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SUBMISSION TO IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 1

An Imaging HF GPR using Stationary Antennas:

Experimental Validation over the Antarctic Ice SheetAlice Le Gall, Valrie Ciarletti, Jean-Jacques Berthelier, Alain Reineix, Christophe Guiffaut, Richard Ney,

Franois Dolon, Sbastien Bonaim

Abstract Ground penetrating radars (GPR) are commonlyused on the Earth to probe the subsurface and the moderatemass and power resources they require make them a most usefultool in planetary exploration. In most cases, GPR need to bemoved and perform soundings at various locations to retrievethe image of the underground layers or reflectors. Yet, TAPIR(Terrestrial And Planetary Imaging Radar) is an innovativestationary HF GPR that allows to image the reflectors in thesubsurface through the processing of measured electric andmagnetic components of the reflected waves. This instrumentwas originally developed in the frame of the NetLander project

to perform deep soundings of the Martian subsurface and hasbeen tested during a validation campaign on the Antarctic icesheet. Combining the corresponding observations and numericalsimulations of the operation of the instrument we demonstrateits imaging capability and evaluate its performances.

Index Terms Ground Penetrating Radar, deep soundings,subsurface, wave propagation, FDTD, ice, Mars

I. INTRODUCTION

Imaging underground layers and reflectors with ground

penetrating radars (GPR) is usually achieved by performing

soundings from a number of positions. These positions may

be either disposed along an approximately linear 1D path over

the surface to provide underground profiles over long distancesor organized in a 2D network over the surface to provide 3-D

profiles of the subsurface in a more restricted volume beneath

the surface. However, even on Earth, moving a GPR and its

antennas over complex terrain may be difficult (especially

when operating at frequencies in the order of magnitude of

a few MHz, when the size of the antenna exceeds tens of

meters) while it is readily impossible in the case of planetary

subsurface exploration from stationary landers. Our objective

was thus to develop an innovative GPR with imaging capability

that could be used from a stationary position.

This work was initially performed in the frame of the former

NetLander project lead by CNES that aimed at exploring

the subsurface and deep interior of Mars. This project calledfor landing 4 small geophysical stations spaced in longitudeand at low latitudes, each of these landers including a GPR.

A major goal of the radar was to search for liquid water

reservoirs that, according to geological models of Mars [14]

[37], may be found at kilometric depths. An HF frequency

of operation was thus selected; it allows to reach such large

depths on Mars due to the low moisture content of the soil.

To overcome the problem faced by a stationary instrument,

an innovative imaging technique was proposed [8] [9]. Such

a radar may also be of great interest on Earth, for example

to probe the Antarctic ice cap and to map the bedrock at

depths of hundreds to thousands of meters. A slightly enhanced

version of the NetLander radar called TAPIR (Terrestrial And

Planetary Imaging Radar) was thus developed to be operated in

the RANETA (RAdar of NEtlander in Terre Adlie) validation

campaign in Antarctica [10].

In this paper we present the method for local subsurface

imaging based on the processing of GPR pulses emitted from

a set of stationary antennas and use the data obtained in the

Antarctic to validate the concept of the radar and demonstrate

its performances. We postpone to a further paper the "geolog-ical" analysis of the results to retrieve detailed information on

the topographic features of the bedrock. In the present stage of

our work, sounding the Antarctic bedrock has the advantage of

providing a simplified geologic target which helps in validating

the principle of operation and data processing in a natural

environment devoid of too much complexity. As described in

the above mentioned references, the use of stationary antennas

to image a conical volume beneath the radar requires the ability

to resolve the parameters that determine the direction, range

and amplitude of the returning signals. A similar objective was

pursued by Moran et al. but using a different techniques based

on the use of a subset of antennas. In our case we only use

two crossed dipoles for transmission and reception as well asa magnetic antenna that provides the 3 magnetic componentsof the reflected waves. Our first objective is to resolve from

these data the range and direction of the returning waves that

provide the depth and inclination of the facets of the bedrock

that reflects or diffract the transmitted waves. Our experimental

work was backed by numerical simulations using a FDTD code

that helps in interpreting and validating the field observations.

Section II is devoted to a brief description of TAPIR,

its modes of operation and the RANETA campaign. The

description of the test sites is given in section III. We describe

the data processing method in section IV and the analysis of

several soundings is presented in section V. A discussion of

the results and some indications of future works are given inthe last section (section VI).

I I . DESCRIPTION OF TAPIR

A. Instrument Description

The detailed description of the instrument and of its princi-

ple of operation can be found in [9] and [13]. They are briefly

reviewed in this section.

1) Principle of the GPR: The TAPIR is an impulse polari-

metric ground penetrating radar. It was specifically designed

for large penetration depths of more than 1km. The radar


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operates in the HF range at low frequencies, from 2 to 6MHz.The pulse lengths can be varied to optimize the sounding

of the subsurface at different depths. The shortest pulses are

0.5s long, corresponding to a range resolution of 60meters and a blind zone of 70 meters. The longest pulsesare BPSK coded 10s pulses to probe the underground atthe largest possible depth, beyond 1km on Mars. In order to

reduce interferences and ambiant noise, a bi-phasing scheme

with alternated polarities of the transmitted waveforms is used

at transmission. To increase the radar sensitivity, coherent

additions, up to 224, are performed.Since the NetLander GPR was to operate from a fixed lander

in a mono-static mode, it was not possible to rely on the

usual mode of operation of ground penetrating radars while

obtains depth profiles by making a series of soundings over a

network of positions [4] [28] [12] [40]. Our GPR provides a

simplified imaging of the subsurface reflectors by measuring

not only the propagation delay but also the direction of arrival

of the reflected waves in order to determine both the distance

and the orientation of the reflectors. This innovative concept

derives the direction of the propagation vector of the returningwave from the measured values of 5 components of the wavefield: 2 horizontal electric components and the 3 magneticcomponents.

