IFEI IEU
F_,-IEI -IVSIE5
ELSEVIER
Journal of Applied Geophysics 33 (1995) 77-91
Analysis of GPR data: wave propagation velocity determination
Sylvie Tillard a, Jean-Claude Dubois b
a Direction du Cycle du Combustible, D~partement d'Entreposage et de Stockage des Dgchets (CEA/DCC/DESD),
13108 Saint Paul lez Durance cedex, France
b lnstitut Frangais du P~trole, BP 311, 92506 Rueil Malmaison, France
Received 27 November 1992; accepted 27 December 1993
Abstract
The detection of millimeter-wide discontinuities such as fissures in subsurface geological formations may be possible by
means of GPR soundings, but establishing a law for the electromagnetic wave propagation velocity from field data in order to
interpret radar data and to localize these discontinuities in depth is not easy. In order to optimize the interpretation of such radar
surveys carried out at various sites, we turned our attention to the accuracy by which the electromagnetic wave propagation
velocity may be determined. In a granitic quarry, with the help of a borehole cored 40 m deep, we were able to appraise the
limits of velocity analysis based on normal move-out corrections. We characterized the degree of error caused by slightly dipping
reflectors and we showed the instability of interval velocity calculations caused by uncertainties in reflection time and RMS
velocity assessment. The velocity profile derived from laboratory measurements of dielectric permittivity of the granite samples,
for various depths of cores, proved to be insufficient for an exact mapping of the fissure network. At a limestone quarry site, we
showed that by working on several paths of electromagnetic waves, direct velocity determinations could help in differentiating
rocks in the same formation, based on quality of the field data. Finally, velocities calculated in an anisotropic environment and
in geological formations covered by a road or a concrete surface were analysed. Using data recorded in schists, we obtained an
example of a non-uniform distribution of velocity in the same formation. Using data recorded in sands and in granite, we
demonstrated that a surface material had negligible effect on the determination of the subjacent geological environment velocity.
I. Introduction
Ground penetrating radar is becoming increasingly
successful in geophysics and in civil engineering. Many
effective radar surveys and results are being presented
in highly diverse fields o f application. However, many
users interpret the records using only a superficial
examination of the images to simply specify that an
object has been detected or that a reflector exists. A
depth scale is sometimes indicated but depth uncertainty margins are seldom added. The wave propagation velocity may have been roughly deduced from
dielectric permittivities published in the literature without taking into account the complex nature of this
0926-9851/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved
S S D I 0 9 2 6 - 9 8 5 1 (94)00023-H
parameter in a lossy environment. When the measuring
system allows the transmitting antenna to be physically
isolated from the receiving antenna, wide angle or common mid-point measurements may be carried out to
determine the velocity on the basis of assumed direct
path of the underground wave and then applied to the
whole formation. In the case of a fairly homogeneous
environment such as a granitic block or a salt formation,
this approximation is generally realistic but it provides
only a rough estimate for multilayer terrains having a
variable porosity or variations in water saturation.
To assess the quality of the depth scales usually
indicated, we examined various possibilities o f determining radar velocities. Our aim was to look for any
78
S. Tillard, J.-C. Dubois / Journal (~[Applied Geophysics 33 (1995) 77 91
difficulties inherent in the methods and to define their
limitations. The importance of this survey subject
should not be underestimated since, in the case of positive conclusions about target localization accuracy
based upon improved velocity data, GPR could be considered as a continuous non-destructive prospecting
method, theoretically allowing destructive soundings
and soil samplings to be suppressed (or at least
decreased) for calibrating the surveys with the geological characteristics. In addition, we will also consider
the type of information that can be extracted from the
velocity values in order to help characterize the propagation environment.
In this paper we present measurements carried out in
the laboratory to determine the real and imaginary components of dielectric permittivity of cored rock samples
and we compare these results with radar field data. With
regard to the latter, processing methods borrowed from
seismic data analysis were applied because of the direct
similarity between electromagnetic and acoustic propagation (Tillard, 1991; Dubois, 1992; Fisher et al.,
1992). The advantage of basic processing consisting,
for instance, in spectral analysis and various filtering is
fairly obvious. On the other hand, the use and merits
of velocity analysis remains to be demonstrated with
respect to GPR data.
Most of the data presented in this work were collected with a PC-based, digital radar system ~, in a granitic quarry where we had a 40 m deep cored borehole
at our disposal in order to validate the techniques used
to calculate velocity vs. depth. Other data from experiments performed on limestone, glacial, sandy, and
schistous formations are also studied. With the radar
system used in the measurements, three frequency
ranges centered on 50, 100, and 200 MHz were available. The transmitting antenna was independent from
the receiving antenna in all of the tests.
