419
LABORATORY IllEASUREIVENTS OF ATTENUATION IN ROCKS
AT ULTRASONIC FREQUENCIES
by
Christophe Gonguet, Karl B. Coyner and M. Nafi Toksoz
Earth Resources Laboratory
Department of Earth, Atmospheric and Planetary Sciences
Massachusetts Institute of Technology
Cambridge, MA 02139
ABSTRACT
The spectral ratio method is used to calculate the quaiity factor (0) in porous
rock samples at ultrasonic frequencies (0.3 - 1.5 MHz). The data were ccllected
using the pulse transmissicn technique with aluminum used as a high 0 standard. The
data set ccnsists of dry, water and benzene saturated rocks at differentia!
pressures from zero to one kilobar. Two sandstones, Berea and Kayenta, Bedfcrd
limestone, and Webatuck dolomite are studied. Water and benzene were chosen as
pore fluid saturants to contrast the effects of two different pore fluids (density,
compressibility, viscosity, dielectric constant, and wetting properties) at ultrasonic
frequencies. The main features observed are: 1) The quality factor 0 increases with
increasing confining pressure; at low pressures the rate of increase is larger. 2) 0
for saturated samples is generally lower than for dry samples. 3) The introduction of
a fluid saturant into a dry rock increases S-wave attenuation more than P-wave
attenuation. 4) In general, given the measurement error and the fact that these
results are preliminary, the differences in attenuation between the two fluid
saturations, water and benzene, are not large. Nevertheless, we observe that
benzene-saturated attenuations are slightly higher than water-saturated vaiues,
particularly at lower pressures (less than 500 bars) for the P-wave.
INTRODUCTION
The contribution of pore fluid to attenuation in rocks has been a subject of
interest and intensive study (Bulau et al., 1984; Murphy, 1982; Spencer, 1981;
Winkler and Nur, 1979; Mavko and Nur, 1979; Johnston et al., 1979; Johnston and
Toksoz, 1980; O'Connell and Budiansky, 1977; Biot, 1956a,b; Wyllie et al., 1962).
Pore fluid can contribute to attenuation in many ways: inertial decoupling,
pressure induced flow; viscoelastic relaxation; local flow between adjacent pores
("squirt flow"); and wetting of grain surfaces that can contribute to chemical and
physical attenuation mechanisms. Although these mechanisms have been studied
extensively, neither the experimental data nor the theoretical studies have been
able to determine quantitatively the relative significance of different mechanisms
(see summary in ToksQZ and Johnston, 1981). Attenuation in fully or partially
saturated rocks is greater than attenuation in dry rocks. For dry rocks, attenuation
(Q-1) varies by orders of magnitude whether the rock is "air dry" (containing at least
a monolayer of water) or totally outgassed by high-vacuum and thermal pulsing
420
Gonguet et aI.
(Pandit and King, 1979; Clark et al., 1980). These data confirm the role of water on
the scale of monolayer thicknesses.
Going from air-dry to fully fluid saturated case, attenuation increases (Johnston
et al., 1980; Toksoz et al., 1979; Winkler and Nur, 1979). The largest effect of
saturation occurs in Qs' In the air-dry case Qp '" Qs and, in fully saturated case
Qs < Qp' Partial saturation may reduce Qp relative to full saturation, but this effect
is generally small (Winkler and Nur, 1979; Johnston and Toksoz, 1980; Frisillo and
Stewart, 1 980).
There is little experimental data on attenuation with fluids other than water and
brine. Wyllie et al., (1962) measured resonant bar attenuation in alundum rods (25%
porosity) saturated with soltrol and water and found that attenuation was lower with
soltrol saturation. Nur and Simmons (1969) measured the relative change in
ultrasonic signal amplitudes transmitted through glycerin- and water-saturated Barre
granite as a function of temperature and conciuded that a resonant peak existed as
a function of fluid viscosity. Spencer (1981) measured the iow-frequency phase-lag
between stress and strain in Navajo sandstone with a sequence of differen.t fluids
and correlated increasing attenuation with larger reductions in surface free energy uf
silica when immersed in the various fluids, with water being the highest. Bulau et al.,
1984, measured resonant bar attenuation with water and iso-octane and noted that
attenuation with water was higher.