The GPR was thus equipped with two horizontal electrical

dipoles, orthogonal to each other, and a magnetic antenna that

could be oriented along 3 mutually orthogonal directions. Each

electrical antenna consists of two colinearly opposed 35m longresistively loaded quarter-wave monopoles [39] with a resistive

profile [22]. These antennas offer a broad enough frequency

bandwidth to allow the transmission of short pulses without

significant distortion except maybe off axis as shown by [2].

They are laid on the surface along directions that will be

taken as the horizontal (Ox) and (Oy) axes with (Oz) beingthe ascending vertical axis (see figure 1). They are made of

simple isolated copper wires of 1mm in diameter. Giventhis dimension the antennas cannot be shielded and so surface

clutter cannot be avoided. The radiating characteristics are

presented in the following section. The magnetic antenna is

a HF search coil with a central frequency of 3MHz and a 2MHz bandwidth at 3dB. The ability of using the two electricantennas to transmit and to receive allows full polarimetric

measurements, a capability of great interest because waves

reflected from inclined and/or rough interfaces or discrete

reflectors will be subject to depolarisation. Polarimetric data

bring useful information on the geometrical properties of the

reflectors.In addition to the normal mono-static radar mode of op-

eration, several other modes were anticipated on the Net-

Lander mission. In particular, one mode was dedicated to the

determination of the frequency dependance of the antenna

impedance by measuring the current flowing through the

electric antenna for several CW signals at different frequencies.

This impedance depends on the electromagnetic characteristics

of the shallow subsurface. In a passive mode, the antenna can

also be used to measure the HF radio-electric ambient noise

and detect EM emissions from possible electrical discharges in

the atmosphere. In such a mode, it was also forseen to use the

instrument as a riometer (Relative Ionospheric Opacity Meter)

to measure the absorption of galactic HF emission in the lower

ionosphere.2) Antenna Characteristics: The radiation pattern of the

electric antennas of TAPIR was computed by modeling it as

a coherent array of elementary dipoles excited by currents

of different magnitudes and phases, as shown schematically

in figure 1. The 34 resistors introduced in each monopoleare located every meter [22]. The first element is directly

connected to the feeding point. The resulting electromagnetic

field is the sum of the elementary fields generated by each 1m-segment and is expressed by formula (1). Figure 2 displays the

calculated far-field radiation pattern of an electric antenna laid

on pure ice at the frequency of 2MHz. As usual, the E-plane

is the vertical plane containing the antenna and the H-plane is

the vertical plane perpendicular to the antenna, at the center

of the antenna. The far-field radiation pattern of an interfacial

infinitesimal dipole [1] [16] is also showed in figure 2.

EM(r,,) =

E0(r,,)

I0

35

i=1

2Ii 12

cos(k(i 12

)sin cos )

(1)

and are the spherical coordinates defined in figure 1.E0 is the field generated by a current I0 flowing through anelementary dipole located at the driving point or current feed

point i.e. at the center of the antenna. Its expression was given

in [16]. Ii 12

is the current flowing in the 1 meter-segment

ni. As shown in [22], Ii 12

depends on the electromagnetic

characteristics of the soil on which the antenna is laid as

well as on the resistive profile of the dipole. Its value for

each segment can be derived from the theoretical expression

given in [22] or computed with the numerical code.k is the

propagation vector of the waves in the medium surrounding the

antenna i.e the interface between the air and the ice. As shownby [38], the propagation vector of the wave at an interface can

be approximated by:

k =k20 + k21

2

1/2=k2air + k2ice

2

1/2(2)

where k0 = kair is the wave number in the upper media andk1 = kice in the lower one.

The computed radiation pattern differs from that of an

infinitesimal dipole mainly by being narrower in the E-plane.

The H-plane patterns are practically identical. Both patterns

exhibit a three-lobe structure with sharp nulls in the E-plane.

These results are similar to those given in [3] which used

a pulse excitation and a cosine current distribution. Yet, in

practice, these nulls may be less pronounced and the E-planebeam approximately 70 wide. This wide radiation patternprovides a large angular field of view for the radar which

thus illuminates reflectors or interfaces that are significantly

away from the vertical direction. The radiated waveforms are

assumed to be identical to those received. Several examples

are given later.

III. TH E RANETA EXPERIMENT

The RANETA campaign was organized under the auspices

of the French IPEV (Institut polaire franais Paul-Emile Vic-

tor) near the cap Prudhomme station in Terre Adlie (139.9E,


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Fig. 1. Schematic view of a resistively loaded monopole along (Ox+) used to establish the expression of the far-field radiation pattern. Ri are the resistorslocated every meter. I(2i1)/2 are the currents flowing in each segment of the monopole. In the symmetric monopole oriented along (Ox

), elementarycurrents are identical but flow in the opposite direction. The angles and are shown.

0.5 1

30

210

60

240

90270

120

300

150

330

180

0

0.5 1

30

210

60

240

90270

120

300

150

330

180

0

Elementary dipole laid on pure cold ice: |rE0|

RANETA resistively damped dipole laid on pure cold ice: |rEM

|

Fig. 2. Far field radiation patterns of an interfacial elementary dipole and ofthe resistively loaded dipoles laid on pure cold ice at a frequency of 2MHz.The radiation pattern of the loaded antenna is more directionnal in the E-plane. Yet, both radiation patterns have a maximum in the vertical directionand illuminate a wide area of the underground.

66.68S) in January-February 2004 [10] at moderate distances

from the coast where the bedrock lies between 200 and 1200m from the ice surface.

A. Ice and Bedrock Characteristics

The electromagnetic properties of ice as a function of tem-

perature and frequency are well documented. They have been

recently reviewed in [17]. Up to 600MHz, the electromagneticparameters are practically independent of frequency. Between

10C and 30C, the relative permittivity undergoesonly negligible changes and the conductivity remains low,

between 106 and 3 105S/m. In the case of RANETAmeasurements, the temperature between the surface and the

bedrock was estimated to be in the range from 10C to20C. Values of the relative dielectric constant and of the

electrical conductivity in this temperature range are typically

r 3.2 and 2 105S/m. HF waves thus experience littleattenuation in ice and sounding depths of several kilometers are

achievable. The wavelengths corresponding to the frequencies

of operation of the radar are much greater than the average

thickness of the small scale layering (isochrone layers) that

corresponds to the yearly accumulation of snow with typical

dimensions of a few centimeters. We neglect also potential

reflexions on internal layers due to volcanic events. Thus, the

propagating medium can be considered as homogeneous.

