Frenkel, 2006]. 5.2. TDR

Figure 4 shows an example of the experimental input admittance, Yin(ν), calculated according to equation (16) for a TDR trace acquired at site 2. The black squares represent the real part, and the red circles the imaginary

part of Yin(ν), respectively. Between 100 MHz and 1 GHz the real part shows several peaks at the resonance frequencies (see equation (17)), which have been used through equation (18) to estimate the complex 0 ″ permittivity. This procedure was applied to all TDR traces, and, for each site, the quantities εs , εs and tanδ were computed for the ﬁrst two resonances. We found that at each location, regardless of the length of the probe and the depth of the measurement, the retrieved dielectric parameters were consistent and only weakly frequency dependent. As a consequence, we used the whole set of TDR data collected at each site to estimate the average values of the above-mentioned dielectric parameters. These values are in Table 2 together with the uncertainty computed as the standard deviation of the mean.

6. Discussion The previous analysis allows us to discuss the potential and the limitations of the proposed method for estimating subsurface losses. We start by making some comments on the qualitative results. As illustrated in Figure 2, no apparent major differences were found between cross sections acquired at 500 MHz and 1 GHz or between TE and TM acquisitions at site 1, and similar results were found at site 2. This fact seems to conﬁrm that the volcanic deposits were homogeneous at the scale of the radar wavelength and not dispersive in the frequency range. However, if we consider the results obtained by applying a quantitative analysis, then we

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extracted more information about the physical properties of the subsurface. In fact, the amplitude and the central frequency values retrieved from the analysis (illustrated in Figures 3b and 3c) are scattered, showing that there is some lateral variability along the propagation path, which can be ascribed to several factors: (i) different antenna/soil coupling; (ii) inhomogeneities inside the medium; and (iii) local variations in the dielectric contrast or roughness of the interface. As for each speciﬁc acquisition condition, we estimated an overall Figure 4. Real (black squares) and imaginary (red circles) parts of the value of the loss tangent; such variability input admittance Yin(ν) as a function of frequency. is accounted for in the uncertainties reported in Table 1. A general comparison between site 1 and site 2 data (see Table 1) shows that the behavior of the retrieved

parameters (ν0 , tan δp and tanδ0) as a function of antenna polarization and frequency is similar, regardless of the measurement site characteristics. Taking into account the uncertainties, the TE and TM values are always mutually compatible for both Gaussian and Ricker analyses. This result agrees with what we observed in the radar cross sections and corroborates the validity of the proposed methodology because very similar

values are retrieved from independent measurements. Furthermore, the tanδp values at 500 MHz and 1 GHz are comparable, conﬁrming the reliability of the assumption made in section 2.2 that the polarization loss

tangent is frequency independent. Conversely, Table 1 shows that the tanδ0values estimated at 500 MHz are always larger than those at 1 GHz. This result is expected as tanδ0 is the sum of polarization and conductive losses (equation (2)), and tanδσ decreases as the frequency increases. The presence of a signiﬁcant

conductive term is also conﬁrmed by the comparison between tanδ0 and tanδp values, because the total loss tangent is always greater than the polarization term. This term can be computed applying equations (1) and (2) as an average value of the data present in 1 (loss tangents from Gaussian analysis) and in 2 (real part of permittivity), and it results that its value is slightly different for the two deposits: (3 ± 1) × 103 S/m and (5 ± 1) × 103 S/m for sites 1 and 2, respectively.

A quantitative criterion to evaluateqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the compatibility between two quantities (x1 and x2) is given by the following formula: x x ≤k u2 u2 (where u are the uncertainties) [Joint Committee for Guides in jj1 2 x1 þ x2 x Metrology: JCGM 100, 2008]. The term k is the coverage factor [JCGM 100, 2008] and accounts for the confi- dence level of the measurement, that is ~68% for k = 1 and ~95% for k = 2. We applied this criterion to

compare Gaussian and Ricker results in terms of tanδp and the total loss tangent tanδ computed from GPR and TDR data. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Table 3 reports all Δ =|x x | and df u2 u2 computed values and clearly highlights a difference 1 2 ¼ x1 þ x2 between site 1 and site 2. In fact, considering the uncertainty intervals and the coverage factor k = 1, the loss tangent values computed for site 1 by using two different wavelets are all compatible; whereas for site 2 the compatibility criterion is fully satisfied using a coverage factor k = 2. This result seems to suggest that in general, the choice of the wavelet does not affect the estimation of the loss tangent and it is consistent with the observation made in section 2.2 according to which, for low loss media, equations (11) and (13) are equivalent.

