57
DETERMINATION OF FORMATION PROPERTIES IN CASED BOREHOLES
USING FUIJ.. WAVEFORM ACOUSTIC LOGS
by
Kenneth ll. Tubman, C.R. Cheng, and ll. Nat!. Toksoz
Earth Resources Laboratory
Department of Earth. Atmospheric, and Planetary Sciences
lIassachusetts Institute of Technology
Cambridge. llA 02139
ABSTRACT
Wave propagation in bonded and unbonded cased boreholes is examined
through the calculation cif synthetic full waveform acoustic logs. The models
consist of a central fluid borehole surrounded by a number of fluid and solid
annuli. Waveforms calculated for a variety of formation and cement parameters
demonstrate that the first arrivals observed on full waveform acoustic logs in
well bonded cased holes are those of the formation and not the casing. Waves
refracted along the casing are generally too small to be observed. The
presence of the steel and cement can make the determination of formation
velocities more ditll.cult than in an open hole. The formation body wave arrivals
are decreased sUbstantially if the cement velocities are near or greater than
the formation velocities. A fluid layer between the steel and the cement
essentially frees the pipe from the cement. The steel arrival then becomes a
large, ringing signal which obscures the formation arrival. The presence of this
layer is a more important factor than its thickness in causing such behavior. If
the fluid layer is between the cement and the formation, the cement can damp
out the ringing of the pipe. If a thick cement layer is bonded to the pipe and
the fluid layer is thin. the casing arrival is small and the formation arrivals are
discernible. A thinner cement layer results in the observation of a body wave
that has a velocity that is an average of the steel and cement velocities.
INTRODUCTION
Previous studies have examined wave propagation in cased boreholes. Most
have been for bond logging applications though, and so concentrated on
determining cement parameters and bonding conditions (Walker, 1968; Riddle,
1962; Pardue et tzl., 1963; Brown et al., 1970). Tubman et al. (1984) made the
assumption that the steel was completely bonded to the cement which was in
turn completely bonded to the formation. Chang and Everhart, (1983)
accounted for other than perfect bonding by allOWing discontinuities in the
axial displacement at the steel-cement interface and reqUiring the axial stress
to go to zero at this boundary. Their formulation did not include any additional
fluid layers.
In this study we examine full waveform acoustic logs in boreholes with
unbonded in addition to well-bonded casing. The situation of unbonded casing
and cement is modeled through the inclusion of fluid layers intermixed with the
(
58
TubmanetaL
solid layers of the steel, cement, and formation.
(
SYNTHETIC :MlCROSEISllOGRAllS
Synthetic full waveform acoustic logs are generated for cased hole
geometries. The borehole geometry is modeled as a number of homogeneous,
isotropic annuli surrounding a central flUid cylinder. The number of annuli is
arbitrary, as well as whether each is a solid or fluld. The only restrictions are
that the central cylinder is fluid and the outer. inflnite formation is solid.
Attenuation is included in the calculations through the use of complex layer
velocities. The synthetic waveforms are calculated using the method of discrete
wavenumber integration (Cheng and Toksi:iz. 1981; Tubman at aI. .• 1984) and
contain all body and gUided waves. The source (the same as that used by
Tubman at a.l., 1984) is centered at 13 kHz. Layers of steel and cement are
Within an infinite formation in the model of a well bonded cased hole. A fluld
layer is placed between the steel and the cement to model poor pipe-cement
bonding, and between the cement and the formation to model poor cementformation bonding. More details of the method are given in Tubman at aI..
(1984) and Cole (1983). The parameters used in the generation of the synthetic
microseismograms are given with each flgure.
(
(
Well Bonded Casing and Cement
Figure 1 shows the micro seismogram for a model consisting of layers of
steel, cement. and formation surrounding the central fluld cylinder. This is the
geometry used to represent a well bonded cased hole. There are fairly clear
body and gUided wave arrivals. The velocities of these waves are determined by
finding the move out of the arrivals with increasing source-receiver separation.