To evaluate whether water versus another type of liquid pore fluid affects
ultrasonic attenuation significantly, we made a systematic study of the dynamic bulk
and shear moduli, (K, j1.), and the quality factors, Qp and Qs' in dry, water- and
benzene-saturated rock samples. Measurements are made over a hydrostatic
confining pressure range up to 1 kbar. Rock samples include sandstones (Berea and
Kayenta), a limestone (Bedford) and a doiomite (Webatuck). The measurements are
made at uitrasonic frequencies (200-1500 kHz).
The effects of water versus benzene on P- and S-wave velocities and dynamic
and shear moduli are discussed elsewhere In this report (Coyner and Cheng). In
short, the differences between velocity measurements with benzene and water are
not easily interpreted strictly on the basis of density, compressibility, or viscosity
differences. At low pressures water- saturated P- and S-wave velocities are higher
than benzene-saturated values. At high pressures (greater than about 300 to 500
bars) in the sandstones the water-saturated velocities tend to fall below the
benzene-saturated values. Conversion of velocities into dynamic shear and bulk
moduli as a function of pressure indicates that the effect is concentrated in the
shear modulus. Water-saturated bulk moduli are consistently higher than benzenesaturated values while water-saturated shear moduli, initially slightly higher at low
pressures, fall below benzene-saturated values and even the dry shear moduli at
higher pressures. In this paper a portion of the signal waveforms collected by Coyner
(1984) were analyzed for p- and S-wave ultrasonic attenuation with the hope that a
similar effect would be measured. Contrary to what was expected, benzenesaturated attenuation is higher than with water, particulariy at low pressures for the
P-wave. At high pressures water-saturated attenuation tends to be slightly higher
although the amount is on the order of experimental error.
Attenuation Measurements
. 421
ATTENUATION MEASUREMENTS
In this study we determine attenuation of p- and S-waves using ultrasonic
pulse transmission and the spectral ratio method. In this method, a jacketed sample is placed in the pressure vessel with source and receiver transducer attached. The sample is cylindrical, 5.08 cm ( 2 inches) long by 7.62 cm ( 3
inches) diameter. The source and receiver piezoelectric crystals are contained
within a titanium alloy housing. Details can be found in Coyner (1984).
Ultrasonic P- and S-wave signals are propagated through cylindrical cores or
rock. An aluminum cylinder, same size as the sample, is used as a high-Q standard for
calculation of the spectral ratio. Center frequencies of the signals are approximately
400 to 850 KHz depending on pressure and sampie. Temperatures are laboratory
ambient. Confining pressures are systematically cycled up to levels of 1000 bars
and pore pressures are either vacuum (20 J.l m Hg) or 100 bars for the benzene and
water saturations. The difference between confining and pore pressures is. taken to
be the "effective" pressure in determining attenuation. Each sample was first
measured vacuum dry over a cycle of confining pressure, then saturated with
benzene reagent (100 bars) and again measured over a cycle of confining pressure.
Samples were then removed from the sample apparatus, soaked and washed with
acetone, and dried for at least 24 hours in a vacuum at 80" C. Next the sample was
rejacketed, measured dry again as a check for repeatability, and then measured over
a cycle of confining pressure after saturating with water at 100 bars pore pressure.
Attenuation values were determined using the spectral ratio technique (Toksiiz
et al., 1979). Specially developed transducers provide broadband P- and S-waves.
Examples of waveforms for dry, benzene- and water-saturated Kayenta sandstone
at 100 bar? are shown in Figure 1 and a fit using the spectral ratio is shown in Figure
2.
The experimental procedures used for both the sample and the aluminum
reference are similar. Therefore, we have relative measurement of attenuation and
such we minimize the effects of the transducer, the coupling between transducer,
titanium holders and the sample. The Q of aluminum is about 150,000 (Zemanek and
RUdnick, 1961) , roughly 3 to 4 orders of magnitude higher than those of rocks in this
study, and is constant with frequency (Savage and Hasegawa, 1967).
For plane waves, wave amplitudes can be expressed as:
(1)
and
(2)
=
=
where A = amplitude, I
frequency, x = distance of propagation, k =2,,1 I v
wavenumber, v = velocity, G(j ,x) is a geometrical factor which includes beam
spreading. Subscripts 1 and 2 refer to the reference and the rock sample
respectively. a(/) is the attenuation factor and related to Q by
.