2. D e t e r m i n a t i o n of a velocity vs. depth law
2. I. Veloci O, analysis
in radar sounding, two kinds of velocity measurements can be carried out depending on whether the
Pulse E K K O IV, manufactured by Sensors and Software, Mississauga. Canada.
antenna offset is fixed or can be raised. Wide angle
( W A ) reflection or common mid-point (CMP) measurements provide the data necessary for calculating
propagation velocity. In the first case, one antenna
remains stationary while the other is moved along the
profile direction. In the second case, both antennas are
simultaneously moved apart on either side of the midpoint of the profile. Below, a review of the equations
governing the wave path for these radar sections are
presented.
In the case of a horizontal reflecting plane in a homogeneous medium, the two-way bistatic traveltime of
the reflected wave can be written as:
x ~ 4h ~
t2 =--4 + t, ~
(1
l, 2
where t is two-way traveltime ( s ) ; x is offset (m) ; h is
mirror depth (m) ; and r is propagation velocity ( m /
s).
For each hyperbola of the form indicated by Eq. 1 ),
a traveltime, A to, is defined by the difference between
the two-way traveltime for a given offset t(x) and the
vertical two-way traveltime at the origin to for x = 0
(normal move-out [NMO] corrections).
At~=t(x)-to=to
+~-
1
(2)
where At~ is the NMO correction (s).
From this relation, when the offsets are small in
comparison with the depth of the refector:
X2
At~,~
(3)
2r2to
In the case of an inclined reflector, if there is no dip
correction, the hyperbola slope overestimates the propagation velocity. In this case, the corrected two-way
traveltime is:
t- = ~ ( x - + 4h- + 4hx sing0
(4)
l!-
and
I/2
(~'/cosq~)-]
(5)
where q~is the dip of the reflector (rad).
In practice, vertical variations of velocity are generally observed. It can be shown that, for an environ-
s. Tillard, J.-C. Dubois / Journal of Applied Geophysics 33 (1995) 77-91
ment made up of several horizontal homogeneous
layers and when the transmitter/receiver offset distance
is small compared with the investigation depth, the
velocity value in Eq. (1), referring to path conditions
which are unknown to us, can be approximated by a
root mean square (RMS) velocity given by:
N
(6)
VZN= ~_, t, v2~/t
where vN is the root mean square velocity between the
surface and the base of layer N, ( m / s ) ; t is the vertical
one-way traveltime from the surface to the base of layer
N (s); tn = vertical one-way traveltime in layer n (s);
and vn wave propagation velocity in layer n ( m / s ) .
RMS velocities are frequently defined in seismic
studies by means of a process called "velocity analysis". This process consists of a computerized move out
correction Atc for a succession of velocity values starting from the slowest up to the fastest likely to be
encountered in the prospected field. By this' 'hyperbola
flattening" technique, we numerically specify the
hyperbola along which the signals corresponding to a
reflection on a particular reflection point are placed. In
other words, in the processed radar section scans, the
correction, Ate, corresponding to the velocity at which
the reflector appears most accurately horizontal, is
sought. If the velocity is too high, the reflector dips
downward; if it is too low, it dips upward.
Having determined the RMS velocities for various
vertical two-way traveltimes, we can use Dix's formula
(Yilmaz, 1988) to calculate the velocity in a given
layer:
t
2
-
V~-- NVN--~-I
ts-ts-i
~2
N--I
(7)
where VNis the interval velocity ( m / s ) ; vN is the RMS
velocity up to the bottom of layer N ( m / s ) ; vN-l is
the RMS velocity up to the bottom of layer N - 1 ( m /
s) ; tN is the vertical two-way traveltime up to the bottom
of layer N (s); and tN_ t is the vertical two-way traveltime up to the bottom of layer N - 1 (s).
For parallel dipping reflectors, the following approximation in Dix's formula is adopted:
2
Vu-
t
my 2m COS2 q~-- tN_
2
i/~N-- I
tN--tu-i
COS2~o
(8)
79
The relations concerning the wave path presented
above involve terrains with elementary planar geometry. Although complex reflection models are generally
necessary in order to develop a practical velocity vs.
depth law, we start by testing the simple cases referred
to here, using data from our radar records. In some
situations, it must be pointed out that we often must
apply the NMO corrections under marginal conditions
because of the low ratio of investigation depths to the
chosen offsets. Indeed, if we take the example of a
granitic environment, our GPR system allows measurements to a 25-30 m depth, whereas the antenna
offset distance may be up to 20 m so as to ensure a
reliable calculation of the direct underground wave
velocity by a simple assessment of the time~listance
curve slope.