The body wave velocities determined in this manner correspond to the
formation velocities and not those of the casing or cement. This is
demonstrated further by modifying individual parameters of the model. The
formation velocities are lowered in the model used in the calculation of the
micro seismogram of Figure 2. All other parameters remain unchanged. The
compressional and shear velocities are lowered so as to maintain a constant
v" I V. ratio for the two formations. It the observed arrivals were from the
casing. and not from the formation. little ditIerence would be expected between
the waveforms. It is clear, though. that the velocities determined from the
micro seismograms in Figure 2 are ditIerent from those in Figure 1. The
velocities measured from Figure 2 again correspond to the formation velocities.
It is interesting to note that. while the body wave arrival times have changed
significantly, the Stoneley wave arrival time has changed only slightly. This
indicates that the dominant influence on the Stone ley wave (aside from that of
the borehole fiuid) is from the steel and the cement, with the formation having
very little etIect. The thickness of the cement layer is important in controlling
the nature of the StoneIey wave. The formation has more influence if the
cement layer is very thin or non-existent.
The presence of the steel and the cement can make determination of
formation velocities more difficult though. This is illustrated in
micro seismograms shown in Figures 3 and 4. The cement velocities used in
model for Figure 3 have been raised so that they are now close to those of
3-2
(
(
(
the
the
the
the
(
CuedHme~croge~nmm
59
formation. As can be seen from the figure, the amplitudes of the body waves
have decreased considerably relative to the previous cases. This is because the
contrast between the steel and cement is less so there is less energy directed
back to the receiver. The pseudo-Rayleigh mode is also reduced in amplitude.
The faster cement pushes the pseudo-Rayleigh dispersion curves to higher
frequency, but since the center frequency of the source remains constant,
there is a smaller frequency range over which these waves are excited.
The model used in the calculation of Figure 4 has a formation with
velocities which are comparable to those of the steel casing. The P wave arrival
is clear and can be determined to be the formation velocity. In this case, there
is a large amount of ringing between the P wave arrival and the Stoneley wave
arrival. This ringing has a wavelength which is about four times the thickness
of the cement layer. It appears that a low velocity layer of cement trapped
between the higher velocity steel and formation sets up some resonance
phenomenon that is dominating this portion of the signal. It is difficult to
identify any distinct arrivals between the first P wave and the Stoneley wave.
Thus, it is clear that in well-bonded case holes, one can generally determine the
formation velocities. The identification of the formation arrivals, particularly
the S wave or pseudo-Rayleigh wave arrival, depends on the relative velocities of
the cement and the formation.
No Steel-Cement Bond. Good Cement-Formation Bond
Unfortunately, bonding conditions in boreholes do not always match the
perfect bonding situation modeled above. In general there are two locations
where the bonding can be less than ideal: at the steel-cement interface, and at
the cement-formation interface. The first situation is examined here by
inserting a layer of fiuid between the steel casing and the cement. This is the
free pipe situation. The synthetic micro seismograms calculated for this case
are shown in Figures 5, 6 and 7. In Figure 5, the fiuid layer between the steel
and the cement is taken to be 0.5 inches thick. As shown in the figure, there is
a large. distinct arrival at the beginning of the signal. The velocity of this
arrival corresponds to the plate velocity of the steel. not the velocity of the
formation. With the pipe not well bonded to the cement, the casing arrival has a
large amplitude and long duration. The formation P wave arrival is completely
overpowered by this signal. The above observation is consistent with field data.
(Walker. 1968; Grosmangin et a.l., 1961).