13-3
Gonguet et aI.
422
(3)
Taking the ratio of amplitudes given by equations (1) and (2) and the natural
logarithm of this ratio gives
(4)
If we assume that a is a linear function of the frequency, i. e. constant Q, then
a(J)=-yf.
(5)
Q=.J!...
(6)
where I' is a constant, and
'lll
We can rewrite (4) as
(7)
The term In(A 11 A 2 ) is the ratio of the spectral amplitudes of the reference to the
sample. The term In(G 11 G2 ) , may be frequency dependent because of beam
spreading.
(8)
A1
G1
where F(f) = In( A )-In( G ). Since Q of the standard is very high, 1'1 can be taken
2
2
equal to O.
For plane waves the geometric factors G1 and G2 have similar frequency
dependence, In( G1 1 G2 ) is independent of frequency. In this experiment the
transducer diameter is 2.5 em (1 inch), and the sample diameter is 7.62 em. As a
result the energy beam spreads and this spreading is dependent on frequency. Seki
et al., (1956) and Papadakis (1975) studied the beam spreading problem for a
cylindrical source. They found that amplitude decrease due to beam spreading is
about 1 db per a 2 1 A, where a. = source diameter and A = wavelength. The beam
spreading correction is highest at lower pressures where velocities are low and
decreases with increasing velocity. Correction to Q due to spreading is always less
than 10 percent and generally within the limits of error. For the preliminary
attenuation values in this paper diffraction corrections have not been made. In the
analysis of data P- and S-wave pulses are selected visually. The duration of pulses
is between 4 and 5 microseconds and in the average correspond to 450 digital
samples. The window is tapered by a cosine window (over 10 time samples at each
end) and Fourier transformed. The natural log of the amplitude ratios are computed
13-4
Attenuation Measurements
423
versus frequency. Attenuation constant, 7 , is determined over the frequency
interval where both the sample and reference spectra have adequate power (i.e.
when signal to noise ratio is high). An example of spectra, the ratio, and frequency
window over which a least squares linear fit is made are shown in Figure 2. The data
quality is good for all samples.
RESULTS
The four samples for which a values are determined include Kayenta (p=23.1 %)
and Berea (p=17.8%) sandstones, Bedford limestone (p=11.9%), and Webatuck
dolomite (p=0.5%) Sample descriptions for all but the Webatuck dolomite are given at
in the Appendix of the paper by Coyner and Cheng elsewhere in this report.
Webatuck dolomite is a foliated metamorphic dolomite. The properties of the
saturating fluids are given in Table I.
In Figure 3 is plotted the calculated P- and S-wave attenuation (1000/0) for
dry, benzene-, and water-saturated Kayenta sandstone as a function of the
difference between confining and pore fluid pressure. Fluid-saturation increases
attenuation for both P- and S-waves. The increase in S-wave attenuation is
proportionally larger, however, especially at higher pressures. Attenuation in the
benzene saturated sample is higher than for the water saturated case for both the
P- and S-waves except at higher pressures (greater than 400 bars) for the Swaves. Attenuation of the P-waves in the benzene-saturated sample is greater than
that of the S-waves, particularly at lower pressures (less than about 300 bars).
In order to separate the P-wave attenuation into bulk and shear attenuation
(Spencer, 1979) we-calculated QE and QK using observed Qp' Qs' and Poisson's
ratio v from the velocity data.
Q _
(1+v)
E- (1-v)(1-2v) 2v(2-v)
Qp
+ =:'':::Qs:''''':''<''''
Q _
(1+v)
K 3(1-v) 2(1-2v)
Qp
(9)
(10)
Qs
with
v=
vfi-2v§
2Cvp-v§)
(11 )
The calculated bulk and extensional attenuations versus pressure are shown in Fig.
4. These again show that benzene-saturated rock has the highest attenuation. For
bulk attenuation the benzene-saturated values are approximately twice as large as
the water-saturated vaiues which are in turn slightly larger than dry.