The bedrock is mainly composed of gneiss with a dielectric

constant in the range 4-9 [35], probably close to 7. Noinformation on the bedrock topography is available over the

area where the soundings have been performed. However,

according to the BEDMAP data base [24] its average elevation

lies close to the sea level and often slightly below in the

first 50km of the ice cap. The highly irregular topography ofthe islands around Dumont dUrville and on the coast near

Cap Prudhomme station suggests that the bedrock surface is

similary irregular.

B. RANETA Observations

1) Radar soundings: During the RANETA field survey, 8soundings of the ice sheet were performed at distances from

the coast from 5km to 45km with altitudes above the sealevel from 285m to 1100m. The ice-bedrock interfacewas detected for all the soundings with clear signals on both

electric and magnetic antennas. In good agreement with [24],

the ice thicknesses measured between the coast and 45kminward are consistent with a bedrock close to the sea level.

In several occasions more than one echo was detected. A full

set of data (5 components of the electromagnetic field) was

recorded for 4 of the 8 soundings and we present in this paper

a data processing method which allows the various echoes to


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be distinguished and to determine the orientation and position

of the reflecting facets of the bedrock.

2) Antenna impedance measurements: The quantitative

analysis of the GPR soundings requires the knowledge of

the geoelectric characteristics (r, ) of the subsurface. Asmentioned in the previous paragraph, the subsurface can be

considered homogeneous and thus the average geoelectric

characteristics can be taken equal to those of the shallow

subsurface. These parameters, needed to convert propagation

delays into distances, can be derived from the measurements

of the antenna impedance.

As indicated above, when an antenna is lying on the surface,

its current distribution, hence its impedance, depends on the

electrical parameters of the ground and this coupling can

be used to retrieve the electromagnetic parameters of the

subsurface. A detailed study based on the numerical FDTD

method was recently performed by Le Gall et al. [22] for

the antennas which were used in the RANETA experiment.

They show that the impedance is controlled by the shallow

subsurface within 2m from the surface.During the RANETA field survey, the impedance of eachdipole was measured from 400kHz to 8MHz, a range which

covers most of the frequency spectrum of the radar pulses.

Figure 3 displays the best fit between the measured and the

modeled real and imaginary parts of the antenna impedance

corresponding to r 3 and 105S/m. These valuesare in very good agreement with published ones (see section

II-B-1). The estimated error in r is 0.25. The conductivityis obtained with less accuracy, with an error of 3 105S/m.Its value is larger than those given in [17]. A possible reason

stems from the fact that the shallow ice layer is warmer than

the deeper layers and may even contain liquid water.

In the following the complex permittivity is defined by:

c = j = 0cr = 0

r j

0

, (3)

where 0 = 8.854 1012F/m, j =1 and = 2f.

IV. DATA PROCESSING

The objective of the data analysis is to sort the echoes

and compute their propagation times and directions. Prior to

resolving the range and direction of the different detected

echoes, data must be denoised and the measured magnetic

components must be corrected from a parasitic effect that will

be described in this section.

A. Filtering and calibration

Figure 4(a) shows an example of a full set of data. We

have applied a low frequency filtering in order to suppress the

high frequency part of the electronic and ambient noise and a

Wiener filter allowed us to improve significantly the signal to

noise ratio.

Comparison of the transmitted waveform at 4MHz (see

figure 4(b)) with the received signal, in particular with the

copolar component Ex (see figure 4(a)), shows that the signaldid not distort during propagation and reflection, r and areindependent of frequency.

In addition, the only way to obtain true electric field

values from the output voltages at the receiver is to use a

numerical model of the antenna operation. On the contrary,

the magnetic components are directly converted into Teslas

from the calibration curves of the magnetic antenna.

B. Correction of the Measured Magnetic Field

The measured magnetic field components are the sum of (i)the true magnetic component

Br of the reflected waves and

(ii) the magnetic fieldBA induced by the currents flowing in

the electric antennas when excited by the the electric field of

the reflected wave. The sum of 2 induced magnetic fields must

be removed from the measurements to get the actual vertical

magnetic component of the reflected waves (see figure 5).

With a significantly good approximation,BA can be com-

puted from the simple modelBA of a current in an infinite

electric wire given by Amperes law such that:

BA

0|I|2d

e (in Tesla) (4)This approximation was checked numerically and is under-

stable since the magnetic antenna was located close to the

center of the dipoles and directly on the soil.

The induced magnetic fieldBA is thus in the plane normal

to the dipole so vertical at the location of the magnetic antenna.

Therefore the measured vertical magnetic component must be

corrected. Since the magnetic antenna is very close (less than 2

meters) to the electric antenna, the measured magnetic field of

the reflected waves has in practice no phase shift with respect

to the electric field and thus withBr. Therefore, we used

the co-polar and cross-polar measurements from the electric

dipoles to infer the current flowing along the two antennas. In

most soundings, the copolar signal is larger than the crosspolarone hence the current travelling in the transmitting electric

antenna Ico is larger than the current in the orthogonal antennaIcross. As illustrated by figure 5, the induced vertical magnetic

Fig. 5. Above view of the electric and magnetic antennas configurationof operation. This figure indicates how the currents flowing though the 2orthogonal electric dipoles induce two parasitic components of the magneticfields: Bco and Bcross along two opposite directions.

component can be computed from the formula:

BA 0

2

|Ico|yM

|Icross|xM

ez (in Tesla) (5)


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0 1 2 3 4 5 6

x 106

0

500

1000

1500

2000

2500

Frequency (Hz)

Re(Z

a)()

0 1 2 3 4 5 6

x 106

10000

8000

6000

4000

2000

0

Frequency (Hz)

Im(Z

a)()

Measurements on the Antarctic continent

Numerical simulation: r=3,

e=10

5S/m

Fig. 3. Real and imaginary parts of the measured and numerically computed antenna impedance as a function of frequency on the Antarctic ice sheet, duringthe RANETA campaign. Masurements were made with a network analyzer HP8753C. Simulations were conducted with a FDTD 3D code. The best fit isobtained for the following electric characteristics: r = 3 and e = 105S/m (see [22]).

