11 - 6
GDS
HEGGY ET AL.: MARTIAN GEOELECTRICAL MODELS
Table 1. Geoelectrical Model for a Shallow Aquifer Associated With Local Geothermalisma
e0
e00
s 10À6, S/m
m
2 MHz
20 MHz
2 MHz
20 MHz
2 MHz
20 MHz
2 MHz
20 MHz
Dust layer
3
2.7
0.25
0.22
28
240
1.5
1.1
Eroded basalt
8
7.2
0.5
0.45
56
500
1
1
Ground ice
7
6.3
0.1
0.0 7
5
12
1
1
Wet basalt
36
32
12
10.5
1344
11724
1
1
a
Similar material can have different dielectric properties as the geophysical conditions (porosity, temperature, grain size) in each layer are different.
Finally for the basalt basement we used a compacted
waveform is a modulated Gaussian vertically polarized,
Djiboutian basalt powder.
with a central frequency of 2 MHz and 2 MHz bandwidth.
The same antenna measures the backscattered electric field
echo E in the two cross polarizations Ex and Ey.
4. Radar Echo Simulation
[21] We mainly considered the backscattered electric field
in the X-directed polarization at the surface for each geo-
[19] The final step in our approach, to monitor the
electrical model. We used the Y-directed component of the
variations in the ability of the 2 MHz sounding radar
backscattered field as an additional information source to
instruments to detect the possible presence of shallow
distinguish between interface signal and simulation noise
subsurface water in the Martian upper crust, is to simulate
for low dynamic ranges (À150 to À200 dB). Simulations
backscattered radar temporal response for each of the
were performed in the time domain to observe reflections at
described sites. We used the Finite Difference Time Domain
each interface and thus evaluate the radar ability to penetrate
(FDTD) technique to solve the Maxwell equations and to
down to the water-saturated layer for each of the volcanic
obtain the magnitude of the backscattered electric field at
model.
each point inside the geoelectrical profile. Few electro-
[22] Figure 5 shows the backscattered radar echo simu-
magnetic methods can be adapted to describe properly the
lated for the four previously described geoelectrical models,
wave propagation in such relatively conductive materials.
at a 2 MHz frequency corresponding to the Netlander GPR
The advantage of the FDTD algorithm is its generality in
characteristics. The results for each site are presented in two
terms of material, geometry and frequency [Kunz and
graphs. The upper graph indicates the losses in decibel
Luebbers, 1993]. The method is a transient marching in
versus the wave round trip time across the geoelectrical
time approach, in which time is divided into small discrete
model. This informs us about the penetration depth corre-
steps [Yee, 1966], and the geoelectrical model is built with
sponding to a given dynamic range. The lower graph shows
elementary cubic cells in the simulation space. Each cell
the X component of the received electric field versus time,
describes the relative permittivity, conductivity and relative
which illustrates the wave reflection at each geological
permeability of the occupied volume. Once excited by the
interface. The dotted lines indicate the location of each
radar pulse, it gives the three-dimensional components of
subsurface interface calculated from the mean wave velocity
the electric and magnetic fields at each time step corre-
inside each layer.
sponding to the wave propagation across the geoelectrical
[23] The top left of Figure 5 (denoted by 2.1) presents the
model. We set the elementary cell dimension to be 5 m, in
simulation of the geoelectrical model of a shallow aquifer
order to get the typical value of 10 cells per wavelength in
associated with local geothermalism shown in Table 1 and
the most conductive material in the profile (excluding the
Figure 1. We can see that the first three thin layers act as a
wet basalt layer), to obtain sufficient temporal accuracy and
single thick layer that absorbs exponentially the radar
respect the algorithm stability conditions. To reduce the
signal. The thickness of the first layers not being important
simulation noise, we used the Perfect Matching Layers
compared to the wavelength inside the material, none of the
(PML) algorithm as an electromagnetic absorbent around
interfaces could been identified on the backscattered echo.
the simulation space.
[20] We simulated for each geoelectrical model presented
Even in the presence of a sufficient dielectric contrast, it is
in Tables 1 to 4 the case of 30 m mono-static monopole
quite difficult to distinguish the second layer from the
antenna in a perfect contact with the surface layer, which
surface response at this frequency. The eroded basalt and
roughly corresponds to an ideal configuration of the Net-
the ground ice interface can be hardily distinguished by the
lander GPR instrument. The emitted pulse is a spherical
mean of the backscattered electric field because of the low
wave with maximum amplitude of 10 V/m. The emitted
dielectric contrast at this interface. We can only note in this
Table 2. Geoelectrical Model for Outwash Plains in the Northern Hemispherea
e0
e00
s 10À6, S/m
m
2 MHz
20 MHz
2 MHz
20 MHz
2 MHz
20 MHz
2 MHz
20 MHz
Dust layer
3
2.7
0.25
0.22
28
240
1.5
1.1
Fluvial sediments
5
4.4
0.5
0.46
56
513
1
1
Lava flow
7
6.2
0.5
0.3
56
335
1.5
1.3
Wet basalt
36
32
12
10.5
1344
11724
1
1
Ground ice
9
8
1
0.6
112
670
1
1
a
Similar material can have different dielectric properties as the geophysical conditions (porosity, temperature, grain size) in each layer are different.