The data processing programmes used are borrowed
from GEOMAX or GEOVECTEUR software 2. The programmes imply working with distance and time quantities expressed in meters and milliseconds. Rather than
resample the radar traces, the input parameters are
deliberately distorted. The fictitious correspondence is
as follows: a time sample on a radar record is equal to
1 ms. This detail is noted here only to justify the nonrounded values of frequencies and velocities mentioned
later in the paper.
2.2. Example o f application
Our experimental granitic site presents nearly all the
ideal geological conditions required for the tests
referred to above, since the rock was stratiform: the
quarry was made of a succession of " b e d s " we shall
call, as a first estimate, subhorizontal. In the constant
offset radar records shown in Fig. 1, in which the horizontal and vertical scales are highly disproportionate,
a variable inclination is discernible but it is not very
marked (determined to be 5-15 ° of apparent dip; maximum 20°). The bed thickness increases with depth
(some decimeters at the surface, 2-3 m at - 4 0 m).
Fig. 2 shows a block-diagram of the granite quarry
formation. The beds are limited by joints or fissures of
just a few millimeters. It was possible to locate these
in depth by means of the 40 m cored borehole. Some
of the fissures were very apparent in the radar sections
2CGG registered trade mark; software available at the French
Petroleum Institute,Rueil Malmaison,France.
80
S. Tillard, J.-C. Dubois / Journal of Applied Geophysics 33 (1995) 77 ~)1
Distance fro)
10
20
30
40
10
20
10
16o
~3
E
320
480
Q
®
®
®
26 m
®
(9
4
®,h,"
o
46m
!
|
o
: cored borehole
®
Fig. 1. Constantoffset 100 MHz radar data, recorded in three directionsin a granitequarry.
recorded for all of the offsets and they constitute the
reflectors which are of interest to us in this survey. At
this granitic site, the piezometric level was 8 m deep.
Fig. 3a shows an example of raw data collected in
the field to determine radar propagation velocity. Interfering reflections which preceded the direct under-
S. Tillard, J.-C. Dubois / Journal of Applied Geophysics 33 (1995) 77-91
2
T',o
~
J
15-
~to
Profil 3
Fig. 2. Schematic illustration of the geology of the stratiform granite
experiment site: only the main subhorizontal beds limited by joints
or fissures are plotted.
ground waves were eliminated by operating a " m u t e "
before applying NMO corrections. These reflections
could have been processed but they would make the
operation unnecessarily more complex. In Fig. 3b, an
extract of the NMO corrections is presented: only data
corrected according to the procedure described above
with velocities for the interval 75-162.5 m//xs are
81
shown ( 12.5 m//xs step, eight sections). In this figure,
it can be seen that all the reflection hyperbola picked
up between 80 and 400 ns are not flattened for a unique
velocity value. For the data set in Fig. 3a, the most
interesting sections correspond to the 112.5-125 m//xs
corrections in Fig. 3b.
For the complete process, we extended the velocity
range from 50 to 300 m//xs; 300 m//zs is not a "geological" velocity, it corresponds to radar propagation
in the air. This value was nevertheless tested since, in
some environments, airborne reflections do occur. The
latter are recorded because the dipole antennas of the
EKKO system are not shielded. The technique
described here allows airborne arrivals to be identified
since only these reflections will be correctly flattened
for an NMO correction corresponding to 300 m//xs. If
their arrival times are known, they can then be localized
on constant offset records and therefore they will not
be mistaken for geological events.
As explained above, velocities "calculated" at different depths (or times) lead to a RMS velocity profile
corresponding to a single field acquisition (one frequency, one profile direction). We repeated the operation for the fourteen WA or CMP sections available
at the granite site for the three prospection frequencies
and the three selected profile directions. We thus
obtained fourteen RMS profiles; we then superposed
these profiles to define the RMS velocity law vs. depth
to be used at our experimental site to calculate interval
velocities.
