167
ANALYSIS OF FULL WAVEFOIDl ACOUSTIC LOGGING DATA
IN "SOFT" FOIDlATIONS
by
C. Barton. C.R Cheng and lioN. Tolaroz
Earth Resources Laboratory
Department of Earth, Atmospheric. and Planetary Sciences
lIasBachusetta InBtitute of Technology
Cambridge. llA 02139
ABSTRACT
Direct recording ot tormation shear wave travel time is not possible in
"soft" tormations where the shear velocity is lower than the borehole tluid
velocity. The borehole Stoneley wave is quite sensitive to changes in tormation
shear wave properties and may be used to indirectly determine shear velocity.
This paper presents a method to calculate tormation shear velocity through
inversion ot the dispersion equation for the propagation ot borehole Stoneley
waves. The Stoneley wave group velocity and etrective attenuation are also
computed in this data analysis.
INTRODUCTION
The simultaneous measurement of compressional and shear wave velocities
in a borehole Is possible wIth the full wavetorm acoustic logging technique. This
extension ot the conventional sonic log can provide tormation compressional
and shear velocities as well as attenuation. Compressional and shear wave
veloclty data have been extracted from a variety of lithologies with various tool
contlgurations (Paillet, 1980; Cheng and Toksoz, 1981; Ingram et al., 1981; Willis
and Toksoz, 1983). There remain some obvious limitations in the determination
ot tormation properities in certain geologic settings, tor example, thinly
interbedded sediments. highly tractured zones. or, for the case addressed in
this paper. "sott" formations where the shear wave velocities are lower than the
borehole tluid velocity. The borehole shear wave is actually a compressional
wave in the borehole tluid that is converted to an SV wave at the borehole wall.
It is critically refracted into the tormation at this intertace, travels in the
tormation, and is retracted back Into the borehole tluid as a P wave. Critical
refractions of shear waves do not exist in "sort" formations and thus it is
impossible to directly measure the tormation shear velocity in such cases.
Tools with non-axisymmetric sources and receivers have been developed to
excite formation shear waves in "sott" formations (Kitsunezaki. 1980; Zemanek
et Cll.• 1984), however, these are not yet commonly aVailable tor routine logging
operations.
168
Barton et al.
For conventional full waveform acoustic logs, it has been established that
borehole guided waves are qUite sensitive to formation properities (Cheng et a.L.,
1982). Formation shear wave velocities and attenuation appear to have a major
etrect on the propagation of guided waves. The intl.uence of shear velocity and
attenuation on the Stoneley wave is especially pronounced in "sort" sediments
and provides a means of calculating shear formation parameters. Cheng and
Toksoz (1983) presented a study of the intl.uence of formation shear wave
velocity and attenuation on the Stoneley waves in "soft" formations and a
method to determine formation shear wave properties from the Stoneley wave
properties. In this paper, their method is used to determine formation shear
wave velocity and attenuation from full waveform acoustic logging data
obtained in a "soft" formation.
THEORY
(
Velocity Dispersion
The period equation that detl.nes the dispersion characteristics of seismic
wave propagation in an open borehole is given by (Biot, 1952; Cheng et a.L.,
1982):
( 1)
where
(
c2
1
1
L =.1: (1- -)*
= eJ(--)*;
0. 2
c 2 0. 2
c2
1
1
= Col(--)*.
c2
p2 '
c2
1
1
= Col( - -)*;
c e a'j
m =k(1- -)*
p2
If =k(1- - ) *
a'j
(
Col is the angular frequency; c is the phase velocity; k = Coli c is the axial wave
number; a, p, and a/ are the P and S wave velocity of the formation and the
borehole tl.uid velocity, respectively; R is the borehole radius; p and Pf are the
formation and fiuid density; and 1i. and .Ii:; are the moditl.ed Bessel functions of
the i l /\ order. The roots of the period equation as a function of frequency
define the dispersion characteristics of the seismic waves propagating in an
open borehole. For Stone ley waves, the propagation characteristics are detl.ned
by those roots of the period equation that correspond to phase velocities less
than both the formation shear wave velocity and the borehole tl.uid velocity.
