2.4. CMP measurements CMPs were recorded in compartment 2, which is
composed of seven horizontal layers of the different materials. The bistatic acquisition device consisted of
two antennas that were moved symmetrically apart from a central point. The resulting data set — CMP
gathers — is composed of a series of scans with the same CMP, and recorded with increasing transmit-
ter–receiver offsets. This measurement configuration is used to estimate velocity variations with depth by
Ž .
applying the appropriate Normal Move Out NMO Ž
corrections to each scan Fisher et al., 1992; Tillard .
and Dubois, 1995; Greaves et al., 1996 . In our case, this operation was repeated so as to obtain 13 differ-
ent CMPs distributed along the x-axis with measure- ments realized for each using 500 MHz antennas
every 0.2 m with offsets ranging from 0.4 to 5 m. Fig. 6a shows an example of a CMP gather. NMO
Ž . analyses were processed using Eq. 6 , giving the
expression of the time correction D t as a function of velocity V and offset x:
1 r2
2
x D t s t 1 y
. 6
Ž .
2 2
ž
V t The appropriate velocity law was then estimated
Ž from the semblance diagram, calculated with Neidel
. and Taner, 1971 :
2
n y1
A t , j
Ž .
Ý
ž
j s0
S t s
. 7
Ž . Ž .
n y1
2
n A t , j
Ž .
Ý
j s0
For each CMP, the corresponding semblance dia- Ž
. Ž .
gram Fig. 6b was calculated from Eq. 7 giving the best velocity law found from the NMO correc-
tions. These velocities were then converted to inter- Ž
. val velocities Fig. 6c according to the Dix equation
Ž .
Dix, 1955 . Depending on the CMP gather, the number of constant velocity layers varies from five
to seven, and depending on the layer considered, the interval velocity ranges from 0.07 to 0.17 m
rns. Lateral velocity variations are observed within lay-
ers. Two principal causes can be proposed, the first involving the processing sequence and essentially
due to errors introduced when picking velocities as maxima of semblance diagrams, and the second re-
lating to lateral velocity variations due to the differ- ential compaction of materials constituting each layer.
In order to image appropriately the monostatic sec- tion recorded in compartment 2, a smoothed velocity
field was computed from previous velocity analyses Ž
. Fig. 6d . A correlation between borehole informa-
Ž .
tion and the migrated section Fig. 6e indicated that most of the reflections are related to dielectric con-
trasts due to lithology. Because the materials in compartment 2 are the
same as those used to fill the other compartments, the CMP averaged velocities and those calculated
from the tomograms or estimated from the 2D pro- files are compared in Table 1.
3. Synthesis and discussion
We shall now compare and discuss the data recorded at the LCPC test site using the different
GPR acquisition techniques and the results obtained from the various types of processing. After a synthe-
sis concerning radar wave penetration, resolution, velocity and attenuation for each sounded material,
we will consider the effective contribution of GPR applied to civil-engineering auscultation.
3.1. On penetration and resolution The GPR profiles in Fig. 4 show reflections from
Ž . the boundaries of the test site P , and some diffrac-
Ž . Ž
. tions from a void D or pipes E1–E9 buried in
compartment 3. The frequency effect of the source is clearly illustrated in terms of penetration and resolu-
tion.
In order to estimate the penetration and resolution of radar waves according to the physical character-
istics of the different compartments, we tried to match observed GPR profiles with those calculated
by forward modeling. The advantage of this method is the full integration of the wave propagation phe-
nomena. The modeling principle, taken from Bitri
Ž .
and Grandjean 1998
and fully presented in the Appendix, is based on upward extrapolation of the
wavefield in the frequency–wavenumber domain by using a phase-shift technique. The medium parame-
ters are explicitly introduced in the numerical grid as the relative permittivity:
´ K
s ,
´
void
and the quality factor: 1
v´
X
v
Ž .
Q s
s ,
Y
tan d s q v´
v
Ž .
Ž .
taken as the reverse of the loss tangent Bano, 1996 . It was demonstrated in these studies that the medium
parameters are respectively associated to propagation parameters, namely velocity, attenuation and wave
dispersion. As suggested by Turner and Siggins Ž
. 1994 , the approximation of a constant Q attenua-
tion model leads to consider the Q values as valid only in a restricted frequency bandwidth. Conse-
quently, identical models calculated with very differ- ent frequency bandwidths should not be comparable.
A trial and error match of the modeled and observed sections was performed to estimate these quantities
characterizing the materials composing the site. The position and nature of the buried objects was known
and imposed in these models. The section presented in Fig. 4c was modeled
according to the dielectric models presented in Fig. 7a and b; the corresponding synthetic section is
presented in Fig. 7c. The dielectric models were adjusted so that the curvature of the hyperbolas and
the limit of GPR signal penetration respected Fig. 4c, indicating a good estimation of the wave velocity
and attenuation. This procedure was repeated for all the GPR profiles. The values of the K and Q
parameters attributed to the different media of the compartments, and the related parameters for the
extreme 300 and 900 MHz frequencies are presented in Table 1.
The response to the heterogeneities also merits analysis because this depends on resolution com-
pared to size. When objects are sufficiently large Ž
. compared to wavelength e.g. blocks, voids, etc. ,
their interpretation is facilitated because the reflected signal contains complete information about their
Ž . Ž .