A situation that is less well understood is when the thickness of the
intermediate fluid layer becomes very small. The thin layer of fluid is commonly
referred to as a microannulus. The model of Chang and Everhart (1963) is the
limit of this situation with the thickness of the fiuid layer equal to zero. In
Figures 6 and 7 we present synthetic micro seismograms in two different
formations each with a microannulus of thickness 0.001 inches surrounding the
casing. Even with such a thin fiuid layer, the first arrival in Figure 6 is a ringing
signal from the casing. Changing the formation properties has little effect on
the nature of the waveform. The velocities (both compressional and shear) of
the formation in Figure 7 are less than those in Figure 6. The remainder of the
model parameters are the same in both figures. There are no changes in the
first arrivals in these cases as there were in the well bonded situations.
3-3
60
TubmanetaL
Good Steel-Cement Bond. No Cement-Formation Bond
Another common occurrence in cased holes is good steel-cement bonding
but poor cement-formation bonding. In Figures 8 - 12 we present synthetic
micro seismograms modeling this situation. The intermediate fiuid layer is
between the cement and the formation so the steel casing is now clad with a
layer of cement. In Figure 8 the thickness of the fiuid layer is 0.0625 inches
and the thickness of the cement layer is 1.6875 inches. The cement is
sufficiently thick here to damp out the ringing of the casing observed in the
free pipe situation. The arrival from the casing is very small. The velocity of
the first obvious arrival corresponds to the P wave velocity of the formation.
The formation S wave arrival is also clear. To check that these are indeed the
formation arrivals. the casing parameters are held constant and the formation
velocities are modified. The resulting microseismograms are shown in Figure 9.
It is clear from this figure that the arrival times and velocities of the body
waves have changed as the formation velocities change. Velocities determined
from this figure confirm that the observed arrivals are from the formation and
not from the casing.
If the cement layer is thinner it will not be able to damp out the casing
arrivals effectively. Figure 10 shows the synthetic microseismograms from a
model with a cement layer thickness of 0.5 inches and a fiuid layer thickness of
1.25 inches. The amplitude of the first arrival has increased relative to the
previous cases of thicker cement. The duration of this portion of the waveform
has also increased substantially. The formation shear and pseudo-Rayleigh
wave arrivals are now much more difficult to identify due to overlapping with
the ringing of the earlier arrival. Changing the formation parameters has little
effect on the shape anc;l. velocity of this first arrival. This is seen in Figure 11,
which was calculated with the same geometry but with a slower formation. The
first wave packets on waveforms in both Figures 10 and 11 are virtually
identical. The velocity of this first arrival is determined to be between the plate
velocity of the steel and the velocity of the cement. In Figure 12 the velocities
of the cement have be increased so that they are now comparable to the
formation velocities. This relationship between the cement and formation
velocities in the well-bonded cased hole resulted in significantly reduced
amplitudes of the first arrival (Figure 3). Here, the amplitudes and shape of the
first arrival are almost unchanged. The velocity has increased slightly though,
due to the faster cement. The amplitUde and velocity of this wave increase With
decreasing thickness of the cement layer. A similar amplitude variation of the
casing signal with cement thickness was observed by Walker (1968) using data
from test wells.
(
(
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CONCLUSIONS
Three types of bonding situations commonly encountered in cased holes
are studied through the calculation of synthetic full waveform acoustic log
micro seismograms.
In the case of good bonding between steel and cement and between cement
and formation, the layers of steel and cement generally have only a small
infiuence on the formation body wave arrivals. It is possible for these layers to
make the determination of formation velocities more difficult than in an open
3-4.
(
Cased Hole llicroseismograms
61
hole. If the cement velocities are comparable to those of the formation the
amplitude of the formation arrivals can be significantly reduced. The steel and
cement. along with the flUid, exert the dominant influence on the Stonely wave.
A fluid layer between the steel and cement effectively frees the steel
casing. The result is that the casing arrival becomes larger in amplitude and
longer in duration. The casing signal in this situation dominates the formation
P wave signal. There is little change in the nature of the waveform as the I
thickness of the fluid layer is changed. It is the the presence of this layer, not
its thickness. that is the most important factor in the behavior of the casing
arrival.