There
are
significant
ditrerences
in
full
waveform
acoustic
micro seismograms recorded in "fast" and in "slow" formations. Specifically,
the P wave train appears to be of longer duration, the pseUdo-Rayleigh waves
(or normal mode) no longer exist, and the Stoneley waves are more dispersive
and are shifted to lower frequencies (Cheng and Toksoz, 1983). The dispersion
characteristics of the Stone ley wave in "fast" versus "siow" formations are
7-2
Soft Formations
169
shown in Figure 1. The dispersion curve for Stoneley waves in "fast" formations
(Figure 1a) shows very little' change in velocity with frequency. In "soft"
sediments (Figure 1b) the Stoneley wave is more dispersive. For this particular
set of formation and tluid parameters, the phase and group velocities start at
the tube wave velocity (White, 1983), which is about 0.75 the tluid compressional
velocity and decrease with increasing frequency. Since the frequency of the
Stoneley wave in "soft" formations observed in full waveform acoustic logs is of
the order of 1 to 5 kHz, it is clear that the calculation of shear velocities
through Stoneley wave data in "soft" formations cannot be accomplished using
either a high or low frequency approximation due to these dispersion
characteristics. The frequency of the Stoneley wave must be determined for a
valid analysis.
The Importance of variations in formation and tluid parameters on the
Stoneley wave velocity has been examined in detal! by Cheng and Toksoz (1983).
There is an almost one to one relationship between formation shear wave
velocity and the Stoneley wave phase velocity in a "solt" formation. The
Stoneley wave phase velocity Is seen to increase with increasini formation to
tluid density ratio and to decrease with increasing borehole radius. Changes in
formation compressional wave velocity appear to have relatively little effect on
the Stoneley wave velocity.
Attenuation
The attenuation of the Stoneley wave is a linear sum of the formation and
tluid body wave attenuations multiplied by their respective partition coefficients
(Cheng at cU., 1982). The partition coefficients are the normalized partial
derivatives of the phase velocity of the Stoneley wave with respect to the
formation and tluid body wave velocities. The relative etrects of the formation
and tluid attenuation on the the Stoneley wave attenuation in a "soft"
formation are clearly shown on the plot of the partition coefficients versus
frequency (Figure 2). The effects of the formation shear wave and fluid
attenuation are similar at lower frequencies and the formation shear wave
attenuation has an increasing effect with increasing frequency, becoming the
dominant etrect at higher frequencies. The formation compressional wave
attenuation has very little effect on the Stoneley wave attenuation at all
frequencies.
DATA ANALYSIS
Full waveform data and companion logs from a sandstone sequence that
has a compressional velocity of approximately 10,000 ft/sec were analyzed in
this study. The stratigraphic section used to test the inversion of the
dispersion equation for formation shear velocities includes 300 feet of the data
at an unspecified depth where there is some variation in lithology from sand to
shale (Figure 3). In this paper all depths are referenced to the top of the data
set. A 10 foot shale layer occurs at depth 60 feet and a 25 foot layer at ZOO
feet. Both compressional and shear wave velocities measured in this analysis
may retlect a sensitivity to the associated changes in lithology at these depths.
The tool design for this data is of one source and three receivers at
. distances of 15, 20 and 25 feet. The recording frequency range is from 1 to 25
7-3
(
170
Bartonet aL
kHz. although no significant signal is recorded beyond about 12 kHz. probably
because of attenuation. The recording interval is 5 microseconds/foot. Details
of the tooi are given in Williams st at. (1964). The compressional wave arrival
can be easily traced on the variable density plot (Figure 4) as can the Stoneley
wave arrival. k; expected. there is no distinguishable shear wave arrival.