6 8 10 12 1420

0

20

Ex

Wiener filter

6 8 10 12 140.5

00.5

Ey

6 8 10 12 142

02

x 1014

Bx

6 8 10 12 141

01

x 1013

By

6 8 10 12 141

0

1x 10

13

s

Bz

6 8 10 12 1420

0

20

Ex

Raw data

6 8 10 12 140.5

00.5

Ey

6 8 10 12 142

02

x 1014

Bx

6 8 10 12 141

01

x 1013

By

6 8 10 12 141

0

1x 10

13

s

Bz

(a) February 1st , 2004 sounding, raw and Wiener filtered data. The GPR was operating at the centralfrequency of 4MHz in a transformer matching mode. The x-axis is the delay time in s, and the unitof the y-axis is mV at the output of the electric receivers and in Teslas for the magnetic channels.

1 0 11

0

1

2MHz 500s

1 0 1

0.5

0

0.5

3MHz 500s

1 0 11

0

1

4MHz 500s

s

(b) Waveforms of the antennainput potential at the centralfrequencies of operation 2, 3,4MHz in mV. The length of eachpulse is about 500ns.

Fig. 4. Full set of data and transmitted waveforms.

where xM and yM are the horizontal coordinates of thelocation of the magnetic antenna in the (Oxyz) frame of

reference defined by the electric dipoles. The currents Ico andIcross are deduced from the measured voltages of the outputof the electric antennas divided by the antenna impedance Za.

The ratio between the vertical magnetic field of reflected

waves and the induced magnetic fieldBA depends on the

inclination of the propagation vector of the reflected waves. If

the reflecting interface is nearly horizontal, the magnetic field

of reflected waves is also nearly horizontal and its vertical

component is very weak compared to the induced magnetic

fieldBA. If reflection occurs from a strongly inclined facet

of the bedrock, the reflected waves have a propagation vector

which is also strongly inclined with respect to the horizontal

plane and their vertical magnetic component may be of the

same order of magnitude as BA.

V. DATA INTERPRETATION : IMAGING OF THE SUBSURFACE

A. Time of Arrival of the Echos versus Elevation above the

Bedrock

The times of arrival of the detected echos were determined

by cross-correlating the received signals with the derivative of

the transmitted waveform. For each sounding, we computed

the average value of the delays obtained independently for dif-

ferent frequencies of operation and transmission polarisations.

The standard deviation provides an estimate of the irregular


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topography of the subsurface. These delays can be converted

into distance according to the relation:

d =ctd

2

r1(6)

where r1 is the relative permittivity of the ice.Figure 6 displays the distances of the first (and usually)

main reflector from the radar along the RANETA soundings

track. These distances may differ from the actual depths of the

reflecting facets since some of them may be out-of-plane. The

altitude of each sounding site is also indicated.

0 5 10 15 20 25 30 35 40 45200

300

400

500

600

700

800

900

1000

1100

1200

Distance from Cap Prudhomme station along the track (km)

meters

01/31

02/0502/04

01/2901/22

01/3002/01

01/23

01/24

02/26

Altitude above the sea level

Distance of the main subsurface reflector from the radar

Fig. 6. Measured distances between the bedrock and the source at each sitealong the RANETA survey track. 8 soundings where performed during 10days. Altitudes above the sea level of each site are also indicated.

In good agreement with [24], the bedrock appears to belocated close to or a few tens of meters under the sea level.

The large standard deviation recorded on the 30th of Januarysuggests a very irregular hilly topography of the bedrock.

B. Determination of the Direction of the Propagation Vector

The method to retrieve the direction of propagation of

the reflected waves is based on a comparison between the

measured components Ex, Ey , Bx, By and Bz and a theo-retical expression of the electromagnetic field obtained for the

reflection from an inclined facet.

1) Theoretical modeling: As shown in [11], the far-field

limit is < 100m in the ice at 2MHz. Thus, for all the sound-ings discussed in this paper, the reflection of the transmitted

waves occurs in the far-field region. In these conditions we

consider the reflections to be locally plane waves with the

incident electric and magnetic fieldsEi and

Bi perpendicular

to each other and to the propagation vectorki . The large

wavelengths of operation of the radar allow to consider that

the bedrock surface roughness has no effect. Moreover, we

assume that the waves reflect on a plane surface with large

enough dimensions so that diffraction at the edges can be

neglected. This hypothesis was prompted by the result of a

stringent computation of the budget power: it shows that the

predicted and measured electromagnetic field (corresponding

to the bedrock reflections) agree quite well which indicates

that the size of the reflecting facets must be close to the size

of the Fresnel zone and that the propagation medium can be

considered homogeneous; the Kirchhoff approximation is thus

valid. Nevertheless, some of the observed weaker echos might

be due to diffraction processes on the wedges of the bedrock

large scale topography. In such case, we should be able to

determine the direction of arrival of these diffracted waves

too [13] and to take the diffracting structures into account in

imaging the subsurface.

With a mono-static radar, the detected reflected waves arise

mainly from normal (specular) reflections on one or several

facets (in case of multiple echoes). To compute the returning

wave vector kr one possible solution could be to derive themissing vertical electrical component from:

Erz = BrxErx + BryEryBrz

(7)

and to use the relation: kr =cn1

Er Br. Er and Br are the

returning electric and magnetic fields. However, this simple

method is precluded in most cases since the reflecting facets

are often weakly inclined and, as a consequence, the reflected

waves propagate close to the ascending vertical. The received

vertical magnetic component Brz is thus small which canentail large errors in the computed value Erz .