When there is poor bonding between the cement and the formation but
good bonding between the steel and the cement. the situation is more
complicated. It may be possible to discern the formation body wave arrivals
even in the presence of a fluid layer between the cement and the formation. If
the flUid layer is thin and there is a large amount of cement bonded to the pipe,
the cement will act to damp out the ringing of the pipe. making the formation
arrivals clear. If the cement layer is sufficiently thin. it will ring along with the
steel casing. The flrst arrival in this situation will be from the combination of
the steel and the cement and will have a velocity intermediate to their
velocities.
ACKNOWLEDGEllENTS
This work was supported by the Full Waveform Acoustic Logging Consortium
at M.LT. Kenneth Tubman was partially supported by a Phillips Petroleum
Company Fellowship.
3-5
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62
TubmanetaL
REFERENCES
Brown, H.D., Grijalva, V.E., and 1.L. Raymer, 1970, New developments in sonic
wave train display and analysis in cased holes: Trans. S.P.W.L.A., paper F.
Chang, S.K and Everhart, A.H., 1983, A study of sonic logging in a cased
borehole: J. Pet. Tech., v.35., p.1745-1750.
I
(
Cheng, C.H. and Toksoz M.N., 1981, Elastic wave propagation in a fluid-filled
borehole and synthetic acoustic logs: Geophysics; v.46, p.1042-1053.
Cole, S.P., 1983, Guided wave dispersion in a borehole containing muitiple fluid
layers, B.S. Thesis, Department of Physics, Massachusetts Institute of
Technology, Cambridge, MA.
(
Grosmangin, M., Kokesh, F.P., and Majani, P., 1961. A sonic method for analyzing
the quality of cementation of borehole casings: J. Pet. Tech., p.165-171.
Pardue, G.H., Morris, R.L.. Gollwitzer, 1.H., and Moran, J.H.,1963, Cement bond log
- A study of cement and casing variables: J. Pet. Tech. p.545-555.
Riddle, G.A., 1962, Acoustic wave propagation in bonded and unbonded oil well
casing: S.P.E. paper number 454.
Tubman, KM., Cheng, C.H., and Toksoz, M.N., 1984, Synthetic fuil waveform
acoustic logs in cased boreholes: Geophysics, in press.
Walker, T., 1968, A full-wave display of acoustic signal in cased holes: J. Pet.
Tech., p.818-824.
c
(
(
3-6
(
63
Cased Hole lficroseismograms
R
VP
RHa
VS
(FT)
1FT IMS]
1FT IMS]
0.15~167
5.5000
20.0000
9.2590
16.0000
II. 0000
5.6700
8.5300
0.187500
0.333333
O.
0.00
0.50
1.00
O.
TIME
1.50
IMSl
os
OP
IGM/CCI
1• 2000
7.5000
1.9200
2.1600
.00
2.50
20.00
1000.00
~O.OO
60.00
3.00
O.
1000.00
30.00
60.00
3.50
·
Q
Q
Q
Q
Q
Q
--
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Q
Q
Q
Q
""T1
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-I
-I
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N
:"
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0
;n
Q
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0.00
0.50
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I. 50
TIME
2.00
2.50
3.00
3.50
IMSl
FIG. 1. Synthetic microseismograrns in a well bonded cased hole for offsets
varying from 10 ft. to 15. ft at .5 it intervals. R is the outer radius of the
layer; Vp and V. the compressional and shear velocities; p the density; and
Qp and ~ the compressional and shear quality factors. The bottom layer
(R 0.) is the infinite formation.
=
3-7
64
Tubman et aI.
VP
1FT IMS)
VS
1FT IMS)
0.15~167
5.5000
20.0000
9.2590
13.1200
I!. 0000
5.6700
7.0000
0.187500
0.333333
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0.00
0.50
1.00
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TIME
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TIME
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FIG. 2. Same as Figure 1. with a slower formation.