Figure 4 clearly shows the sensitivity of the Stone ley wave to changes in
lithology. The Stoneley wave essentially disappears at depth 220 feet where
there is a 25 foot layer of shale. This phenomenon could be due to high
formation shear wave attenuation.
(
(
Velocity Determination
Shear wave velocities were determined for this data set by solving the
period equation (Eq. 1) given the compressional velocity and the Stone ley wave
phase velocity as well as certain parameters from the companion logs. The
borehole radius was taken from the caliper log (Figure 5) which indicates the
borehole radius is approximately 4 inches. The formation density was
determined from the compensated density log (Figure 5). The density recorded
for this sandstone varies between 2.0 and 2,3 gms/cc. The borehole fiuid
velocity was assumed constant at 5000 ft/sec. as was the tluid density at 1.1
gms/cc. The formation compressional velocities were measured using the
threshold detection semblance correlation technique developed by Willis and
Toksoz (1963).
A frequency domain analysis was performed between the waveforms
recorded at the tlrst and second receivers and between the second and third
receivers to measure the Stoneley wave phase velocities. The routine developed
to accomplish this analysis windows each waveform around the Stoneley wave to
isolate this pulse from interference from the other wave types recorded on the
trace. A sine taper is applied to the endpoints of the windowed waveform.
Figure 6 shows a typical waveform from this data set and the corresponding
windowed Stoneley wave pulse.
The windowed time series are transformed to obtain the Fourier phase
between the receiver pairs. The resulting phase spectra are then phase
unwrapped through the adaptive integration routine of Tribolet (1977). Figure
7 is a plot of typical power spectra for the windowed portion of the three
receivers. The amplitude spectra for the windowed Stone ley wave pulse is
consistently between 1 and 2.5 kHz. The peak amplitude frequency of the
Stoneley wave is used in the computation of the phase velocity by:
(2)
where f is the frequency. I"r 1 and I"r2 are the unwrapped phase spectra for the
nrst and second receivers. tiz the receiver spacing, and n an arbitrary
constant. The peak amplitude frequency is usually about 1 kHz.
The algorithm developed to perform this velocity analysis also computes
the group velocity of the Stoneley wave through a straight cross correlation
with sync interpolation of the Stone ley waveforms. The optimum lag. or
moveout (tit). between receivers occurs at the highest value of the correlation
7-4
(
(
(
(
Soft Formations
171
coefficient. The group velocity is calculated from:
IJ.z
IJ.t
u:: -
(3)
The phase velocity is computed via Eq. 2 for n::O, 1 and 2. These values are
then tested against the group velocity to isolate the closest value above the
group velocity. This value is considered the Stoneley wave phase velocity for
that depth. Should the test fail to provide a reasonable value the routine
displays the waveforms again so that the window picks may be adjusted and the
phase velocity recalculated.
Etfectift Attenuation
Etrective attenuation or quality factor, Q, values for the Stoneley wave at
each depth were calculated using the spectral ratio method. The log ratio of the
amplitude spectra of the receiver pairs is first determined and Q is given by
(Johnston and Toksoz, 1981):
IJ.z I
Qc([)
1T
(4)
where A.o is the amplitude at the i l /\ receiver, Q the quality factor, and G, the
geometrical spreading factor at the il/\ receiver. Again, the peak amplitude
frequency of the Stoneley wave power spectrum is used for the values of the
frequency for each computation. There is no geometrical spreading in borehole
gulded waves and Eq. 4 is simplified to;
rrllJ.z
Qc([)
(5)
The attenuation or Q of the Stoneley wave as a function of frequency can
be determined from the measured log amplitude ratio using Eq. 5. However, in
order to determine the formation shear wave attenuation or Q" we need to
know the Q of the borehole t1uld. Alternatively, we can determine the Stoneley
wave Q at a number of frequencies, and assuming there is little frequency
dependence of the body wave Q's, we can then solve for the formation shear
wave Q, by a least squares technique. However, in this paper, the t1uld
attenuation was not available, and the Stoneley wave pulse is not broad banded
enough to allow a measurement of its attenuation as a function of frequency.