Using equation (1) which provides a theoretical analytical

expression of the far-field is also impractical due to the

presence of deep minima between the main lobe and the

secondary ones, which may yield computational issues for

some configurations. Also, the true radiation pattern minima

between the primary lobe and the sidelobes may be less

pronounced than the theoretical one making the expression

(1) inaccurate. We have thus developed a different methodusing a more general expression of the electromagnetic field.

Its principle can be described as follows.

We let (ex, ey , ez ) be the reference frame and and , theangles defining the direction of arrival of the reflected waveskr (see figure 7(a)) are = (

z , kr) and = (x , krh) wherekrh is the horizontal component of the reflected wave vectorkr:

kr =

sin cos sin sin

cos

. (8)

As depicted in figure 7(b), we define a new frame of

reference (OXY Z) where Z is alongkr , X is obtained by

a rotation of x around Z (hence x1) followed by a rotation around y1 and Y is in the horizontal plane perpendicular

to (OXZ). In the (OXY) plane,E makes an angle with

(OX).The reflected fields are then given in (Oxyz) by:

Er(r, t) = E0f(...)

cos cos cos sin sin cos cos sin + sin cos

cos sin

(9)

and

f(...) = f(t,d,1, 2, ) =

2de

2d g( krr (t )), (10)


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(a) Schematic view of the GPR in Terre Adlie and of the referenceframe. The electrical dipoles are lying on the ice and define the x andy-axis.

(b) Frames and angles of reference.

Fig. 7. Notations and frames of reference.

where E0 is the amplitude of the transmitted signal, d is thedistance between the radar and the reflecting facet, g is thewaveform of the transmitted signal, is the coefficient ofreflection on the ice-bedrock interface, = 2d

r1/c is the

propagation time of the wave, is the coefficient of attenuationdefined by:

=1

21

0

0r1(11)

and

Br =n1c kr Er. (12)

r1, 1 and 0 are the electric relative permittivity, electricconductivity and magnetic permeability of ice, 2 is the di-electric constant of the bedrock.

Hence,

Br(r, t) =

E0Z1

h(...)

sin cos cos cos sin sin cos sin + cos cos

sin sin

(13)

where

h(...) = h(t,d,1, 2, ) =

2de

2d w( krr (t )) (14)

and Z1 =

1

= cn1 is the impedance of the ice. The quantity

w is the waveform of the magnetic signal.2) Implementation of the method: The unknown attenuation

factor can be eliminated by using values of the electric and

magnetic components that are normalized with respect to a

reference waveform. The reference waveform is extracted from

the signal and takes into account the distortions induced by

the amplifier, the coupling between its output and the antenna

as well as those in the reception channel. As mentioned in

section III-C-1, the propagation time , hence the distanced, can be derived from the cross-correlation of the received

electric signal with the reference waveform at the transmitted

frequency. However, since we used simultaneously the electric

and magnetic channels with different delays in the electronics,

we did not use this method but kept the distance to be

determined together with the other parameters.

We are thus left with 4 unknowns: d, , and , and 5non linear equations from equations (9) (without the analytical

expression of Erz) and (13). An iterative procedure based onthe minimization of the least square error between theoretical

and observed electromagnetic field components was used toinfer the desired parameters.

Lastly we accounted for the refraction of the wave at the

exit from the ice. Vertical and horizontal angles, and , ofinclination of the detected subsurface facet were derived from

the computed values of and from:

= arcsin

sin

r1

and = (15)

The refraction prevented us from determining the actual

value of vertical inclinations that exceed the critical anglec = sin

1(1/

r1). Beyond this value, waves exit from theice with a direction parallel to the interface as anticipated

by Goos and Hnchen [18] (the Goos-Hnchen effect is alsoresponsible for the existence of sidelobes in the radiation

pattern of a dipole in the vinicity of an interface). At the

interface air/ice, c is equal to 34.

C. Validation of the Method on Simulated Data

XLIM1 has developed a 3D FDTD (Finite Difference Time

Domain) code called TEMSI-FD for a wide domain of appli-

cations. A detailed description of this TEMSI-FD can be found

1Formely the IRCOM, Institut de Recherche en Communications Optiqueet Micro-ondes (Limoges)


8/14


in [25], [11] and [5]. We have used it to perform numerical

simulations of the operation of the radar in simplified or

realistic environments.

The simulations used two different configurations of the

bedrock interface, one located at a depth of 400m and thesecond one at 700m. They are shown in figures 8(a) and9(a) where the directions of the expected specular reflections

are indicated. The dimensions of the computational box in the

three orthogonal directions (Ox), (Oy), (Oz) are respectively(300m, 300m, 400m) and (500, 500, 700m). The mesh sizeis 1 meter in all directions which is small enough to preventnumerical dispersion. In modeling the ice we have neglected its

conductivity and set its permittivity equal to 3.2. The bedrockis substituted by a perfectly reflecting metal. This does not

modify the relative magnitudes of the components of the EM

field of the reflected waves; hence does not introduce any error

in the retrieval of their direction of arrival.1) Simulation 1: single reflector case: The bedrock is

modeled as a single inclined facet with a normal defined by

= 60 and = 10. Figure 8(b) compares the TEMSI-FD simulated data at

4MHz and the electromagnetic field

components derived from the analysis described in section V-

B.1. There is obviously a very good agreement between these

two sets of curves. The adjusted parameters inferred from the

optimal fit are: td = 4.325s hence d 363m, = 61, = 9.9475. They are consistent with the actual parametersof the facet. It must be noted that these fits were obtained by

minimizing the least square errors between the 5 simulated and

theoretical components of the electromagnetic field: Ex, Ey ,Bx, By and Bz. Nevertheless, it gives a good result for thevertical electric component Ez which adds to the validation ofthe method. Tests were conducted by introducing conductive

losses ( = 105S/m instead of0S/m) and have shown that the

derived geometric parameters,

,

and d, remain unchanged.The error on the estimation of and can stem from twosources:

the finite steps on , and used to minimize the rmsdeviation

the inaccuracy of the measurements due to ambient

noises, couplings, waves superpositions...