In Figure 5 is plotted the P- and S-wave attenuations for the dry, benzene-, and
water-saturated Berea sandstone as a function of confining pressure. In Figure 6 is
13-5
424
Gonguet et aI.
plotted the bulk and extensional attenuations versus pressure. Compared with the
Kayenta sandstone, attenuations are lower and the difference between benzeneand water-saturated attenuation smaller. At lower pressures P-wave attenuation for
benzene-saturated Berea sandstone is higher than the water-saturated case whiie
S-wave attenuation is only slightly higher at the first two data points. At higher
pressures water-saturated attenuation is slightly larger than for benzene for both Pand S-waves. Benzene-saturated bulk attenuation (Figure 6) is larger than for the
water-saturated case. Compared with the Kayenta sandstone water-saturated bulk
attenuation Is proportionally greater than the dry.
In Figure 7 is plotted the P- and S-wave attenuations for the dry, benzene-, and
water-saturated Bedford limestone as a function of confining pressure. In Figure 8 is
plotted the bulk and extensional attenuations versus pressure. Compared with either
of the sandstones the effects of fluid saturation are much less. Benzene-saturated
attenuation is only slightly higher than water-saturated for the S-wave and for the
P-wave at low pressures.
The important observation in this data is that benzene-saturated attenuation is
often higher than in the water-saturated sample, particularly for the P-wave at lower
pressures. The reduction of water-saturated shear modulus so apparent in the
velocity data for the sandstones is not strongly reflected in the shear attenuation.
This contrasts with the resonant-bar results of Bulau et al (1984), where attenuation
for iso-octane saturated Coconino sandstone was found to be lower than for the
water-saturated sample. An important point to consider is the relative wetting
characteristics of benzene versus water on silicate and carbonate surfaces. Even
though the standard precautions were taken to ensure complete saturation (vacuum
drawn on one end of the sample while fluid saturant introduced at the other end; pore
fluid pressure at 100 bars) it is possible that benzene did not fully penetrate and
wet the small pore and cracks of the sample, partlculariy the clay-rich Kayenta
sandstone in going from a vacuum dry to fully saturated condition. Therefore an
attenuation mechanism which depends on partial-saturation (Mavko and Nur, 1979)
may be present. This may explain the higher P-wave attenuation but not the higher
S-wave attenuation, which has not been observed in partially-saturated rock at
ultrasonic frequencies (Spencer, 1979; Johnston, 1978).
Finally, we consider dry and benzene-saturated attenuation data for Webatuck
dolomite (Figures 9 and 10). Velocity and strain data for this rock indicate that
cracks are dominant in the porosity distribution. Because of the abundance of fine
cracks attenuation decreases rapidly with increasing pressure and reaches very low
values at high pressures. P-wave attenuation in the dry rock is higher than in the
benzene-saturated rock while the opposite is true for the S-wave attenuation at low
pressures (less than about 150 bars). The iower P-wave and bulk attenuation in the
benzene-saturated rock may reflect unrelaxed stresses in the fluid at ultrasonic
frequencies (O'Connell and Budiansky, 1977; Murphy, 1982). Crack geometry and
surface interactions between water and matrix minerals (silica, feldspar and clay
versus carbonates) apparently play an important role.
CONCLUSIONS
Our preliminary measurements of ultrasonic attenuation for several rocks as a
function of pressure for vacuum dry, water and benzene saturated conditions confirm
previous observations while raising questions concerning water versus non-aqueous
13-6
Attenuation Measurements
425
pore fluid saturants. Our observations show that for the Kayenta and Berea
sandstones, benzene-saturated attenuation, in particular for P-wave, is larger than
water-saturated attenuation. For the S-wave the same relationship holds although
the differences are less. In addition, as pressure increases the differences
decrease. Crack geometry and surface interactions between water and matrix
minerals (quartz, feldspar, clay, and carbonates) may play an important role in how
fluids affect attenuation. Speculations on relative significance of different
mechanisms on attenuation must await in depth analysis of all results, including data
from other rocks.
Table 1
Comparison of water and benzene properties:
I
I
benzene
unit
density
viscosity
bulk modulus
glcc
centipoises
kbar
13-7
.88
.602
12.1
water
1.00
1.002
22.3
426
Gonguet et a1.
REFERENCES
Biot, M.A., 1956a, Theory of elastic waves in a fluid-saturated porous solid. I., J.