As a result, only the Stoneley wave Q will be presented and not the formation
shear wave Q,. Assuming that the t1uid attenuation is relatively constant over
the 300 foot interval, the etrective Stoneley wave attenuation should correlate
very well with the ac tual formation shear wave attenuation.
RESULTS
The measured Stoneley wave phase velocities t1uctuate around 3500 ft/sec
for the upper part of the section and are somewhat lower below depth 220 feet
7-5
172
Barton et al.
(Figure 8). The Stoneley wave is difficult to identify between depths 205 and 230
teet and it was necessary to manually window the wavetorms within this depth
interval to obtain the expected low phase velocity values. Figure 8 shows the
phase velocity analysis results ot the Rl/R2 receiver pair depth-corrected to
the R2/R3 receiver pair. There is very good agreement between the separate
computations ot the Stoneley wave phase velocity at each depth. The analysis
successtully measured Stoneley wave phase velocities that are typical ot a sott
sediment.
(
Results ot the Stoneley wave group velocity calculation are very close to,
and show excellent correlation with, the phase velocity determined tor each
depth. These results are theoretically predicted tor Stone ley waves that
propagate at trequencies ot 1.0 kHz. Figure 9 is a depth profile ot the phase and
group velocities determined tor the Rl/R2 .receiver pair.
(
The solution ot the dispersion equation tor tormation shear velocities ot
the RlIR2 receiver pair depth corrected to the R2/R3 receiver pair is shown on
the depth protlle in Figure 10. Again there is relatively good agreement between
the two computations at each depth. The shear velocities vary trom 3500 to
4300 tt/sec in the upper part ot the section and are 3300 tt/sec below depth
240 teet. The variations in the calculated shear velocities match the variations
in lithology quite well. The lower velocities calculated in the lower section show
a sensitivity to an overall 10% increase in porosity below depth 240 teet. With
caretul consideration ot depth intervals where the wavetorms are ot low qUality
due to attenuation ot the medium, this technique proves to be generally very
good at discriminating variations in shear velocities.
Figure 11 is the depth protlle ot the compressional and shear velocities
determined trom the RlIR2 receiver pair tor the depth interval studied. FigJll"e
12 shows this information tor the R2/R3 receiver pair. Compressional velocities
range between 9500 and 11,000 tt/sec above depth 240 teet and are 9000 tt/sec
below depth 240 teet. There is good correspondence between the two
measurements with both receivel' combinations.
The depth pl'ofiles ot compl'essional and shear wave velocity slownesses tor
the two receivel' pairs (Figures 13 and 14) contorm to the defiection sense ot
the other logs and pl'ovide a bettel' means rol' comparison with the lithologic
and companion logs. Decreases in porosity are mOl'e apparent on the shear
wave slowness pl'ofiles. Once the shear velocity pl'ofile has been determined,
calculation ot engineering properties such as Poisson's !'atio is stl'aight
torward. Figures 15 and 16 are the depth protlles ot Poisson's I'atio tOI' each ot
the I'eceivel' pail'S. Poisson's I'atio tor this section is appl'oximately 0.42 which is
a value chal'acteristic ot sort sediments.
A depth protlle ot the et!ective attenuation ot the Stoneley wave phase
velocity calculated between the Rl /R2 I'eceiver pairs is shown in Figure 17. The
Stoneley wave Q obtained is I'elatively stable at 10 tOI' most ot the depth pl'otile
With a slight increase with depth. Due to the low signal level, the Q value
measul'ed at the shale intel'val tl'om 200 to 225 teet is unl'eliable.
7-6
(
Soft Formations
173
CONCLUSIONS
In this paper we have obtained formation shear wave velocity and
attenuation from full waveform acoustic logs in a "sort" formation using the
phase velocity and spectral amplitude of the Stoneley wave. This method
provides formation shear wave information from data that would otherwise be
inappropriate for standard full waveform analysis. The velocity and attenuation
obtained are stable and consistent with local lithology.