As far as simulations are concerned, data can be regarded

as unimpaired by any noise. As aforementioned, the error

function D(, ) illustrated by figure 8(c) exhibits a globalminimum ( = 10 and = 61). The rms deviation isclearly less sensitive to than to thus the uncertainity onthe estimated value of is larger.

2) Simulation 2: multiple reflectors case: In the secondconfiguration, the bedrock interface consists of 2 facets with

their normals inclined at 26 and 17 with respect to thevertical axe and rotated at 45 from (Ox). A third horizontalfacet is located between these two as illustrated in figure 9(a).

In order to increase the time difference between the 3 echoes,

the propagation velocity was decreased by taking a relative

permittivity of9 in place of3.2. Three waves can then be easilydiscriminated: (i) wave 1 arises from the facet inclined at 26,(ii) wave 2 corresponds to a reflection on the facet inclined at

17, (iii) wave 3 originates from the reflection on the plateaubetween the two inclined facets. Wave 1 is expected to exit

from the subsurface with an inclination of 90 with respect tothe vertical since 26 > |c| 19.5 where c is the criticalangle of refraction. Indeed, according to the Snell-Descartes

laws, the energy must be totally reflected downward at the

interface between ice and air. Yet, Goos and Hnchen had

demonstrated that a wave can exit from a more refringent

medium (ice) to a less refringent one (air) when the critical

angle is exceeded [18] [32] [31]. Such a wave, sometimes

existing as a lateral wave, is evanescent i.e. confined to the

interface between the two media. It travels along the surface

before diving again into the more refringent area.

The derived geometric parameters are indicated in the fig-

ures 9(b), 9(c) and 9(d) where we have shown the mean square

deviation for each echo. , and d are quite close to theexpected values. The errors made on the amplitudes of the

various components (arising mainly from the fact that the 3

echos are not well separated) and the sensitivity of D(, )to the horizontal angle account for the error on the estimate of

. The error on remains small. Supplementary simulationshave shown that the uncertainties on the estimate of the angular

parameters

and

increase as the reflecting buried facetbecomes more horizontal.

This example features three interesting events that are ex-

pected in actual soundings:

1) a reflection arising from an interface with an inclina-

tion larger than c: as anticipated by Goos and Hnchen[18], the wave at the exit from the ice is grazing and the

actual inclination of the facet will stay unknown. Onewill only be able to conclude that: c or c. Yet, the horizontal inclination can be determinedwith a good accuracy.

2) a wave reaching the surface with a quasi-normal

incidence: this occurs when the radar is located just

above a horizontal reflector. is no longer defined andthe poor sensitivity of the mean square error D on

leads to errors up to a few degrees on its estimated value.

3) a wave propagating along a direction between 0

and c: in this case, both and can be determined

with reasonable accuracy. The accuracy on will bealways better than the accuracy on .

D. Application to RANETA Data

1) Single reflector case: On the 1st of February, a singleecho was clearly detected on both electric and magnetic

components. Table I provides the derived characteristics of

the returning wave (time delay and direction of arrival). Thepropagation distance d can be determined from the time delaythrough relation (6). Taking into account the vertical angle ,the retrieved depth is h = d cos 700m which comparesreasonably well with the altitude of the radar above the sea

level (641m). The derived angles for the 3 different centraloperating frequencies are in good agreement with each another.

It must be noted that the values of are consistent with thefact that the highest signals were observed on the monopoles

oriented parallel to (Ox) and (Oy+) which implies that:90 < < 180. The vertical inclination is quite high, 24. As indicated in section III-A, it is likely that the


9/14


(a) FDTD simulation 1: the GPR is laid on the surface. In thesubsurface, a facet showing the following inclinations: = 60

and = 10 is capped by 400m of non lossy ice (r = 3.2)

3 3.5 4 4.5 5 5.5 6 6.5 7

x 106

10.5

00.5

Ex

3 3.5 4 4.5 5 5.5 6 6.5 7

x 106

0.05

0

0.05

Ey

3 3.5 4 4.5 5 5.5 6 6.5 7

x 106

0.2

0

0.2

Ez

3 3.5 4 4.5 5 5.5 6 6.5 7

x 106

0.02

0

0.02

Bx

3 3.5 4 4.5 5 5.5 6 6.5 7

x 106

10.5

00.5

By

3 3.5 4 4.5 5 5.5 6 6.5 7

x 106

0.5

0

0.5

s

Bz

Numerical Simulation: *: 60,

*: 10

Fitting theoritical Model: td: 4.325s,

*: 61,

*: 9.9475

(b) The electric and magnetic components of the reflected wave asa function of time are shown as full gray lines. Using the theoreticalexpressions (9) and (13), the best fit (minimizing the least square errorbetween the simulated data and the theoretical model) is obtained forthe following input parameters: td = 4.325s,

= 61, =9.9475 (dotted black lines)

(c) Standard deviation between simulations and the-ory as a function of and . It is normalized byits minimum.

Fig. 8. Validation of the method developed to image the subsurface on FDTD simulated data corresponding to a single buried inclined facet.

bedrock topography is highly irregular and may well account

for this value.

Figure 10(a) compares between the measured components

of the EM field for different central frequencies with the

signals computed using the derived parameters. The goodconsistency between these curves is very clear. Fits are also

good for the component Ez , the vertical electric field obtainedusing formula (7). An appropriate median filter was applied to

avoid numerical aberrance. The worst fitted component, Ey, islogically the weakest one.

The mean square deviation between the theoretical model

and the data is computed at each frequency as a function of

and . Figure 10(b) corresponds to a central frequency of4MHz. It clearly exhibits a global minimum. In the analysisof actual sounding data, the main source of error lies in

the determination of the induced vertical component of the

TABLE I

CHARACTERISTICS OF THE ECHO MEASURED ON THE 1st OF FEBRUARY

2004 DEDUCED FROM THE PROPOSED METHOD OF IDENTIFICATION AT

THREE DIFFERENT CENTRAL FREQUENCIES OF OPERATION 2, 3, 4MHZ.

f td d h

4MHz 9.34s 783m 717m 109 23.7

3MHz 9.24s 775m 698m 105 25.7

2MHz 9.015s 756m 701m 105 25.3

magnetic field. Figure 11(a) shows the resulting errors on the

estimated angular parameters, and , as a function of theerror on the corrected component Bz . In may be seen thateven in the case of a very poor accuracy on the amplitude

of Bz , uncertainities on and remain reasonably low, in

particular for the second one.