Acoust. Soc. Am., 28, 168-178.
Biot, M.A., 1956b, Theory of elastic waves in a fluid-saturated porous solid. II. J.
Acoust. Soc. Am., 28, 179-191.
Bulau, J.R., Tittmann, B.R., and Abdel-Gawad, M., 1984, Modulus and attenuation in
sandstone with hydrocarbon and aqueous pore fluids: Presented at the 54th
Annual SEG Meeting, Atlanta.
Clark, V.A., Spencer, T.W., Tittmann, B.R., Ahlberg, LA., and Coombe, LT., 1980, Effect
of volatiles on attenuation CQsu -0 and velocity in sedimentary rocks: J.
Geophys. Res., 85, 5190-5198.
Coyner, K.B., 1984, Effects of stress, pore pressure, and pore fluids on bulk strain,
velocity, and permeability in rocks: Ph.D. thesis, M.I.T.
Coyner, K.B., and Cheng, C.H., 1984, New laboratory measurements of seismic
velocities in porous rocks: Presented at the 54th Annual SEG Meeting, Atlanta.
Devaney, A.J., Levine, H., Plona, T., 1982, Attenuation to scattering of ultrasonic
compressional waves in granular media: ch.8 in Elastic wave scattering and
propagation by Varadan V.K. and V.V., Ann Harbor Sc.
Johnston, D.H., and Toksoz, M.N., 1980, Ultrasonic P and S wave attenuation in dry and
saturated rocks under pressure: J. Geophys. Res., 85, 925-936.
Mavko, G.M., and Nur, A., 1979, Wave attenuation in partially saturated rocks:
Geophysics, 44, 161-174.
Murphy, W.F., III, 1982, Effects of microstructure and pore fluids on the acoustic
properties of granular sedimentary materials: Ph.D. thesis, Stanford Univ.
O'Connell, R.J., and Budiansky, B., 1977, Viscoelastic properties of fluid- saturated
cracked solids: J. Geophys. Res., 82, 5719-5735.
Pandit, B.I., and King, M.S., 1979, The variation of elastic wave velocities and quality
factor of a sandstone with moisture content: Can. J. Earth Sci., 16,2187-2195.
Papadakis, E.P., 1975, Ultrasonic diffraction from single apertures with application to
pulse measurements and crystal physics: in Physical Acoustics, vol. 11, Academic
press, New York, 151 -211
Savage, J.C. and Hasegawa, H.S., 1967, Evidence for a linear attenuation mechanism:
Geophysics, 6, 1003-1014
Seki, H., 1 956, Diffraction effects in the ultrasonic field of a piston source and their
importance in the accurate measurement of attenuation: J. Acoust. Soc. Am., 282,230-238
Spencer, J.W., 1979, Bulk and shear attenuation in Berea sandstone: the effects of
pore fluids, J. Geophys. Res., 84, 7521-7523.
13-8
Attenuation Measurements
Spencer, J.W., 1981, Stress relaxations at low frequencies in fluid-saturated rocks attenuation and modulus dispersion: J. Geophys. Res., 86, 1803-1812.
Toksoz, M.N., Johnston, D.H., and Timur, A., 1979, Attenuation of seismic waves in dry
and saturated rocks: 1. Laboratory measurements: Geophysics, 44, 681-690.
Toksoz,M.N., and Johnston, D.H., Ed., 1981, Seismic Wave Attenuation, SEG Geophysics
reprint series, No.2.
Winkler, K.W., and Nur, A., 1979, Pore fluids and seismic attenuation in rocks, Geophys.
Res. Lett., 6, 1-4, 1979.
Winkler, K.W., and Plona, T.J., 1982, Technique for measuring ultrasonic velocity and
attenuation spectra in rocks under pressure: J. Geophys. Res., 87, 1077610780.
Zemanek, J., Jr., and RUdnick, I., 1961, Attenuation and dispersion of elastic waves in
a cylindrical bar: J. Acoust. Soc. Am., 33, 1283-1288
13-9
427
Gonguet et aI.
428
KAYEm'A SANJSTOt£
u
..,-----------,
dry P-wave
.. ..,---,--=-------------...,
...