This method requires the proper identification and isolation of the
Stoneley wave pulse. A total loss in the energy of the Stoneley wave signal is
not unco=on in full waveform data that has been recorded in relatively
unconsolldated sediments, regions where the borehole has caved in, and in
formations with high attenuation (such as the shale section in this stUdy). An
improper tool response (no low frequency energy in the source or inadequate
low frequency response of the receiver) will also significantly diminish the
Stone ley wave amplitude. These areas will require more attention during
analysis regardless of the technique used to calculate shear wave velocities.
ACKNOWLEDGEMENTS
The study is supported by the Full Waveform Acoustic Logging Consortium
at M.LT. Colleen Barton was also supported by a Chevron Fellowship. We would
like to thank Mobil Research and Development Corporation for the use of their
data.
7-7
174
Barton et aI.
Biot, M. A., 1952, Propagation ot elastic waves in a cylindrical bore containing a
fluid: Jour. ot Appl. Phys., v.23, p.977-1005.
Cheng, C.H. and Toksoz, M.N., 1961, Elastic wave propagation in a fluid-filled
borehole and synthetic acoustic logs: Geophysics, v.46, p.1042-1053.
Cheng, C.H., Toksoz, M.N., and Willis, M.E., 1962, Determination ot in situ
attenuation trom tull wavetorm acoustic logs: J. Geophys. Res .. v.67, p.547754!\4.
Cheng, C.H.and Toksoz, M.N., 1963, Determination ot shear wave velocities in
"slow" tormations; Trans. 24th Ann. Logging Symp. ot SPWLA, Paper Y.
(
Ingram, J.D., Morris, C.F., MacKnight, E.E.. and Parks, T.W., 1961, Shear velocity
logs using direct phase determination: Presented at 51st Annual
International Meeting ot the Society ot Exploration Geophysicists, October
11-15, Los Angeles, CA.
Johnston, D.H. and Toksoz. M.N., 1961, Definitions and terminology: in Seismic
Wave Attenuatian, Toksoz, M.N. and Johnston, D.H. editors; Geophysics
Reprint Series, No.2, Society ot Exploration Geophysicists, Tulsa. OK.
Kitsunezaki, C., 1960. A new method tor shear-wave logging: Geophysics, v.45,
p.1469-1506.
Paillet, F., 1960, Acoustic propagation in the vicinity ot 'tractures which
intersect a fiuid-filled borehole: Trans. ot 21st Ann. Logging Symp. of SPWLA,
Paper DD.
Tribolet, J.M., 1977. A new phase unwrapping algorithm: IEEE Trans. ot Acoustic,
Speech and Signal Processing, vol. ASSP-25, no.2.
(
White, J.E., 1963, Un.d.rn-gTovlnd. Sound., Applicatian 01 Seismic Waves; Elsevier,
Holland.
Williams, D.M., Zemanek, J., Dennis, C.L., Angona, F.A., and Caldwell, R.L.. 1964,
The long-spaced acoustic logging tool: Trans. 25th Ann. Logging Symp. of
SPWLA, in press.
Willis, M.E. and Toksoz, M.N., 1963, Automatic P and S velocity determination
from tull wavetorm digital acoustic logs: Submitted to Geophysics.
Zemanek, J., Angona, F.A., Williams, D.M., and Caldwell, R.L., 1984, Continuous
shear wave logging: Trans. 25th Ann. Logging Symp. ot SPWLA, In press.
7-8
c
Soft Formations
175
I
1.5
-...
"-
1.4
>-
f-
"-
Phase
"-
r',
1.3
()
o
-l
ll.J
RAYLEIGH
1.2
>
o
1. 1
-l
1.0
...........
ll.J
N
oCt
CC
'-
'-
"'-
'-
......
-- -----...