10/14


(a) FDTD simulation 2: the GPR is laid on the surface. Beneath 700m of a dielectric material(r = 9), in the = 45-plane, the subsurface exibits 3 facets. Their vertical inclinations arethe followings: 1 = 26

, 2 = 17 and 3 = 0

.

(b) Standard deviation used to identify the first echonormalized by its minimum. The derived parameterscorrespond to the minimum of the error: = cand = 46. The input parameters in the FDTDcode are: 1 = 26

> c and = 45.

(c) Standard deviation used to identify the secondecho normalized by its minimum. The derived pa-rameters correspond to the minimum of the error: = 16.691 and = 50. The input parametersin the FDTD code are: 2 = 17

and = 45.

(d) Standard deviation used to identify the thirdecho normalized by its minimum. The vertical anglecorresponding to the minimum of the error is =3.65. The input vertical angle in the FDTD codeis: 3 = 0

. is not defined.

Fig. 9. Validation of the method developed to image the subsurface on FDTD simulated data showing 3 echoes.

2) Multiple reflectors case: In a number of soundings,

multiple echoes were detected. In particular, on the 4th

ofFebruary, at least 3 echoes can be discriminated. Two of these

are less intense at central frequencies of 2 and 3MHz. Thiscan be explained by an improvement in the quality of the

measurements when the frequency, hence the number of half-

cycles of the transmitted signal, increases. For this reason, we

focused as in figure 4(a) our analysis on data measured at

the central frequency of 4MHz. Table II displays the results

derived from the analysis of each echo. The elevation above

the sea level of the radar was 373m.When waves have close time of arrival, their amplitudes

can be slightly enhanced or reduced (due to interference).

Figure 11(b) displays the standard deviations on and

as a function of the error on the amplitude of each componentfor the cases presented in this paper. Standard deviations with

respect to the actual input values of and increase linearlywith this error. The method of analysis showed here thus yields

better results when the multiple echoes are separated enough

in time.

V I . CONCLUSION AND DISCUSSION

This paper intended to present a method allowing to identify

the location and inclination of the reflecting structures of

the subsurface detected by a HF ground penetrating radar

operating with stationary antennas. The methodology was


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9 10 112

0

2

Ex

4MHz td:9.34 s *:109 *:23.7

9 10 11

0.020

0.02

Ey

9 10 111

0

1

Ez

9 10 110.5

0

0.5

Bx

9 10 111

0

1

By

9 10 111

0

1

s

Bz

9 10 112

0

2

3MHz td:9.24 s *:105 *:25.7

9 10 11

0.020

0.02

9 10 110.5

0

0.5

9 10 110.5

0

0.5

9 10 111

0

1

9 10 111

0

1

s

9 10 112

0

2

2MHz td:9.015 s *:105 *:25.3

9 10 11

0.020

0.02

9 10 110.5

0

0.5

9 10 110.5

0

0.5

9 10 111

0

1

9 10 111

0

1

sMeasured signal Envelop Fitting signal

(a) Comparison of the data collected on the 1st of February 2004 in Terre Adlie at the three operating frequencies 2, 3 and 4MHz with the bestfits derived from the proposed method. The vertical electric component Ez was reconstructed with the five other components of the electromagneticfield using the formula (7). The values of the angles providing the best fits at different frequencies are consistent with one another.

(b) Mean square error on the identification of theecho detected on February, 1, 2004. The derivedparameter correspond to the minimum of the error: = 23.711 and = 109.

Fig. 10. Application of the method to data collected on the 1st of February 2004

TABLE II

CHARACTERISTICS OF THE 3 ECHOS MEASURED ON THE 4th OF FEBRUARY 2004 DEDUCED FROM THE PROPOSED METHOD OF IDENTIFICATION AT THE

CENTRAL FREQUENCY OF OPERATION 4M HZ.

Echo 1 Echo 2 Echo 3

d1

1

1 d2

2

2 d3

3

3

410m 140 -15.215 559m 91 -31.9 624m 90 3 < c = 34

successfully validated on simulated data for this purpose.

Numerical simulations were conducted using a FDTD code

able to model complex propagating media. The method was

then applied to real data collected in the framework of the

RANETA campaign during which a series of soundings were

performed over the Antarctic ice sheet in Terre Adlie. In

several occasions more than one echo has been detected and

the developed data processing proved its ability to disentangle

the origin of the various echos and to retrieve the vertical and

horizontal inclinations of the reflecting facets of the ice-bed

rock. The derived results show good consistency.

A stringent investigation on the error in our estimates of

the angular parameters was conducted. It appeared that main

uncertainties stem from the range resolution of the instrument

since the developed method requires separated echos. A signal

processing technique allowing to improve data resolution is

currently investigated. Only applied to atmospheric radars until

now, the frequency domain interferometry [29] [23] [36] is a

method inspired by the spatial domain interferometry that is

likely to bring strong improvements in the processing.


12/14


50 40 30 20 10 0 10 20 30 40 5050

20

0

20

*

*=25.3 *=105

*=15.215 *=140

*=31.9 *=91

50 40 30 20 10 0 10 20 30 40 505010

5

0

5

10

*()

Error on Hz (%)

(a) Uncertainties on and as a function of the error (in %) on thecorrected component Hz .

0 2 4 6 8 10 12 140

2

4

6

std(*)()

0 2 4 6 8 10 12 140

1

2

3

Error on each component(%)

std(*)()

*=15.215 *=140

*=31.9 *=91

*=25.3 *=105

(b) Standard deviation on and as a function of the error on the amplitudeof each component (in %).

Fig. 11. Uncertainties on the estimation of and for 2 sources of error.