Fig. 7. Relative permittivity a , and Q factor distribution b used to model the 2D 500 MHz GPR profile recorded in compartment 3 Ž
. Ž .
compare with Fig. 3c , and the computed synthetic section c . The method for estimating velocity from hyperbola curvature and the limit Ž
of penetration are indicated. P s pit limit reflection; D s void diffraction; E1–E9 s diffraction of three sets of pipes E1–E4–E7,
. E2–E5–E8, and E3–E6–E9 made respectively of iron, PVC filled with water, and PVC filled with air.
shape. On the contrary, when objects are too small compared to wavelength, they are difficult to identify
because diffraction phenomena occur, causing com- plex interactions between the wave and the objects.
Consequently, no major difference was observed be- tween the GPR signature for the cables and the small
pipes, except for the pipe containing water. In this
Ž .
case Fig. 4c , pipe diameter is 4 cm, with pipe E1 made of metal iron and pipes E2 and E3 made of
PVC containing water and air, respectively. The GPR responses to pipes E1 and E2 show one and
two hyperbolas, respectively. For E1, the observed signal represents diffraction of the wave on the
metallic pipe, whereas for E2, echoes from the top and bottom of the pipe are observed, which occurs
Ž .
when the medium inside the pipe water in this case has a sufficiently low velocity to separate the two
echoes of the returned signal. In comparison, the signal of pipe E3 containing air shows a different
pattern because the velocity through air is higher, thus rendering the two echoes mixed and indis-
cernible.
3.2. On Õelocity and attenuation The velocity values obtained from surface–bore-
hole tomography, 2D profiling and CMP analysis are summarized in Table 1. For each compartment of the
site, the deviation between the velocity values esti- mated from the three considered techniques is only a
few centimeters per nanosecond, which indicates coherent results and a good reliability for each
method. However, local heterogeneities in the medium can produce a dispersion of the attenuation
and velocity values, leading to some difficulties in recovering the main structures. For example, Fig. 6d
and e shows the complexity involved in correlating the information derived from interval velocity curves
with the a piori known velocity layers. The high
Ž .
velocity value 0.15–0.17 m rns observed for com-
partment 4 using the different techniques could be explained by the high porosity of the gneiss at B
14 r20 mm. The effective characteristics of this ma-
terial, considered as a mixture of bulk rock and air, can be approached by a simple Lichtenecker’s law
Ž .
Olhoeft, 1980 : K
s K
x
1
K
x
2
. . . K
x
i
8
Ž .
1 2
i
where K is the effective permittivity, and K and
i
x the permittivity and volume fraction of the ith
i
medium, respectively. Assuming that bulk gneiss Ž
permittivity is that of compartment 5 6.9 — gneiss .
at B 0 r20 mm and thus low porosity , that air
Ž permittivity is 1, and that K
s 3 i.e. the permittiv- .
Ž . ity measured in compartment 4 , Eq. 8 gives a
porosity for compartment 4 of about 0.3, which is in good agreement with the sample measurements.
On the contrary, the values of attenuation factor estimated from the attenuation tomography and 2D
profiling show a higher disparity, insofar as the former are systematically lower than that latter. Be-
cause the surface–borehole and 2D surface surveys
Ž .
were carried out respectively with low 100 MHz Ž
. and high 300, 500 and 900 MHz antennas, this
disparity could result to the approximation intro- Ž
duced in the constant Q attenuation model Turner .
and Siggins, 1994 . This model assumes that Q, taken as the slope of the attenuation factor a vs.
frequency, is constant for restricted frequency band- widths, but not for a wide range in frequency, for
example 100 to 900 MHz. The increasing value of Q with frequency observed here has already been de-
Ž .
scribed by Powers and Olhoeft 1994 and Hollender Ž
. and Tillard 1998 . This shows the limitations of the
constant Q model and prevents representation of a material attenuation by a single parameter because it
also depends on the frequency used.
In the case of the LCPC test site, the maximum depth of penetration and resolution vary respectively
from 1 to 5 m and from a few centimeters to 0.25 m, depending on the considered frequency and the di-
electric properties of the medium. The present study has demonstrated the potentiality of three different
GPR techniques when applied to civil-engineering investigations, provided that the appropriate recom-
mendations are respected.
v
When boreholes are available, velocity and at- tenuation tomography is suitable for estimating the
dielectric properties of a medium. Heterogeneities can also be imaged provided that they are larger than
the wavelength. The ray coverage and angular reso- lution used in the reconstruction algorithm must also
be adapted.
v
2D surface profiling is best suited to quickly imaging small diffracted objects such as pipes, voids,
etc. During migration of the GPR sections from time
to depth domain, out-of-plane signals generate arti- facts when the structures are not perfectly cylindri-
cal. For advanced studies, modeling algorithms can be used to estimate dielectric properties of the
medium and heterogeneities.
v
For sub-horizontally layered media, CMP pro- cessing by NMO analysis and semblance diagrams
can be used to recover velocity variations with depth. This technique offers a resolution in relation to the
frequency used. In our case, the 100 MHz signal has too large a wavelength to resolve the velocity layers,
but the velocity distribution found gives a first ap- proximation of the medium properties.
Consequently, the GPR experiments carried out on the LCPC test site led us to consider the different
capabilities of these techniques for civil-engineering sounding applications in urban environments. Al-
though velocity and attenuation distributions can be efficiently recovered by surface–borehole tomogra-
phy, boreholes are generally not available. In this case, velocity distribution with depth can be success-
fully estimated from CMP measurements, provided that the medium is sub-horizontally layered. Monos-
tatic 2D surface profiling is well adapted to quickly locating underground heterogeneities with a rela-
tively high reliability and, provided that control by modeling is carried out, velocity and attenuation data
can be approximately estimated.
4. Conclusion