Table 2. TDR Data Analysis 0 00 εs εs tanδ Site 1 7.39 ± 0.56 0.44 ± 0.09 0.065 ± 0.014 Site 2 4.52 ± 0.09 0.32 ± 0.04 0.069 ± 0.007

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Table 3. Compatibility Analysis of GPR and TDR Retrieved Values

tanδp(Gaussian Versus Ricker) tanδ(GPR Versus TDR) Δ df Δ df

Site 1 TE 500 MHz 0.005 0.011 0.013 0.014 TM 500 MHz 0.008 0.009 0.012 0.014 TE 1 GHz 0.005 0.008 0.026 0.014 TM 1 GHz 0.004 0.007 0.027 0.014 Site 2 TE 500 MHz 0.014 0.010 0.002 0.008 TM 500 MHz 0.009 0.013 0.001 0.008 TE 1 GHz 0.018 0.012 0.029 0.008 TM 1 GHz 0.014 0.011 0.023 0.008

The results of the TDR data analysis (Table 2) show a difference between site 1 and site 2 in the retrieved 0 ″ values of real (εs ) and imaginary (εs ) parts of permittivity but not in the loss tangent. Such differences are probably due to variation in soil texture (e.g., grain size and porosity), mineralogy (see section 4), and water content. Furthermore, the comparison between Tables 1 and 2 illustrates that the relative uncertainties associated with the total loss tangent computed with TDR are larger than those computed with GPR. This fact can be ascribed to several features associated with the TDR data analysis: (i) the resolution in frequency when the resonance is sampled; (ii) the wide frequency range (100 MHz to 1 GHz); (iii) the data averaging along the GPR proﬁles; and (iv) the number of measurements collected at each site. In particular, the latter explains why the uncertainties associated with the values estimated for site 1 (6 measurements) are larger than those for site 2 (24 measurements). It is interesting to note that, according to a previous work [Padaratz and Forde, 1995], we found higher values of permittivity associated with lower

values of ν0 in GPR analysis. In fact, TDR data show that site 1 exhibits greater values than site 2 for both real and imaginary parts of the permittivity and that GPR data highlight that ν0 is lower at site 1 than at site 2 (see Table 1). The comparison between GPR and TDR loss tangent values (tanδ) (see Table 3) shows that, assuming k = 1, the compatibility criterion is satisﬁed (for both sites) only for the 500 MHz antenna, whereas a discrepancy exists between radar data collected at 1 GHz and TDR values. This result might be expected because the central value of the TDR frequency range (100 MHz to 1 GHz) is 550 MHz and the retrieved dielectric parameters have been averaged in this interval. Regarding the application of the proposed method for planetary exploration, it should be highlighted that our analysis has a general validity and can be easily implemented for different types of radars, such as those on board rovers and equipped with suspended antennas (WISDOM, RIMFAX, and CHANG’E LPR) or those on board orbiting spacecraft (MARSIS, SHARAD, KAGUYA LRS, RIME, and REASON). Some of these radars use different types of source wavelets (e.g., chirp and continuous waves), and their transmitted signals, unlike our case, do not depend on soil/antenna coupling. Nevertheless, neither of these two aspects represents a limitation in the application of the method because the spectral attributes, from which the loss tangent can be estimated, only depend on the electromagnetic properties of the subsurface material. As matter of fact, the amplitude decay technique has been successfully applied to the Moon and Mars data [Porcello et al., 1974; Watters et al., 2007; Campbell et al., 2008; Carter et al., 2009; Ono et al., 2009]; however, to our knowledge, the frequency shift method has never been used to analyze planetary radar data. The main contribution of our study is the integration of the two techniques (amplitude decay and frequency shift) to maximize the retrieved information on the electrical properties of the investigated materials. In fact, the estimation of the different loss tangents allows, in principle, to separate polarization and conduction terms which are associated to different physical phenomena. It follows that, from radar data, it is possible to extract three independent electrical parameters (real part of permittivity, polarization term, and conductivity) which can impose better constrains to the interpretation of the composition of the planetary subsurface materials. An important application of this methodology concerns the possibility to discriminate between water ice (conductive term) and dry soil/rock (polarization term) when the ice is not visible on surface like in the case of the Frozen Sea on Mars, a difference that cannot be distinguished by using only the real part of permittivity [e.g., Pettinelli et al., 2003]. Moreover, as the conductivity is strongly temperature dependent [Heiken et al., 1991] (i.e., it is much more sensitive to soil temperature