In order to retrieve the direction of arrival of the backscat-tered waves, we assumed that the measured echos arose from

reflections on large facets (with scale comparable to the Fresnel

zone) of the subsurface. The overall power budget showed

that this simple assumption was acceptable. Yet, it may entail

errors in the reconstruction of the bedrock. To correctly image

the conical volume beneath the stationary antennas of TAPIR,

pulse returns have to be resolved not only in range and

direction but also in amplitude to take into account the small

reflecting structures. For this purpose, future investigations

may rely on the work of Beckmann and Spezzichino [6] that

assumes that facet reflections strength is governed by both the

local Fresnel reflection coefficient and the size of the facet.

We have also discarded the idea that waves could be due

to diffraction on the edges of the bedrock. However, Ciarletti

et al. [13] demonstated that, if so, the method still allows

to determine their direction of propagation. We chose not to

consider these waves because their amplitudes are 10 timeslower that the amplitudes of the specular reflections.

Besides, we hypothesized that the ice sheet lying over the

bedrock was homogeneous. However, several authors men-

tioned the presence of bright internal layers in the Antarctic

ice sheet that can be a significant source of interference in

the frequency range of TAPIR [40] [21]. Acting as isochrones,

these layers can be due to past atmospheric changes or volcanic

eruptions and their brightness can locally rival bed echoamplitudes. Yet, internal layers are intermittent. In particular,

they are often absent within ice streams. We ignore whether

or not such bright layers exist along the sounding track of

the RANETA survey but, once again, our work focused on the

interaction with the bedrock and the power budget showed that

if they do, their impact on the measured waves is weak. Future

investigations will be dedicated to the study of the waves

recorded before the bedrock response in order to determine

their origine.

Work is in progress to extend the reported studies to more

realistic and detailed descriptions of the actual 3-D geometry of

the Antarctic bedrock structure. More refined processing willbe developed but the preliminary results obtained with simple

assumptions are quite promising. They exhibit the key role that

ground penetrating radars can play in the effort of investigation

of the Antarctic continent. They can provide information of

prime interest to understand the processes involved in the

dynamics and long-term evolution of the Antarctic polar cap

and glaciers. In particular, ground penetrating radar soundings

are among the most useful instruments to measure the ice

thickness and reveal the Antarctic ice-bed rock topography.

Such information is required to properly model the dynamical

behaviour of the ice sheet and help predicting its future.

The updated version of the NetLander GPR, TAPIR, hasbeen proposed to fly on board of the ESA ExoMars spacecraft

(experiment EISS in the GEophysical Package of ExoMars).

The subsurface exploration of Mars still arouses a great

interest. This interest has been recently enhanced by the

unprecedented observations of the Mars Advanced Radar for

Subsurface and Ionospheric Sounding (MARSIS) instrument,

onboard the European Space Agencys Mars Express orbiter

[30] [34] [20]. MARSIS has demonstrated its capability to

detect structures and layers beneath the Martian surface. In

particular, it provided a low-resolution map of the base of the

Polar Layered Deposits, penetrating up to 3.7km the ice-rich upper layer of Martian South cap. Ground penetrating

radar appears as a unique tool in planetary research to exploredeep surbsurface. Other methods of investigation such as active

seismic measurements, in spite of their extremely high interest,

require large resources and a heavy operational logistics.

MARSIS results allow to predict that TAPIR which operates in

the same frequency range but from the surface and can perform

a larger number of coherent additions will be able to reach

deeper burried Martian structures. RANETA results also promp

our expectations of the usefulness of such an instrument on

board of a future mission to Europa. This Jovian satellite might

hide a water ocean under an icy crust and ground penetrating

radar soundings would be of very high interest.


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ACKNOWLEDGMENT

The authors would like to thank IPEV (Institut Paul-Emile

Victor) who was in charge of the organization of the RANETA

campaign and CNES for funding the development of the radar

under grants 793/CNES/99/7947 and 737/CNES/00/826. We

are very grateful to S.A. Arcone for his constructive review.

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Alice Le Gall graduated in radio-communicationand electronic engineering from the Ecole SuprieuredElectricit (SUPELEC). She received in 2004 the"Astrophysics and Astronomy" DEA degree from theUniversity Paris Diderot (Paris 7), France. She iscurrently pursuing a Ph.D. degree in planetary sub-surface exploration by ground penetrating radar fromthe Centre dEtude des Environnements Terrestre etPlantaires (CETP-IPSL).


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Valrie Ciarletti graduated in engineering degreefrom the Ecole Centrale de Paris in 1984 and re-ceived, in 1989, a Ph.D. degree from the UniversityParis 6, France. Since 1990, she has been an asso-ciate professor at Paris 13 university in the field oftelecommunication engineering. In 1993, her field ofinterest turned to microwave remote sensing (GroundPenetrating Radars and Radars devoted to surfaceremote sensing) She was involved as the deputyPI in the NetLander GPR project and is PI of the

WISDOM and EISS experiments proposed on theExoMars mission.

Jean-Jacques Berthelier graduated from Ecole

Polytechnique in 1961. He has been active in spacephysics since 1965 starting with studies of the polarionosphere with rocket experiments. He was involvedas a PI or CoPI in several space projects to measurethe dynamics of the terrestrial, cometary or plane-tary plasmas and plasma waves. He has also beenactive in the field of atmospheric electricity bothon Earth and on future planetary missions. Fromhis own experience in works measurements in spacehe became interested by ground penetrating radar

and subsurface propagation being the PI of the ill-fated NetLander mission.He is presently CoPI of the WISDOM, EISS GPR experiments and ARESexperiment on ExoMars.

Alain Reineix graduated from the University ofLimoges (France). In 1986, he received a PhD inElectronic and Communications from the IRCOMlaboratory of Limoges. He joined the CNRS, firstas a researcher, then as a Professor. Since 2000, hehas been the head of the Electromagnetic Diffraction(DEM) Team of the XLim laboratory (formerlythe IRCOM). He was the first to introduce timedomain methods (FDTD approach) in radar cross-section computation of complex structures aroundtheir resonant frequencies and in the modelling of

photoconductors for switching energy or generating short pulses.

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