205
DETECTION AND CHARACTERIZATION OF FRACTURES
FROM GENERATION OF TUBE WAVES
by
Ernest Hardin
and M. Nafi ToksQZ
Earth Resources Laboratory,
Department of Earth and Planetary Sciences,
Massachusetts Institute of Technology,
Cambridge, MA 02139
ABSTRACT
Field testing has been conducted to evaluate a model which predicts the
permeability and orientation of a permeable zone, in a deep water weil in crystalline
rock. Tube waves are generated by seismic P-waves incident on a fracture
intersecting the borehole, a process observed in vertical seismic profiling (VSP). The
behavior is explained by fluid exchange between the fracture and borehole, and the
observed efficiency of conversion is theoretically related to fracture permeability.
Additionally, fracture orientation may be obtained from multiple-source-offset VSP
surveys. Conventional temperature, caliper, resistivity and televiewer logs show the
presence of fractures and their orientation, and provide indirect evidence of
associated flow. Open fractures are simultaneously sampled over the full borehole
depth by hydrophone VSP methods. The tUbe wave generation model produces results
which compare favorably to independent estimates of fracture parameters.
INTRODUCTION
Increasing importance of natural and artificial fractures in resource recovery
and in site characterization for waste storage has created the need for methods of
identification and for quantifying fracture parameters: permeability and orientation. It
has long been known that sonic and full waveform acoustic well logs exhibit effects
of fractures (Paillet, 1983), and more recently VSP has been demonstrated to be
useful. Huang and Hunter (1981) observed tube waves originating at distinct
depths, when conducting checkshot VSP surveys using a hydrophone streamer. They
attributed tube wave generation to the presence of open fractures intersecting the
borehole. In a similar survey In Hamilton, Massachusetts we also observed the
generation of tube waves (Figure 1). These and other field studies have shown that
the tube wave generation response is commonly observed in hard rock geological
settings, and is observable in fractured reservoirs of sedimentary origin.
The motivation for this study is to demonstrate the application of the tube
wave generation model of Beydoun, et al. (1985) for several fractures in a single
well, and if possible to evaluate the model assumptions of laminar flow and the low
frequency approximation. The setting for the field study is optimal since the relative
homogeneity of the granite formation prevents scattering of the original P-wave
206
Hardin & Toksoz
pulse (which can result in multiple phases in the VSP record and render interpretation
difficult). Additionally the intrinsic attenuation of the formation can be presumed
negligible for the VSP travel paths and frequency band used. For the purposes of this
study formation permeability is considered solely due to structural features such as
joints or shear zones which can be located by conventional well logs, borehole
television, borehole televiewer images and driller's logs.
TUBE WAVE DESCRIPTION
Tube waves are low frequency Stoneley waves, a fundamental normal mode
which propagates along the cylindrical borewall interface of a fluid filled borehole. In
a hard rock formation where the formation shear velocity is significantly greater than
the borehole fluid velocity, tube wave velocity and dispersion are minimally
dependent on formation properties (Cheng and Toksoz, 1983). Tube wave phase
velocity is always lower than that of the borehole fluid, and particle motion is
elliptical at the borewall, grading to linear along the borehole axis (Biot, 1952).
Displacement amplitude in the solid decays approximately exponentially away from
the borehole.
For a homogeneous formation, linear elasticity predicts some dispersion with
the phase velocity asymptotic to the fluid velocity at high freqeuncy. (Cheng and
Toksoz, 1981) The dispersion relationship for a given survey is dependent on the
fluid and formation properties, and the hole diameter. Within the VSP frequency band
(10 to 1000 Hz.) phase velocity is nearly constant and principally dependent on
formation properties. At higher frequencies such as are encountered in acoustic
logging the phase velocity becomes increasingly dependent on borehole radius.
A guided wave effect may not exist if the formation shear velocity is much
less than the borehole fluid velocity; this limit is determined exactly by the formation
and fluid properties. (Schoenberg, et aI., 1981) In crystalline rock and many other
rock types the shear velocity exceeds this limit and tube waves can propagate
without geometric attenuation or spreading. At exploration seismic frequencies most
of the total strain energy of the tube wave is trapped in the fluid. For this reason
the amplitude of a tube wave excited by a periodic source In the fluid can be
approximated by equating the source strength to the dilatancy associated with the
induced tube wave. Neglecting phase response, body waves radiated into the solid,
and strain energy in the solid which is associated with the tUbe wave, a
correspondence can be developed between fluid flow and tUbe wave pressure
amplitude.
