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GPR response and FDTD modeling to water and fuel
infiltration in a sand box experiment
by Maksim Bano Maksim.bano_at_eost.u-strasbg.fr Ecole
et Observatoire des Sciences de la Terre (EOST),
5 Rue René Descartes, 67087 Strasbourg FRANCE
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• Outline
• Introduction
• Whats GPR? Effect of the frequency and humidity
  on the GPR data.
• Presentation of GPR experiment in the lab
• Experiment set up, data acquisition, comments on
  the measurements.
• Water content estimation
• Comparison with real water volume injected in the
  box.
• Conclusions on Water Contents
• Influence of the pollution (gasoil) on GPR data
• Data acquisition, results, evolution of the
  pollution and FDTD modeling
• Conclusions and Perspectives on Pollution

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Introduction
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GPR - Ground Penetrating Radar Principe of GPR
Central Unity
Antennae
Lap Top
Wheel
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Acquisition. Common Mid-Point Data
In a Common Mid-Point (CMP) acquisition, antennae
separation is increased about some central point.
CMP Acquisition
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Effect of the frequencies used
GPR images obtained with 50 (rough-terrain
antenna snake) and 250 MHz Antennae,
Finneidfjord Northern Norway
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Effect of the Humidity on GPR data
Dry soil
Humid soil
The same profile acquired with 500 MHz antennae.
a) in May 2006 and b) in October 2008
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Some important points

• Water Content (volumetric)
• ?wVw/Vtotal ?wf.Sw
• Relative dielectric permittivity (dielectric
  constant) ? ? /?0 with ?0 the permittivity of
  the free space. ?water81 dry rocks ? 3-5
  humid rocks ? 6-30.
• Propagation velocity v c / ?1/2 m/ns. c 0,3
  m/ns is the free space velocity.

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Presentation of GPR experiment in the lab
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Experiment set up
0,98 m
2 m
Sand Box
Sand box and injection system
PVC Pipes
Clay cake
Steel pipe
Steel ball
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Data acquisition
Frequencies used 900 and 1200 MHz
Cross section of the sand box with the projection
of the objects.
Plane view of the sand box with measurement grid
and different objects.
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• Four data set of measurements
• Measurements on dry sand
• Measurements with water level at 72 cm depth
  (26 cm thick)
• Measurements with water level at 48 cm depth
  (48 cm thick)
• Measurements after draining

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Results (1)
TA
T0
Steel
P2?
P03
P36
P56
APVC
EPVC
Steel
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Results (2) Central Profile (P36) with different
saturation states
Water level at 72 cm depth
Dry sand
Water level at 48 cm depth
After draining
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Results (3) CMP and constant offset profiles (P1)
with different saturation states
Water level at 48 cm depth
Dry sand
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Results (4) 3D GPR data sets
a)
b)
B
a) dry sand and b) the water level at 48 cm depth
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Estimation of water contents
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Relative dielectric Permittivity The
determination of the average dielectric
constants, for different depth, is performed from
the propagation velocities (?c²/v²)
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Water contents Relationships between water
content ? and relative dielectric permittivity
? Topp Relationship (Topp et al., 1980) ?
-5,3x10-2 2,92x10-2 ? - 5,5x10-4 ?2 4,3x10-6
?3 CRIM Relationship (Mavko et al.,
1998) Hanai-Bruggemann-Sen Relationship
(Hanai, 1968)
et
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Water Quantities The water quantities (in
liters) estimated (in whole box) by using the
previous relationships
Water quantity (liter)
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Variations of water quantities
Estimates of the amounts of water (in liter)
injected in the sand box (for different
saturation cases) as obtained using the Topp,
CRIM and HBS equations. V1 is the amount of water
for the data set with the water table at 72 cm
depth, minus that of the dry sand case V2 is the
amount of water for the data set with the water
table at 48 cm depth, minus the amount of water
for the dry sand case.
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Variations of water quantities
In each case we underestimated the variation in
the amount of water in the sand box using GPR,
but the final results are very close to the
amount of water injected.
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Conclusions on Water Contents GPR is an
effective method to assess and monitor water in
the case of a vadose zone. By repeating the same
GPR measurements over a controlled vadose zone
(sand box experiment), one can compare and
calibrate the water content obtained from GPR
measurements with the actual water content
present in the soil. The water variations are
underestimated (by the three relationships) but
the final results were very close to the amount
of water injected.
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Influence of a pollution (gasoil) on GPR data
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Data acquisition 2nd Experiment After drainage
we let the sand box resting (two months) and
performed measurements in April 2004 (this state
is considered as dry). Measurements with
water level at 72 cm depth (26 cm thick, 240 l)
in may 2004 We injected 100 l of fuel (gasoil)
and repeated measurements in may 2004 and June
2004 .
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Influence of the gasoil (1)
The trace 40
Profile T0 before injection Profile
T0 after injection
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Influence of the gasoil (2)
Two CMPs acquired after fuel injection. a) CMP16
above the steel ball P1 and b) CMP56 above the
steel ball P2. B indicates the reflections from
the bottom.
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Laterally extension of the plume pollution
Travel time of the reflections from the bottom of
the box. a) Before fuel injection
b) After fuel
injection
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Modeling of GPR data by FDTD
0,98 m
Model used for modeling of profile T0 12 days (in
May 2004) after fuel injection.
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Modeling by FDTD
Modeled profile T0
Real profile T0
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Evolution of the pollution in time Profile T0
May 2004
June 2004
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Evolution of the pollution in time profile P56.
May 2004
June 2004
Trace 19
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Modeling of GPR data by FDTD
Model used to follow the evolution of the profile
T0 45 days after injection
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Modeling by FDTD
Profile T0 modeled
Profile T0 real
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Conclusions and Perspectives The GPR data do not
show any clear reflections from the plume
pollution, however GPR velocities are extremely
affected by the presence of the fuel. The
laterally extension of the plume pollution in the
vadose zone is shown by plotting the travel
times of the reflection from the bottom of the
sand box. It seems that pore water has been
replaced by the fuel through a lateral flow by
creating a high saturated zone far from the fuel
injection point. The forward FDTD modeling method
gave theoretical support to explain the origin of
the observed reflections from the contaminated
vadose zone. Perspective To follow the lateral
flow of the plume, a joint GPR and lateral flow
modeling is necessary.
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Thank you for your attention Maksim.bano_at_eost.u-
strasbg.fr