3-6
3.00
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Cued Hole Ilicroseismograms
VP
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VS
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0.154167
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0.333333
5.5000
20.0000
13.5000
16.0000
11.0000
8.3000
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0.50
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65
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3.00
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o
o
3.50
FIG. 3. Microseismograms for a model with cement velocities close to the
formation velocities. The amplitude scale (gain) is twice that of the other
figures.
3-9
(
66
Tubman et aL
,
/
R
lFT)
VP
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VS
RHO
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CGM/CCI
0.15~167
5.5000
20.0000
9.2590
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11.0000
5.6700
10.5000
0.187500
0.333333
O.
0.00
0.50
1.00
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TIME
1.50
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1.2000
7.5000
1.9200
2.3000
.00
2.50
20.00
1000.00
YO.OO
95.00
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1.50
TIME
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FIG. 4. Microseismograms for a model with formation velocities comparable
to the casing velocities.
3-10
67
Cased Hole llicroseismograms
R
eFT)
0.15~167
0.187500
0.229167
0.333333
O.
0.00
0.50
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5.5000
20.0000
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13.1200
1.00
RHCI
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II. 0000
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7.0000
TIME
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1.2000
7.5000
1.2000
1.9200
2.1600
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2.50
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20.00
1000.00
20.00
40.00
60.00
3.00
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O.
1000.00
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30.00
60.00
3.50
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TIME
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2.00
2.50
3.00
3.50
FIG. 5. Microseismograms for the free pipe situation. There is a .5 inch fluid
layer between the steel and the cement.
3-11
(
68
Tubman et aI.
VP
R
1FT)
1FT IMS)
0.15~167
0.187500
0.187583
0.333333
O.
0.00
0.50
5.5000
20.0000
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9.2590
16.0000
1.00
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RHCI
"(GM/CCI
O.
1. 2000
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TIME
1.50
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20.00
1000.00
20.00
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0.50
1. 00
1.50
TIME
IMSl
2.00
2.50
3.00
3.50
(
FIG. 6. Microseismograms for a model of a microannulus. The fluid layer
between the pipe and cement is .001 inches thick.
3-12
69
Cased Hole Jlicroseismograms
R
IFTl
VP
1FT IMS)
0.15~167
5.5000
20.0000
5.5000
9.2590
13.1200
0.187500
0.187583
0.333333
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0.00
0.50
I. 00
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11. 0000
O.
5.6700
7.0000
TIME
1.50
IMSl
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1.2000
7.5000
1.2000
1.9200
2. 1600
2.00
2.50
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as
20.00
1000.00
20.00
1000.00
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60.00
3.00
O.
O.
30.00
60.00
3.50
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1.50
TIME
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2.00
2.50
3.00
FIG. 7. Same as Figure 6 with lower formation velocities.
3-13
3.50
(
Tubma.n et aI.
70
VP
R
eFT)
WT IMS)
0.15~167
0.187500
0.328125
0.333333
O.
0.00
0.50
5.5000
20.0000
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5.5000
16.0000
1. 00
VS
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o.
II. 0000
5.6700
O.
8.5300
TIME fMSl
1.50
as
OP
IGMICCI
1.2000
7.5000
1.9200
1.2000
2.1600
a
2.50
20.00
1000.00
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YO.OO
1000.00
30.06
20.00.
60.00
60.00
3.00
O.
3.50
0
0
0
0
0
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0
0
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-l
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0.00
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I. 00
1.50
2.00
TIME fMSl
2.50
3.00
3.50
(
(
FIG. 8. Microseismograms for a model with good steel-cement bonding but
no cement-formation bonding. There is a thick cement layer bonded to the
pipe.
3-14
Cased Hole lficroseismograms
R
fFTJ
0.15~167
0.187500
0.328125
0.333333
O.
0.00
0.50
VP
fFT IMSJ
5.5000
20.0000
9.2590
5.5000
13.1200
I. 00
RH~
VS
1FT IMSJ
O.
11.0000
5.6700
O.