Since most of the energy associated with a tube wave propagates in the fluid,
(Cheng, et aI., 1982) pressure response is more easily measured than borewall
displacement. Borehole fluid pressure amplitude is effectively constant over the
cross section of the borehole, (Biot, 1952) varying by only a few percent for any
frequency in the VSP band, thus centralization of the pressure sensors is
unnecessary.
CONVENTIONAL LOGS
Full waveform acoustic log data (Rgures 2 and 3) clearly show that the tUbe
wave generating horizons (from VSP) strongly delay and attenuate the compressional
9-2
Tube Wave Generation
and shear head waves, and the pseudo-Rayleigh packet. The tUbe wave is not
excited efficiently in a borehole of this large radius in a "hard" formation, at the
frequencies employed by the acoustic logging sonde. The various phases arriving
after the compressional head wave are the fundamental and higher mode pseudoRayleigh waves. A suite of conventional logs was acquired including caliper, natural
gamma, sonic (transit time for 0.305m. receiver-spacing, non-centralized), initial
entry temperature log (downgoing recording on first entry into borehole after thermal
equilibration), borehole acoustic televiewer, self potential and resistivity. There are
clear indications of the tube wave generating horizons, except for the electrical logs,
as shown in the comparison plots (Figure 4). The caliper opened fully at each horizon,
indicating natural cavities or displacement of material from the borewall during drilling.
Gamma anomalies at each horizon indicate constitutive differentiation. Apparent
interval transit time increases uniformly from 55 to >100 j.1Sec/ft. at fractured
horizons. The borehole temperature log (Figure 4) Is reduced by the subtraction of a
linear geothermal gradient of 3.0 C 0/ 100m. Temperature anomalies- (app. 0.5 C 0
above background) indicate where warmer formation fluid flows into the well through
open fractures. Images acquired with the borehole televiewer (Figure 10)
unambiguously show tabular features intersecting the hole obliquely at each tube
wave generating horizon.
THEORETICAL MODEL FOR TUBE WAVE GENERATION IN VSP
Intersecting fractures are modelled as idealized parallel-plate systems of
arbitrary orientation which are fluid saturated and embedded in a homogeneous
isotropic elastic medium. The borehole intersecting the fracture system is uncased
and the entire fracture-borehole system is initially at hydrostatic equilibrium. The
fracture width oscillates around the static aperture according to the incident P-wave
displacement and with the same amplitude (Beydoun, et al., 1985).
The fluid flow rate in the presence of a pressure gradient is related to the
fracture permeability by Darcy's law. Elevation gradient terms appropriate to a mildly
dipping «60 0 ) fracture are neglected since the fracture is symmetric with respect
to the borehole (Bower, 1983). The permeability of the parallel plate fracture is
taken from the well known "cubic law" (Snow, 1965). As is common in reservoir
problems (Ziegler, 1976) the determination of flow requires the assumption of an
effective fracture radius at which transient pressure effects are nii; contributions of
fracture flow beyond this radius to tube wave generation are neglected.
The dilatation of the borehole fluid associated with a tube wave is equated to
the dilatation associated with fluid ejected from the fracture (Beydoun, et aI., 1985).
Upgoing and downgoing tube waves of equal amplitude are predicted. Observed tube
wave amplitude is normalized by the pressure amplitude of the direct compressional
phase (White, 1983) at the same sensor. The ratio of tube wave to compressional
wave amplitude can be determined from a single trace if necessary and does not
require hydrophone calibration. The two phases must be represented by recognizable
wavelets and be free of interference from extraneous phases, in order for the
spectral ratio comparison to be meaningful.
VSP SURVEY DESCRIPTION
The test well is a deep water well drilled to app. 570m. in the Cape Ann
9-3
207
208
(
Hardin & Toksoz
granite near Hamilton, Massachusetts. The hole was drilled percussively by a
downhole hammer with a final gauge of app. 30cm., and is uncased except for the
uppermost few meters which pass through a surface layer of loess and glacial debris.
From gyroscopic deviation surveys it is evident that from about 200m. to 300m. the
weil deviates increasingly up to 11 degrees from vertical and remains this way to
total depth.