At first sight, the superposition was very disappointing. For the 50-350 ns time interval, a very large discrepancy was noted for velocities in the 100 and 130
m//xs range, and even more exceptionally up to 140 to
150 m//xs. An average law could therefore not be
derived because the uncertainty was too large. Indeed,
in the cores of the borehole drilled in the quarry where
the fissure density was about 1.3 fissures/m, locating
and differentiating fissures which reflected the electromagnetic signal from those which did not on radar
sections could not be achieved if we work with an
uncertainty about + 15 m//xs. This is illustrated by the
following numerical example: if we take a 230 ns twoway traveltime, a 120+ 15 m//xs velocity leads to a
depth between 12.1 and 15.5 m. In order to correctly
calculate interval velocities, analyses must be gathered
according to the elementary parameters we neglected
82
S. Tillard, J.-C. Dubois / Journal of Applied Geophysic.s 33 (1995) 77 9 I
Normal Move Out correction
0
0
I
75
87.5
'
i
0
100
(m/p.s):
112.5
+!
125
137.5
150
162.5
ri
;'
Distance (m)
c!
~9
[...
160
16(]
.,.":. ~ ..,-.4-~ ~
820
320
480
480
(a)
(b)
Fig. 3. (a) CMP 100 MHz radar data recorded in the granite quarry formation. (b) Extract of NMO corrections performed on the data from
(a).
above. We shall begin by studying the frequency contribution.
A priori, no frequency behaviour can be noted when
we compare Fig. 4a, b, and c in which RMS profiles
obtained through NMO corrections are classified
according to the prospection nominal frequencies. The
relative stability of velocity with frequency is confirmed, at least for the direct propagation through the
rock, by calculations of the time-distance slopes read
on sections provided by the spectral analysis of a CMP
data set. Table I gives these slopes for various dominant
frequencies, indicating that there is no regular dependance of velocity on frequency. However, a very weak
dispersion could occur at the lower end of the frequency
range ( 30-60 MHz) because of the slight decrease in
dielectric permittivity we derived from laboratory tests
on vertical core samples. Fig. 5 presents the results of
measurements on dry and water-saturated granite samples. The fact that this dispersion is not discernible in
terms of velocity is justified by referring to the uncertainty range affecting the velocity calculations based
on the slope determination of time-distance curves.
Twenty-eight laboratory measurements carried out
using a coaxial transmission line sample holder
designed to contain centimeter-sized rock samples give
fairly uniform average values of dielectric permittivity
ranging from 6.6 at 30 MHz to 6.0 at 60 MHz (Tillard,
1991). These figures indicate vertical propagation
velocities ranging from 117 to 122 m / ~ s , but the corresponding values derived from the radar sounding sections overlap because of our error bounds. Depending
on the quality of our raw data, the velocity uncertainties
fluctuate from _+2 to _+5 m/~s.
The previously noted velocity profile disparity is
reduced when we separate the results, profile by profile,
by WA measurements and by CMP measurements as
shown in Fig. 6. in contrast to our first assumptions,
velocities vary differently according to the line of measurement and we observed that the W A acquisitions led
to RMS velocities that were systematically lower than
the CMP acquisitions. Because of the different operating principles for the W A and CMP analysis, in the
case of an inclined reflector, the distance h which
appears in the correction formula, i.e. the perpendicular
S. Tillard, J.-C. Dubois / Journal of Applied Geophysics 33 (1995) 77-9l
83
(a)
1601
140[
12o
t%" ..¢~
"
-- ,=--~ - 2
- -6~
,~--.b:::-::.:'--"Q--:,i-- - -:_-__--t
> 100
s'o
lbo
1so
260
2so
36o
3so
400
Two-way travel time (ns)
W
~160
I
(b)
140 I
I
loo I
5'0
1,50
160
2()0
250
300
350
400
Two-way travel time (ns)
• 1601 .
1401
'~' 1201
•
(c)
..A
...-
.--~ :......D......~o
1oo
.........~
1 'o
~
260
2s0
360
3so
Two-way travel time (ns)
Fig. 4. RMS velocities calculated for various directions in the granite quarry, plotted vs. the prospection frequency; (a) 50 MHz; (b) 100 MHz;
(c) 200 MHz.
to the reflector occuring at an offset mid-point, is not a
constant parameter for the WA measurements.
Although we thought it was possible to disregard this
difference, we now conclude that even slight dips have
a disturbing influence. We shall therefore work with
CMP data for which we know that the effect of slight
dips is minimised and partially rectifiable according to
the relation given by Eq. (8).