..•
~
4===::::::=----\---,~-+--"7L..__\
... ...j===---=--f--!--+-----''=-=:
..
..
~
... -,-------,----------, ..• .-------:::----------,
water sat. P-wave
water sat $-wave
...
...
~ '.1
-J.-==::::....----I,---i---l,---r::::::::=::,-..,J ...
"..
>
-j---=-r---";'~~==-:
."..
1J.l .... t
~
..
Q
Q
...
~ ••• i1 +,....,~.,...+-~-h-~~.,....,-r,....,+~-.,...,
:£
..• -,----------------- ... -,----------------benzene sat. S-wave
benzene sat. P-wave
...
..' -j---=,..L----.::,"'==""--
.... 1
--
TIME }Jsec
T!ME psec
Figure 1. p- and S-wave signals transmitted through Kayenta sandstune at iOO bars
net confining pressure for dry. benzene-, and water-saturations.
13-10
Attenuation Measurements
429
I~
.
a.
o
a _
I"
,
le(
\
a:
\
:E
\
e(
\
.
..J
\
\
\
\
W
\
cr
\
\
\
• .Z..l
\
\
Sample
\
,,
, ...
,
....
....
...., ....
", ,
,
I
--+-.-.. . . ~-.-+-....,.-.-..,......,.-t-..,.....,::::::;::=::;=-t-I .•
•••
I.'
FREQUENCY (MHz)
1.1
....
'
.....:.;;.'...,.-,.-000\--11
....
a.•
Figure 2. Spectral ratio (long-short dash) with amplitude spectra for aluminum
(dashed Iin"e) and vacuum dry Kayenta sandstone (solid line) at 500 bars conti,ling
pressure.
13-11
Gonguet et aI.
430
o
KAYENTA
SANDSTONE
1511
P WAVE
...o
...oo
o
11313
sa
A
i
g 8
8
8
~
A
A
A
A
a-+--o--+----,--!-.---I!r--r---I
zaa
a
eaa
~aa
saa
PRESSURE, bars
20ar----------------_.-0
Isa1:
!:!
g
~
~
0
laa---+-I
J, A
1
sa-+-i
rl o s~~~~~~~NE
It[
0
BENZENE
WAVE
roo~o
og c 0
WATER oog 0
r.
0
Q
0
0
e
A
~
A
A
A
g
AAA
AAAAA
DRY
A
at-.---j---,---I----.--I--r-~
a
zaa
~aa
eaa
saa
PRESSURE, bars
Figure 3. P- and S-wave attenuation (1 OOO/Q) versus differential pressure for vacuum dry, benzene-, and water-saturated Kayenta sandstone.
13-12
(
Attenuation Measurements
431
KAYENTA SANDSTONE
0
waoo
........
0
0
0
,....
~ ~00
A vacuum dry
0........
o water sat."
0
0
0
0
0
o benzene' sat. ,....
0
lS0
0
300
0
0
100
o 0
o 0
COCb
COCb
a08
cq;gSE}
A
A
90
~,
~AAAAA
€I
c
e
100
A
~~
o
A
Clem
U8G238
ase
508
"lSI
Pressure bars
,
a
5M
Pressure bars
Figure 4. Extensional and bull< attenuation versus differential pressure for vacuum
dry, benzene-, and water-saturated Kayenta sandstone.
13-13
ij
Gonguet et aI.
432
2ea
Pwav•
. BEREA SANDSTONE.
a
"0
0
Isa
0,..,
c::
,g laa
-'"
vacuum dry
0 water foiat.
a benzene sat.
~
<U
o
:::l
c::
<l)
0
00 0
o
sa
0
COo
0
0
Co 0 0
AA
AAA
AAAAA
a
0 g
<:>
9
e
8
0
A A A A A
A
A
A
A
A
i
21313
a
8
41313
saa
eall
pressure bars
2ea
1131311
12aa
S wave
-
-
CJ 1513- - 0
"00
...c::
.-- laa- 0
00
0
<U
Oc
0
:::l
c::
-'"
<l)
sa- '"&:
-
a
a
"'A
vacuum dry
water sat.
benzene sat.
~
0
Cos
0
OS
lJ
Go<:>o~
0
0
AAA
9
9
0
a
0
A
A
'"
t
(
A 6 c'A
'" '" A
,
,
213a
'" '"
I .