Two VSP surveys were conducted; the first utilized surface explosive and
weight drop sources, .and a single available shothole. The second survey was
conducted some eight months later and used three shotholes exclusively. Signal
strength from weight drop and surface explosive sources was adequate for
generation of identifiable tube wave phases, but not for capture of the direct
compressicnal wavelet necessary for data interpretation. Multiple shot trace
stacking was not used.
I
The three shotholes penetrate well below the surface layer, as depicted In
Figure 5. Muitiple offsets are used to exploit the dependence of the model on survey
and fracture geometry. The three shotholes and the central well are filled naturally
with water up to the bottom of the surface layer. Source strength varies up to 0.45
kg. charges of ammonium-nitrate based explosive, electrically detonated. In the
exemplary field section, (Figure 1) the phases are well separated, with tube wave
events generated at depths of 146m., 210m. and 290m. In apparent coincidence with
the direct compressional arrivals. No direct shear arrival or reflected body wave
arrival of any type is identifiable in the section. Numerous tube wave reflections and
events possibly originating deeper in the well extend late into the acquisition
window. Importantly, the receiver spacing Is much smaller than the separation of
tube wave generating horizon.s, thus giving multi-sensor coverage of tube wave
events close to their depth of 'Jelleration, where interference from other phases is
least likely.
.
HYDROPHONE-VSP DATA ACQUISITION AND FILTERING
Borehole fluid pressure Is recorded digitally from the output of a six-channel
hydrophone streamer with receiver spacing of 3.0m. Hydrophone pressure amplitude
response is uniform to better than 3db over the seismic source band. Each
hydrophone (Benthos, Inc. AQD-1) contains an integral preamplifier; analog signals are
conveyed to the surface by a seven-conductor wireline cable. Traces are acquired
using a 12-bit digitizer with fixed gain, sampling rate 4 kHz., and total time window of
500 msec.
The arrIVIng P-wavelet for each acquired trace is temporally windowed and
transformed using the fast Fourier transform (FFT). The trace spectra are normalized
and combined to produce a composite amplitude spectrum for each section which is
equally weighted with respect to individual traces. (Figure 6) Based on evaluation of
the source spectra the traces are digitally bandpass-filtered using a 3-pole
Butterworth recursive filter and applying the filter twice to the data, in opposite
directions to suppress phase shifts. The corner frequencies of the passband are 150
and 400 Hz.
The traces are further filtered to suppress line noise (60 Hz. and harmonics)
present during acquisition, using a predictive scheme based on nonlinear least
9-4
Tube Wave Generation
squares inversion. The time window beginning at shot detonation and ending at the
P-wave arrival is analyzed to determine the amplitude and phase of sinusoidal noise
components which fit the data in a least squares sense. A solution is obtained via a
Marquardt inversion algorithm (Marquardt, 1963), and subtracted from the data
trace. Errors in predicted noise amplitude or phase caused by variability of these
properties of the actual noise are not observed In the resulting traces (Figure 7).
Stationarity and phase effects are thus limited to components of the noise whose
amplitude is small compared to the useful components of the signal.
EVALUATION OF FRACTURE PARAMETERS FROM TUBE WAVE GENERATION
Each tube wave event is evaluated independently, using traces from the
three filtered VSP sections. For each trace the arriving P-wavelet and the selected
tube wave event are temporally windowed, and their tube-to-P amplitude ratio
spectrum calculated as a simple spectral ratio. A spreading correction is made to
each P-wavelet spectrum, based on the difference between source-receiver
separation for the recording hydrophone and the direct path from the source to the
generating fracture. These distances are known from orientation surveys obtained for
the observation well and the shotholes. For each section composite P-amplitude and
tube-to-P amplitude ratio spectra are prepared by stacking the results for all
applicable traces (Figure 8). Since for each section many (>15) traces are used to
produce the composite ratio spectra, a ratio standard deviation can be used as an
estimator of the significance of the resulting amplitude ratio spectrum. For each
section this estimator was substantially less than the calculated ratios except at the
edges of the pass band (Figure 8).
The tube wave pressure model is nonlinear in all three parameters: fracture
strike, dip and permeability. The Marquardt algorithm is used to match theoretical
tube-to-P amplitude ratio curves for the three sections with the curves of Figure 8.
Each VSP section yields a set of residuals at discrete frequencies, which are
weighted by the ratio of the normalized source amplitude to standard deviation of the
tube-to-P amplitude ratio, for the appropriate frequency and VSP section. The
results are shown in Figure 9 for the fracture at 290m., and the corresponding
fracture parameters are summarized in Table 1.