When we consider uncertainty calculations obtained
using Dix's formula, we can expect a substantial instability of interval velocities both in seismic (Yilmaz,
1988) and radar surveys. Our experiments are no
exception. The sources of error to be taken into account
in the velocity analyses are:
( 1 ) determining the origin time to in Eq. (3), which
may not correspond to the exact top of the hyperbola;
(2) appraising the horizontality of a corrected reflector:
this operation can be in error because of the large discrete 12.5 m//zs scan step chosen for the convenience
in the NMO hyperbola corrections; and (3) working
with large offsets which favour the existence of
reflected-refracted waves or lateral waves at ground
surface (Clough, 1976): they are all parallel to the air
wave but with different delay time and they interfere
with the hyperbola slopes. We do not control this third
source of error which seems difficult to detect.
All of these factors are far from being insignificant.
This is illustrated by Fig. 7. We took into account the
15° dip and we converted two similar RMS velocity
profiles, shown in Fig. 7a, into interval velocities. The
poor quality of our conversion can be noted in Fig. 7b.
We build Fig. 7c from Fig. 7a data by grouping the
terrain layers that provided the most discrepant results
in Fig. 7b. We only considered one layer in the 100200 ns range. We justify this operation by specifying
that if a large uncertainty exists for locating the depth
in time of a layer on a radar record and if it provides
significant interval velocity variations because of the
"instability" of Dix's formula mentioned earlier, this
layer probably reflects only very little electomagnetic
84
S. Tillard, J.-C. Dubois / Journal of Applied Geophysics 33 (1995) 77-91
Table I
Direct underground wave propagation velocity calculated from spectral analyses of Wide Angle data ( granitic quarry ).
Frequency (MHz) Velocity calculated on rawdata
(m/#s)
Filter applied on raw data:
~],f2,f~,f4)"
Velocity calculated on filtered data
(m/p~s)
(MHz)
5(1
117±2
100
117 +2
200
123 _+5
(11,14,17,20)
( !6, 21, 25, 30)
(24, 31, 37, 45)
(36,46,57,67)
(56, 69, 87, 100)
(84, 105, 134, 154)
( 13t, 156, 194, 219)
(27, 35, 42, 50)
(42, 51, 65, 74)
(64, 76, 99, 111)
(97, 112, 126, 141)
( 125, 142, 179, 192)
( 57, 67, 89, 99)
(87, 100, 119, 131)
(117,132,164,179 ~
(162, 180, 225,242)
( 224, 244, 302, 322 )
( 300, 325,400, 425 )
'
"
I It) +3
118±2
12t ±2
1i7t4
118±5
120±3
119.+_2
1233-2
124±3
II9±4
'~
121 ~5
119±5
124±5
121 ± 5
I 19 ± 5
'~= frequency.
energy. Therefore, we conclude that it constitutes a
minor velocity discontinuity. As a result, a simple law
7i
®
®
"o
v
20
1oo
5o0
Frequency (MHz)
Fig. 5. Dielectric permittivity measured on a granitic sample: (a) in
the dry state; (b) saturated with demineralized water.
describing velocity vs. depth is indicated. It is plotted
in Fig. 8 (top, continuous line) by taking into account
the remarks generally made in seismics: interval velocities must be used without neglecting the trends read
on R M S profiles.
In Fig. 8 ( t o p ) , we compare the velocity law mentioned above with the velocities calculated, on the one
hand, using the reflector depths read (in time) at the
hole abscissa for constant offset radar sections and, on
the other hand, using the bed thicknesses, measured on
the cores. Fig. 8 ( b o t t o m ) shows, in addition, the laboratory measurements carried out on saturated rock
samples, taken from the peripheral zones of the fissures;
the permittivity values have been converted into propagation velocity. W e can draw two conclusions from
these comparisons:
(1) Although the permittivity measurements are
reliable for the characterization of different rock samples since we observe, for instance, a C R I M 3 behaviour
for dielectric permittivity vs. porosity (Shen, 1985;
Coutanceau, 1989; Tillard, 1991 ), they are not sufficient to account for global variations of velocity vs.
~Complex Refractive Index Method.
S. Tillard, J.-C. Dubois / Journal of Applied Geophysics 33 (1995) 77-91
85
Profile
160
~
140
.Z'
"~ 120
m tlXl
fie
800
L
I
50
1O0
I
L
I
150
200
250
Two-way travel time (ns)
I
300
3so
400
Profile 2
160
E
.Z,
•~
_o
140
120
>
O9 100
n'-
8O
0
I 0
I
1 O0
I
I
I
150
200
250
Two-way travel time (ns)
I
300
I
350
400
Fig. 6. RMS velocities calculated for the granite quarry formation on wide angle (11) and common mid-point (O) data for two lines of
measurements.
depth in an environment such as the stratiform granite
at the quarry site. The electrical discontinuities are due
to fissures themselves; the contribution of the fissure
peripheral zones is insignificant. The use of this type
of measurement would be more advantageous in the
case of propagation through two distinct materials.