--
--- - --- -- ---
-- -- -------
~
o
Group
PSEUDO- "- "-
0.9
Z
STONELEY
0.8
0.7
o
5
10
WAVE NUMBER x RADIUS
Figure la
iments.
Stoneley wave phase and group velocity dispersion for hard sed-
7-9
(
176
Barton et aI.
0.78
>I- 0.76
(
SOFT SEDIMENT
<.)
0
...J
w
STONELEY
0.74
>
a 0.72
w
N
...J
-< 0.70
::2:
(
CC
0
z
----------
0.68
0.66
0
2
4
6
8
FREQUENCY (kHz)
Figure lb
ments.
Stoneley wave phase and group velocity dispersion for soft sedi-
7-10
10
177
Soft Formations
1.0 r--r---,...--..,---,---.,.---,----,----,---,..----,
---------S_--
~
Z
l.LJ
0.8
<..:l
u.
U.
l.LJ
o
/
./
0.6
/
/'
-
STONELEY
<..:l
Z
o
/
SOFT SEDIMENT
0.4
~
~
cc
<C
a.
0.2
o
p
--------- ------------------------------
'---_-=--'=~_=-.=..-.=.-.=L.-_ - - - J_ _. l . . - _ . . . l . . - _ - l . - _ - l - _ - - l . . _ - - L _ - - l
o
5
FREQUENCY (kHz)
Figure 2
Stoneley wave energy partition coefficients versus frequency
7-11
10
(
178
Barton et &1.
- ..
-
.. -..-
(
(
Figure 3
Study borehole lithologic section
7-12
(
Soft Formations
179
C)
CD
(/J
E
w
:2
-
I-
~.
(i)
~ DEPTH
Figure 4
eft)
.~
Variable density plot of borehole full waveform acoustic data
7-13
180
(
Barton et aI.
CALIPER
inches
DENSITY
gm/cc
.... .... ...• ....m ....
~
~
OJ
~
.l>.
~
~
Cll
~
OJ
OJ
•
•
~
IS
~
OJ
..:.. .m
OJ
OJ
~
.s>
OJ
•
Cll
~
.w
~
~
m
•
~
~
.
--J
~
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.
Cll
fD
~
~
~
-~
•
...
.
~
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~
0
,
F
~
0)
(
o
...l.
I\J
0
C
m
-0
-;
::I:
--
....
co
(
0
(,
w
o
o
(
Figure 5
Density and Caliper logs recorded in study borehole
7-14
181
Soft Formations
~
I
ttt,of"O"""'~_~_~_~_-t
~~:.,of_"'--~-~---~-__;.
,.,.Ii
h_
... ,
..
~,.~
..,"
....... ..... ..n.
1.1M
l: a
\~ t.~'"'_J
1'" . )
,.-...,.---.,---------t
'.llS
t.«'
•.•,.
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.....
:l
r
I
.,J
~ .•.~
I
-1 •• ,01-.-_--~_~
_
t.
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__
,.,"('----1\
1-'-' I
I
. . ...1-_~~
.. "
•·..1,
..
01----1
•• tt
i
""if---IJ V'vr--- I
I
.J
l
;
'.iI"
.......
'.eN
_-__l_
.....
1.1"
.,."JI-_~--_-~,~----J•. "..
' .•11
I.a.
..
l:' 10K
'oU'
t •
1.. [
"J
..
,
:J
-1.nJI--_-_c,-~,'.6'.
".
".~GIJ
......
r--'
c.ln
l.:~J
Figure 6 Typical full waveform acoustic waveforms and windowed Stoneley
waveform
7-15
(
Barton et aI.
182
(
I: :l: 10E
5.60
~J
0=300.00
RI
~.20
(
2.80
1.~0
0.
"..
l: :l: lOE
-4.00
1.26
3..78
2.52
5.• 0~
6.30
(
~J
o ... J00.00
R2
3.00
,,
2.00
1.00
O.