COMPARISON OF RESULTS TO INDEPENDENT OBSERVATIONS
Acoustic borehole televiewer logs of the tube wave generating horizons show
distinctly that these features are tabular and intersect the borehole obliquelY.
(Figure 10) Reasonable agreement Is obtained between the orientation of these
features determined from VSP model inversion, and the orientation from televiewer
images corrected for well deviation and magnetic field orientation. (Table 1)
The observation well was drilled pneumatically, with air as circulating medium,
and thus water inflow during the drilling process could be crudely determined. Drill
pipe was added to the string in 6m. stands; groundwater flow into the empty borehole
was allowed during the drilling hiatus while each stand was installed. Before drilling
resumed the hole was blown clear of water and the pressure required to do so was
recorded. Time of day was also recorded at each juncture giving an indication of the
rate of inflow over the entire length of the hole at different stages of drilling. The
spatial resolution of the method was limited to the length of one stand, and inflow
9-5
209
(
210
Hardin & Toksoz
may at any time have been affected by hydraulic communication between fractures
at some distance from the borehole. Some drawdown behavior was observed
whereby the rate of inflow decayed gradually during a day of drilling, SO that it was
necessary to use the change in inflow from each stand to the next.
As each generating horizon was penetrated inflow increased by roughly 0.03
cubic meters per minute, which is taken as an order of magnitude flow estimate for
calculational purposes. If the corresponding formation pressure is hydrostatic, then
the feature permeability at each horizon from Darcy's Law (Ziegler, 1976) is app. 50
darcys without taking into account deviated hole and dipping hole geometry or
elevation effects. This value is an order of magnitude greater than the permeability
predicted from VSP interpretation.
DISCUSSION
Comparable frequency dependence of the model and the spectral ratios
obtained using the data support the low frequency approximation. This assumption is
used to calculate ejected fluid volume and for the normalizing pressure response due
to the incident P-wave. Fracture-borehole system geometry conforms to the
approximation, since the borehole radius and significant fracture features are much
smaller than the incident wavelength. If the approximation were violated because of
turbulent flow the theoretical and observed spectral ratios would probably have
deviated markedly with increasing frequency.
The premise that fracture parameters determined from inversion are unique,
given that the low frequency approximation is valid, is supported by the agreement
between predicted fracture orientations and independent observations at 210 and
290m. This agreement also suggests that the conversion mechanism is controlled by
fracture closure. However, the actual amplitude of closure and whether closure is
everywhere uniform on the fracture are not clarified by these results.
In principle the model frequency dependence is sufficient to obtain fracture
orientation data from fewer than three VSP offsets. The filter passband was selected
to approximately coincide with the source spectrum. Observed tube wave amplitude
was generally lower than predicted near the edges of this band, suggesting a more
complicated tube wave generation mechanism. In practice, the applicabiiity of the
model assumptions to the real earth is such that three or more offsets are needed to
geometrically resolve fracture orientation.
Survey instrumentation typically available for hydrophone VSP has known
finite dynamic range. In this survey amplifier gain was set to just record the
compressional wavelet, so that the smallest amplitude ratio which could be recorded
with precision was app. unity, leaving most of the 12-bit range for tube wave
recording without clipping. The range of measurable tube-to-P amplitude ratios is thus
about 30 db, corresponding to a theoretical range of permeabiiity of app. 1 to 300
darcys. The presence of noise which cannot be removed from the source band tends
to reduce this range. The range of measurable permeability is then constrained by the
borehole radius, formation and fluid properties, and the source band, and may be
extended somewhat through the use of field equipment with broader dynamic range.
The choice of formation P-wave displacement amplitUde for the assumed
9-6
Tube Wave Generation
amplitude of fracture closure yields a reduced value for predicted permeability. If the
fracture stiffness (resistance to closure) was as high as that of the formation,
closure would be small since the fracture width is much less than a wavelength.
Converseiy, if the fracture offered very little resistance to closure it would behave
similarly to a free surface: closure would be of the order of the P-wave displacement
but there would be no transmitted P-wave. Inspection of Figure 7 shows that the
compresional arrival is only slightly attenuated by transmission, thus the fracture
closure assumption stated above is a compromise which is used in the absence of
known fracture response characteristics and tends to underestimate permeability.
Sounding by conventional wall-lock VSP could be used to image the fracture
reflectivity/transmissibility, which in conjunction with an appropriate fracture model
(White, 1983; Schoenberg, 1980) defines the fracture closure.