(2) The velocity law established from the cored
borehole presents large variations shown in Fig. 8
(top). Even if we take into account the fact that variations can be affected by an error in reflector depth read
on the constant offset radar records, and that this error
might be dependent upon the reflection intensity and
upon the density of the surrounding fissures, our velocity analysis derived from RMS velocities clearly does
not allow so many irregularities to occur over such short
vertical distances. Even strong contrasts can be overlooked: this is particularly the case of the decreasing
velocity (35 m//zs) observed at 50 ns which can
account for the existence of a slow guided dispersive
wave appearing on some of our CMP or W A R R sections.
2.3. Discussion
We made a point of repeating field measurements to
make our survey as complete as possible so as to be
able to come to a definite conclusion on velocity analysis. It is important to note that we worked with records
showing several distinct reflection hyperbola which we
sought to very accurately situate in time. Despite these
favourable assumptions, the resulting velocity analyses
are only partially utilizable. Without a borehole to
derive velocity vs. depth directly, extrapolating the
observed surface velocity to the whole massif would
have led, for a 200 ns one-way traveltime for instance,
to a 4 m underestimation of the depth. Our velocity
analysis reduced this apparent depth error to 2 m, allowing some improved data migration tests as shown in
S. Tillard, J.-C. Dubois /Journal o[Applied Geophysics 33 (1995) 77-91
g6
(a)
loo I
o
if)
rr
1%
s'o
16o
1,~o
26o
Two-waytraveltime (ns)
25o
360
350
(b)
16o~
140 I
loo
r
$
5'o
1so
260
Two-waytravel time (ns)
1~
e-
~
250
360
350
(c)
16o t
.~140 I
• .....
•
|
A. . . . . . . . . . . . . . .
o 120 I
loo
5'0
160
1,50
260
2Ei0
Two-way travel time (ns)
~0
350
Fig. 7. (a) RMS velocities calculated/'or the granite quarry fonr~ation. (b) Interval velocities derived from the RMS velocity profile. ( c ) Interval
velocities derived using two time intervals combined.
°1i
Ol
~o
360
~o
Boo
Two-way travel time (ns)
A 135
.~, 125
o
o 120
11.~
•
AA
&&
s
•
1'0
•
•
~'s
•
A
~
~
30
35
Depth (m)
Fig. 8. Variations of velocity vs. depth in granite quarry formation, O - O = velocities calculated with time depths read on records and with
thicknesses of granitic banks measured on cores; - - = velocity vs. depth law, deduced from interval velocities (cf. Fig. 7c); * = velocity
calculated from laboratory dielectric permittivity values vs. depth.
S. Tillard, J.-C. Dubois/ Journal of Applied Geophysics 33 (1995) 77-91
87
Distance (m)
I0
o
,,
• ;i
20
I ,i'
~!
40
30
I
[
•
i ~
I!
,I
,!'
L
t: ,I
"~
q
~r~3
480
Distance (m)
0
g
1Q
20
40
30
LLt ,IILLL LI Lt,LLIU!JJ,I:I:J iI
0 : v.i? , , : .
,
,
:
i~ ' i!f
, ,
J-
Fig. 9. Migration test ( 100 MHz data) for granite quarry formation.Top: unprocessedrecord; bottom: migrated record.
Fig. 9. Mapping multiple fissures cannot be envisioned
with any accuracy if it is based upon these velocity
data. As a guide, in our case an assessment of the fissure
density gave 1.3 fissures/m in the 0-30 m range. The
type of processing we studied here is not wholly satisfactory, but we do know now that, if it is used, working
with a velocity profile similar to that deduced from the
RMS values is enough to establish a representative
velocity vs. depth profile providing that the antenna
offsets are small in comparison with the reflector depth.
In contrast, because of the strong instability of interval
velocity calculation caused by uncertainties in the
reflection time and RMS velocity assessment, velocity
analysis using Dix's formula is not an advantageous
process.
3. Utilization of direct traveltime arrivals
3.1. Rock differentiation in a limestone formation
Conclusions identical to those given above concerning the efficiency of NMO corrections were deduced
from the use of CMP measurements recorded on two
levels of a limestone quarry, cut into descending
benches. At this site, the limestones are in the form of
horizontal beds, a few meters thick, separated by joints
of a few centimeters thick, generally filled in by decalcification clays; corresponding altered or fissured zones
can measure up to 1 m thick.