I
A
1
I
I
I
4aa
sea
saa
pressure bars
I
laaa
,
12aa
Figure 5. P- and S-wave attenuation versus differential pressure for vacuum dry,
benzene- and water-saturated Berea sandstone.
13-14
Attenuation Measurements
433
BEREA SANDSTONE.
w·...
o.....
o
o
o
,..
::.:: ,...
o.....
Ll vacuum dry
o
o
o
o water sat.
'50
--
Cl
-
,..
benzene sat.
-
-
--
-
75
- 0
-0
-0
-
:0,
"
.'" --<9
5.
-
-'0
-
80g0e
50 - -
-
•
DO
- 0
I
I
AAAAA A A A A
I
I
I
I
I
I
I
....
o -t-r-,..,.,-,.-;--1\-.,.,,.--r-,,.,-I
...
,
5...
Pressure bars.
Pressure bars
Figura 6. Extensional and bulk attenuation versus differentiai pressure for vacuum
dry, benzene-, and water-saturated Berea sandstone.
13-15
Gon Quet et aJ.
434
20a
BEDFORD LIMESTONE
-
a
.....
· a
15e- 1-
-
0
0
0
....
c:
-
.2
o
0
o
4.
a
0
a
000
g
AAAAAo
AA
10e- -
-
°A
i
~ 2
-
a3
2 Ii
-
:::
c:
-
Pway.
5e-
CIS
0
A. vacuum dry
-
a)
o
o· water sat.
·
a benzene sat.
·
I
I
200
0
0
I
,
,
,
I
4013
pressure bars'
2013
S09
-
150- '-
·
0
0
0
·
·
....
c:
-
.-a:!
0
1013- ~oo
·
-
:::
ca)
CIS
S0a
S wave
-
a
.....
,
I
00
A
-
50-
A
vacuum dry
0 water sat.
c benzene sat.
~
0
° 00 000
AAAAAA
0
A
8
A
0
A
8
A
,,I
0
0
2,ea
I
I
0
A
8
A
,
4013
(
2
I
I
6013
S00
pressure bars
Rgure 7. p- and S-wave attenuation versus differential pressure for vacuum dry,
benzene-, and water-saturated Bedford limestone.
13-16
Attenuation Measurements
435
BEDFORD LIMESTONE:
0
Waeo
.....
0
0
0
,...
0 ~- - 0
.....
- 0
0
.:i vacuum dry
o water sat.
- I--
lse
0
0
o benzene· sat.
,...
0 0
AO 0
-"';
-
ISO
'~e
-
-
-
-&3
- 1--0 0 0
1"
0
-
-\
s. -
0
ctq,
AAAA All. OQ
AA~22~
-
•
e
~
oG~6~
I
I
I
- I--
I"
-
a
A
0
so- l -
-
--
I
I
...
I
I
,
...
Pressure bars
,
0
0
...
I
-eo
,
Pressure bar~.
Figure 8. Extensional and bulk attenuation versus differential pressure for vacuum
dry, benzene-, and water-saturated Bedford limestone.
13-17
...
Figure 9. P- and S-wave attenuation versus differential pressure for vacuum dry,
benzene-, and water-saturated Webatuck dolomite.
13-18
Attenuation Measurements
437
WEBATUCK DOLOMITE
OW.e.
.......
~
fl vacuum dry
0
.......
o water sat.
0
0
O
-
o
o
o,..
,..
o benzene sat.
as,
-
- n-
at.
-
.6.
- f-4
A
9JA
-44
-ro A
-
1O, -
f-A
A
aA
aA
-
aA
at - -
Cb~
Cbg
50- ~
a
-a
A
A
°ae e ~ ~ Q
• -+~Ir-~
,,,,,-~
,+-r--r'--'r-.:r--'t'
, ,
,
•
6"
•ot.
Pressure bars
•
A
A
A
~
'hn:tm AA
AAA
aaaaip
, , ,
•
I
e,
~
Q D
I
,
itt
Pressure bars
Figure 10. Extensional and bulk attenuation versus differentiai pressure for vacuum
dry, benzene-, and water-saturated Webatuck doiomite.
13-19
1_
438