,,~
I:
1.26
2.52
3.78
5.• 0~
e.~0
,~J
0-300.00
R3
(
0.Si-
0.78
0.65
0.52
0.3S"
0.26
00133
0.
~~
(
- ......-._,...-
1.26
2.52
frequency
Figure 7
3.• 78
5.. 04
6.• ~a
kHz
Typical power spectrum for windowed waveforms of Figure 6
(
7-16
Soft Formations
183
5
R1..-R2
R2"-R3 :.. - ---
U
E
1.
0
4
C
I
T
'-I
:3
K
F
T
..-
S
S
E
C
1
I
0
I
50
I
I
r-rl
I
I
Irr~1
150
100
200
I
a50
DEPTH FEET.
Figure 8 Depth profile of calculated Stoneley wave phase velocities for the
RlIR2 receiver pair depth corrected to the R2/R3 receiver pair
7-17
1
300
(
Barton et al.
184
(
5
PHASE VELOCITY
GROWP VELOCITY - - -- ...
V
E
L
0
C
I
T
Y
(
-.
:3
K
F
T
/
2
S
c:'
C
-
(
1
13
50
100
150
200
250
:300
DEPTH FEET
(
Figure 9 Depth profiie of Stoneley wave phase and group velocities for the
Rl/R2 receiver pair
7-18
Soft Formations
185
5
RVR2 - R2/R3 - ---
V
E
t.
0
C
"'
I
T
y
3
..•
K
F'
T
/
S
E
C
'TIl
1
0
S0
I
I
r I I
I
I
I I I
150
100
200
250
3130
OEPTH FEET
Figure 10 Depth profile of calculated shear wave velocities for the R1/R2
receiver pair depth corrected to the R2/R3 receiver pair
7-19
(
Barton et 81.
186
(
(
15
R1/R2
V
E
TO
C
I
10
T
y
K
F
T
/
t
5+
S
5
E
C
,
I
I
I
0
0
....1
50
r1
I
I
100
I
I
150
,II
200
I
I
250
I
I
300
DEPTH, Fi
Figure 11 Compressional and shear wave velocity profiles for the R1/R2 receiver pair
7-20
(
(
Soft Formations
187
Figure 12 Compressional and shear wave velocity profiles for the R2/R3 receiver pair
7-21
188
Barton et al.
o
50
100
150
200
250
IJt;PTH, FT
Figure 13 Compressional and shear wave slowness profiles lor the R1/R2
receiver pair
7-22
300
189
Soft Formations
,
600
R2"-R3
S
L
0
W
N
E
S
S
M
I
C
s
5OO
"!00
s
:300
ae0
..-
F
T
P
100
o
50
100
150
2130
250
:3013
DEPTH, FT
Figure 14 Compressional and shear wave slowness profiles for the R2/R3
receiver pair
7-23
190
Barton et aI.
a.5-.,...-----------------------,
F'
0
I
S
s
(
a.'!
0
N
S
R
A
T
I
0
a.3
rrrf-r
a.2
a
5a
I
I
f-r.-r-r.....-l-........-r~..,...,.....~--r--r-........-1
10a
150
20a
250
300
DEF'TH. F'T
(
Figure 15 Depth profile of Poisson's ratio for the R1/R2 receiver pairs
7-24
191
Soft Formations
0.5~-----_:"""""_------------,
RS/R3
F'
0
I
S
S
0
0."!
N
,
S
R
A
T
I
0.3
0
o
50
100
150
200
250
DEPTH, FT
Figure 16 Depth profile of Poisson's ratio for the R2/R3 receiver pairs
7-25
300
(
192
Barton et ai.
(
(
o -l---'-""""'-'-lr-"T"l--.-.,..,..,.I-r·-.-..,.......,-.-....-.,....,--r--r--r--T-.-~.,.....,. ........-.-,.....,..-l
50
150
100
2130
2513
DEPTH FEET
(
(
Figure 17 Depth profile of quality factor determined from the Rl/R2 receiver pairs
7-28