Here we shall not be concerned with the accuracy of
determining the depth or thickness of the multiple beds
but rather with the possibility of differentiation by GPR
S. Tillard, J.-C. Dubois /Journal of Applied Geophysics 33 (1995) 77-91
88
Distance (m)
o
Distance (m)
o
"i.
0
to
,
10
.•z - . . .
,,,,,It--...
-
0
s
10
20
"'~Ii
200
2oo
i.-
"
E
.~
20
o
,
200
Distance (m)
.
?
|lill|ltl
....
40O
400
400
:!(a)
Co)
(c)
Fig. 10. Velocity measurements for three geological formations with different electrical properties: ( a ) sand and clay; t b ) limestone; ( c ) ice.
of two kinds of limestone, one oolitic and one comblanchien outcropping, respectively, at benches 1 and
2. Because of the uncertainties previously mentioned
concerning NMO corrections, RMS velocities wilt not
be derived since the variations we are looking for are,
a priori, slight if we consider the results provided by
electric and acoustic loggings ( Dubois, 1992). Instead,
we focus attention on the information to be obtained
from the utilization of the direct wave path.
The CMP profiles recorded on benches 1 and 2 of
the quarry give surface velocities of 77 + 4 and 85 __+4
m//xs, respectively. According to measurements of the
rock dielectric permittivity, if the difference of 8 m//zs
between these layers is real and not attributable to
measurement uncertainties, there is an apparently
larger porosity for the comblanchien limestone than for
the oolitic limestone. It therefore seems possible to
apply this test to limestone differentiation.
To check this point, we used a rough simulation of
a vertical seismic profile performed on the wall separating the two benches. For this purpose, one radar
antenna remained stationary on the top level, 2.5 m
from the edge of the wall, whereas the second antenna
was moved down the wall at 0.5 m intervals. The use
of the oblique wave path on the records thus obtained
yielded an average velocity of 80 m//xs, a velocity
value compatible with the previously given values.
Indeed, if we attributed a propagation velocity of 85
m / ~ s to comblanchien limestone and 77 m//,~s to
oolitic limestone, the path of the radar waves through
4 and 8.5 m of those different limestones, respectively,
results in a two-way traveltime of 315 ns. In the earlier
tests we also found this time to correspond to an average
vertical velocity of 80 m//~s for a total path of 12.5 m.
By means of these tests, we showed that a study of
direct propagation velocity would allow the differentiation, in a same formation, of rocks of similar quality
on the basis of direct velocity measurements. To optimize this work and to specify its accuracy, we should
be able to interpret the velocity discrepancy in terms of
petrophysical parameter (e,g. density, porosity, etc. ),
but these parameters for the two limestones have not
yet been studied.
S. Tillard, J.-C. Dubois / Journal of Applied Geophysics 33 (1995) 77-91
"x x
x
~x
Xx
xXXXX x
z x
Xx x x
xx
KX X x x
XXxx x x
xx
1
XX
.M. '
Xx
3
X Xx ~
x
i
20
100
2OO 30O4O0
Frequency (MHz)
Fig. 11. D i e l e c t r i c p e r m i t t i v i t y m e a s u r e d on s c h i s t s a m p l e s .
+ + + = sample shaped perpendicular to the schistosity, - - = sample shaped parallel to the schistosity.
Although this interpretation is applicable to terrains
favourable to electromagnetic propagation, its practical
use is questionable in electrically conductive formations. Indeed, in this case, even if propagation is possible, it is generally very difficult to carry out CMP
measurements since the antenna radiation pattern is
more directive (Annan et al., 1975), making direct
horizontal propagation measurements difficult. Moreover, slope calculation on steep time--distance curves
tend to have a greater uncertainty.
Applying this methodology to terrains with high
velocities can also raise problems. In this case, the
uncertainty arises from the difficulty encountered in
separating the direct airborne wave from the direct
underground wave. This mainly concerns glaciers in
which the superficial layers are aerated. In an experiment on such a formation, we calculated values that
reached 220 + 20 m / p s . Case history data corresponding to the different propagation velocities mentioned
are shown in Fig. 10.