LAURO ET AL. EM SIGNAL PENETRATION IN PLANETARY SOIL 1401 Journal of Geophysical Research: Planets 10.1002/2016JE005192

variation than real part of permittivity and polarization), such technique could provide unique information on soil composition if applied on data collected at the same site at different times (diurnal or seasonal radar data acquisition). Despite the scope of the present study was mainly methodological, we would like to brieﬂy comment on the retrieved loss tangents (0.04–0.07) in comparison with data collected on the Moon and Mars. First of all, it should be highlighted that our data are comparable to those estimated by other authors (0.02–0.05) in (almost) dry terrestrial volcanic deposits assumed to be a good analogue of Martian surface [e.g., Heggy et al., 2006]. These values are 1 order of magnitude larger than those collected on site by SEP experiment (Apollo 17) on lunar regolith [Strangway et al., 1977] and more recently at 5 MHz on lunar maria during Kaguya mission [e.g., Ono et al., 2009]. This fact is expected, because on Earth the water is ubiquitous and it is virtually impossible to collect GPR ﬁeld data in dry conditions typical of planetary surfaces. As a consequence, our results should be considered an upper limit for planetary volcanic soil analogues. In this condition, we can safely state that the retrieved loss tangent values are mainly due to soil water content and any other effect (e.g., the concentration of Fe/Ti oxides), if present, is totally masked by the water. In fact, the strong effect of even small quantities of liquid water (in soil and rocks) on the loss tangent is well known since the time of lunar soil exploration and sample management and analysis [Strangway et al., 1977; Alvarez, 1974]. At that time only after applying a procedure to completely remove the water from the samples (measurement in vacuum), it was possible to suppress the dependence of loss tangent on moisture and highlight

the well-known dependence on FeO and TiO2 concentration [Strangway et al., 1977]. In any case, the loss tangent measured on the Moon or in laboratory on lunar soil samples is always lower than 102 [Heiken et al., 1991]. A value of the order of 103 has also been found in Mars terrains; for example, MARSIS data acquired on the Medusae Fossae Formation on Mars provided loss tangent values (at 4 MHz) between 0.002 and 0.006 [Watters et al., 2007], which was associated to pyroclastic deposits. A value of the same order or slightly larger (0.005 ÷ 0.012) was also found on Vastitas Borealis Formation in Amazonis Planitia by Campbell et al. [2008] and interpreted as dry, moderate-density sediments (although the presence of the basalt was not completely excluded). Conversely, a loss tangent of the same order of our values (0.01 ÷ 0.03), together with permittiv- ities ranging between 7.0 and 14.0, were measured by Carter et al. [2009] in a very dry Martian environment (lava ﬂow ﬁelds northwest of Ascraeus Mons) and interpreted as being due to dense rocks probably similar to ilmenite-rich lunar basalts.

7. Conclusions We proposed and tested a method to retrieve the total loss tangent and its polarization component from GPR data collected on volcanic deposits considered good analogues of planetary surfaces. The proposed methodology is generally valid any time a sharply dipping reflector is detectable in the radar cross section, regardless of the depth of the interface (i.e., for shallow or deep investigations). Furthermore, the technique applies to any type of terrestrial or planetary subsurface radar system (on board a lander/rover or orbiter) independently from source wavelet and the type of antenna. The loss tangent is, in general, not sufficient to unequivocally identify the lithological properties of the subsurface; in fact, estimation of both real and imaginary parts of permittivity (i.e., velocity and attenuation) is fundamental in order to introduce some constraints and make the interpretation of the subsurface structure more reliable. In this work it was not possible to estimate the real part of permittivity from GPR measurements due to the lack of electromagnetic scatterers in the subsurface, which can generate hyper- bolic events, and the use of a single offset configuration of the radar system. In order to estimate such parameter, several techniques are available and relatively easy to implement for planetary radars. For systems working in proximity of the planetary surface (i.e., when the radar is on board a rover or a lander) the hyperbola calibration is probably the most suitable method. On the other hand, for velocity evaluation from orbiting GPR, the most common technique used is the “geomorphology analysis” [e.g., Nouvel et al., 2006]. The results shown in this work together with the large literature in this field highlight that GPR is undoubtedly the elective geophysical method for planetary exploration. However, to fully exploit its potential, it is of primary importance to combine the information obtainable from the radar images with those retrievable from a robust and reliable quantitative analysis.

LAURO ET AL. EM SIGNAL PENETRATION IN PLANETARY SOIL 1402 Journal of Geophysical Research: Planets 10.1002/2016JE005192

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