7.0000
TIME
1.50
71
QP
QS
fGM/CCI
1.2000
7.5000
1• 9200
1.2000
2.1600
[MSl
2.50
20.00
1000.00
O.
~O.OO
1000.00
30.00
20.00
60.00
60.00
3.00
O.
3.50
,
-
c
c
c
:'
c
c
-
oN
N°
c
c
0
0
""T1
--I
.,
--I
'"cc
I~
-
~
'"
c
c
c
c
.
oC
C
C
c
.
1-'"
0
c
c
0.00
c
c
0.50
1.00
I. 50
TIME
[MSl
2.00
2.50
3.00
FIG. 9. Same as Figure 8 with lower formation velocities.
3-15
3.50
(
72
TubmanetaL
R
VP
1FT IMS)
1FT)
0.15~167
0.187500
0.229167
0.333333
O.
0.00
0.50
5.5000
20.0000
9.2590
5.5000
16.0000
l. 00
RHO
VS
1FTIMS)
O.
II. 0000
5.6700
O.
8.5300
TIME
l.50
(MSl
QP
QS
(
fGM/CCI
1.2000
7.5000
1.9200
1 . 2000
2.1600
.00
2.50
20.00
1000.00
O.
YO.OO
1000.00
30.00
20.00
60.00
60.00
3.00
O.
!
C
3.50
.
I~
0
0
0
(
• N
N'
0
0
0
0
'"T1
.."
-j
-j
'"
'"
0
0
0
0
-
~
~
0
0
0
0
-
'"
0
0
0
0
.
-
(
~
0
0
0.00
(
0
0
0.50
l. 00
l. 50
TIME
(MSl
2.00
2.50
3.00
3.50
(
F1G. 10. Microseismograms lor a model with a thin layer 01 cement bonded
to the pipe and a thick tl.uid layer between the cement and the formation.
(
3-16
Cased Hole llicroseismograms
R
eFT)
0.154167
0.187500
0.229167
0.333333
O.
0.00
0.50
VP
1FT IMS)
5.5000
20.0000
9.2590
5.5000
13.1200
J. 00
RHO
VS
1FT IMS)
O.
11. 0000
5.6700
O.
7.0000
TIME
J.50
IMSl
73
OP
OS
IGM/CCl
I .2000
7.5000
1.9200
1.2000
2. 1600
.00
2.50
20.00
1000.00
40.00
20.00
60.00
3.00
,
O.
1000.00
30.00
O.
60.00
3.50
.'"
'"
'"'"
'"'"
N:-
"
'N
'"'"
'"'"
--I
--I
-'"
w
I~
-
'"'"
'"'"
'"'"
.
w
;=
'"'"
'"'"
0.00
"
0
'"
'"
0
0
0.50
J. 00
J. 50
TIME
IMSl
2.00
2.50
3.00
F1G. 11. Same as Figure 10 with lower formation velocities.
3-17
3.50
74
Tubman et aL
R
efT)
0.154167
0.187500
0.229167
0.333333
O.
0.00
0.50
VP
(FT IMS)
5.5000
20.0000
13.5000
5.5000
16.0000
11.0000
8.3000
O.
8.5300
1.00
RHO
VS
1FT IMS)
1.50
OS
20.00
1000.00
40.00
20.00
60.00
1000.00
30.00
(
IGM/CCl
O.
TIME
Of
1.2000
7.5000
1.9200
1.2000
2.1600
IMSl
.00
2.50
3.. 00
O.
O.
60.00
(
3.50
-
·
0
0
0
0
0
0
N'
'N
o
o
0
0
I)
"'TJ
.....
Mf\/'o~-----h",
·'"
o
o
0
0
1jIj'v'V\A~--+;;;
~
o
o
0
0
""
o
o
0
0
·
\N'vV'./V\/V'---;-.c,
o
o
o
o
0.00
0.50
1.00
1.50
TI ME
2.00
IMSJ
2.50
3.00
FIG. 12. Same as Figure 10 with higher cement velocities.
3-18
3.50
(