We have referred to "superficial layers" without
indicating the thickness parameters. In this regard, it is
important to know what portion of terrain may be
affected by direct propagation, since the wavelengths
89
involved in most radar surveys are of the order of one
meter. This question is indirectly addressed in the study
presented below where we investigated whether or not
data recorded on an asphalt road over a sand dune
modified the soundings significantly enough to prevent
the accurate determination of the depth of the piezometric level under the dune ( -- 15 m). The road surface
was made of asphalt, ballast (25 cm), and of a waterdraining synthetic textile coating. CMP measurements
performed at two different locations of the dune on the
road surface provided direct underground wave velocities of 141 ___4 and 139 + 2 m//xs. We then calculated
the depths in time to the fresh water level using data
collected from three available boreholes along the profile resulting in an average vertical velocity of 140 m /
/zs. Because of the satisfactory agreement of the experimental and calculated data, we concluded that there is
a non-quantifiable influence of the superficial asphalt
road layer described above on the velocity parameter.
An identical conclusion was put forward after comparing velocities measured in a granitic formation in a
mine gallery, at a location where the ground was covered by a concrete surface 20 cm thick and where transmission measurements were recorded along the walls
of a pillar.
3.2. Propagation velocity variation in case of
anisotropy
Among the many questions associated with radar
surveys intended to provide geological information, we
note in particular the problem of polarization rotation
of electromagnetic waves in an anisotropic medium. In
a survey relevant to this question (Tillard, 1991), data
were recorded for four relative positions of the transmitter/receiver antennas along the profile (antennas
first both perpendicular then both colinear to the line
of measurement, and finally with the transmitter perpendicular to the receiver, the latter being first colinear
and then perpendicular to the line of measurement). To
simulate intermediate positions (any angle of the
antennas with respect with the line of measurement)
using these four basic configurations, we implemented
software designed by the French Petroleum Institute
for the study of shear wave birefrigency (Alford,
1986).
In such anisotropy tests, we have to appraise attenuation, reflectivity, and velocity variations among the
90
S. Tillard, J.-C. Dubois / Journal ~'Applied Geophysics 33 ( 1995~ 77- 91
Direction of schistosity
_____~R~
105 m
T = Trarmmller
R = Receiver
14 m
R
R
T
Cross-cut
Gallery
Distance (m)
1
to
O,
0
160'
160
320 ~
320,
1
I
lO
i~
[.-,
Fig. 12. 100 MHz transmission data recorded in a cross-cut ( l e f t ) and in a gallery (right) in an underground schist quarry with the antenna
positioned vertically against the walls.
various antenna configurations. In this paper, we report
only the information on the velocity parameter measured in an underground schist quarry. Laboratory measurements illustrating the frequency dependence of both
the real and imaginary components of the dielectric
permittivity of rock samples are shown in Fig. 1 1. We
complete the test with transmission radar data recorded
in a gallery and in a cross-cut, parallel and perpendicular to the schistosity direction, respectively. We
observe that the anisotropy in the schist formation leads
to significant dispersion in the electromagnetic signals
and variations in velocity values that depend on the
schistosity direction considered. The radar records
obtained in the gallery indicate a velocity of 100 + 5
m//xs whereas the velocity in the cross-cut was found
to be 5 0 + 10 m//.ts at a frequency of 100 MHz. The
uncertainties are higher in the case of a wave path
perpendicular to the schistosity because of the higher
attenuation when the electric field is orientated parallel
to the schist lamina as shown in Fig. 12. Despite the
S. Tillard, J.- C. Dubois / Journal of Applied Geophysics 33 (1995) 77-91
large margins of error specified in the velocity values,
the impact of schistosity on the magnitudes of the
velocity values is obvious.
In this paper, the presentation of a few results concerning the effects of anisotropy empasizes the fact that
the attention must be given to the interpretation of radar
experiments carried out at sites where a geometric anisotropy, even slight, is likely to lead to a non-uniform
velocity distribution.
4. Conclusion
By means of the GPR field experiments reported
here, several methods for determining propagation
velocity in geological media have been presented. We
are interested in the velocity because we must quantify
the GPR performance in terms of investigation depth
and reflector localization in the corresponding depth
interval. In addition, the analysis of velocity in terms
of petrophysical parameters will lead to a better knowledge of the propagation environment. The knowledge
thus gained is more representative of the whole formation than that deduced from laboratory measurements of rock samples.
In most cases, determining velocity is not an easy
task and although it is possible to apply seismic migration processing to radar data, establishing a velocity
profile law vs. depth is difficult. We have shown that
only repetitive measurements in the field allowed calculation uncertainties to be reduced, but this procedure
is insufficient to ensure errors of less than 10% when
using velocity analysis with NMO corrections.
91
Finally, it is often difficult to determine the influence
of certain information parameters on the calculated
velocity. However, recording transmission measurements in various geographical directions may help to
improve the wave propagation velocity assessment, and
thus increase the quality of GPR surveys intended to
provide accurate interpretation results.
References
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