CONCLUSIONS
The results of this study are summarized as follows:
1. The spectral method for comparison of the incident P-wavelet and generated
(VSP) tube waves is effective given sufficient signal strength, yielding values for
fracture parameters which are in reasonable agreement with independent
observations.
2. The dynamic range of the VSP survey equipment and the level of seismic and
electrical noise place practical limits on the range of permeability of features which
can be investigated.
3. Determination of meaningfui ratio spectra requires separation of interfering
phases. In heterogeneous formations where body wave scattering is important, it is
likely that the source signature and seismic structure of the formation will be needed
for phase separation. Such measures as monitor phone deployment and conventional
wall-lock VSP survey may be applicable.
4. The low frequency approximation is probably justified from the agreement
obtained. However, divergence of the predicted and observed amplitude ratios near
the edges of the passband suggests a need for additional data sets to evaluate
model assumptions under a broad set of geologic conditions.
5. Discrepancies between the independently estimated permeability and values
obtained from VSP interpretation should be investigated first by resorting to a more
reliable independent method of permeability determination. If necessary the fracture
closure assumption can be evaluated by examining body wave reflectiVity at the
fracture interface, using a method such as wall-lock VSP.
ACKNOWLEDGEMENTS
The authors would like to thank Dr. F.L. Paillet of the USGS for valuable
comments and for the acquisition of FWAL and borehole televiewer data. The
hydrophone VSP data were obtained through the joint efforts of MIT/ERL and Weston
Geophysical of Weston, Mass. Ths study benefitted greatly from the enthusiastic
support of Mr. Peter Britton, Reiss Foundation, Hamilton, Mass. This work was
9-7
211
(
Hardin & Toksoz
212
sponsored In part by the National Science Foundation (Grant
a Chevron Fellowship.
# EAR-8311286)
and by
Table 1. Summary of Fracture Parameters
DEPTH
(m)
290
210
146
VSP Offsets 7 9 10
Model Inversion
STRIKE
DIP
K
(a)
(a)
( darcv)
4.7
N5E
""20
1.7
N35W
""30
",,20
5.8
N5W
Televiewer
STRIKE
DIP
(a)
(a)
N10E
N40W
""30
""40
•••
••• not acnuired
REFERENCES
Beydoun, W.B., c.H.Cheng and M.N.Toks6z, Detection of open fractures with vertical
seismic profiling: JGR, in press, 1 985.
Biot, M.A., Propagation of elastic waves In a cylindrical bore containing a fluid: Journal
of Applied Physics, 23, 997-1005.
Bower, D.R., Bedrock fracture parameters from the Interrpetation of well tides: JGR,
88, n.B6, p.5025-5035, 1983.
Cheng, C.H. and M.N.Toks6z, Elastic wave propagation in a fluid filled borehole and
synthetic acoustic logs: Geophysics, 46, p.1042-1053, 1981.
Cheng, C.H.; M.N.Toks6z and M.E.Wlllis, Determination of In situ attenuation from full
waveform acoustic logs: JGR, 87, p.5477-5484, 1982.
Cheng, C.H. and M.N.Toks6z, Determination of shear velocities in "slow" formations:
Transactions, 24th Annual SPWLA Logging Symposium, Calgary, Alberta,
Canada, June 27-30, 1983.
Huang, C.F. and J.A.Hunter, The correlation of "tube wave" events with open fractures
in fluid filled boreholes: Current Research, Part A, Geological Survey of
Canada, Paper 81-1 A, p.361-376, 1981.
9-8
Tube Wave Generation
213
Marquardt, D.W., An Algorithm for Least Squares Estimation of Nonlinear Parameters,
SIAM: journal of applied mathematics, 11, (2), 1963.
Paiilet, F.L, Acoustic propagation in the vicinity of fractures which intersect a fluid
fiiled borehole: Transactions, 21 st Annual SPWLA Logging Symposium,
Lafayette, Louisiana, July 8-11, 1980.
Paillet, F.L, Frequency and scale effects in the optimization of acoustic waveform
logs: Transactions, 24th Annual SPWLA Logging Symposium, Calgary, Alberta,
Canada, June 27-30, 1983.
Schoenberg, M., Elastic wave behavior across linear slip
Acoustical Soc. Am., 68, n.5, p.1516, 1980.
interfaces: Journal
Schoenberg, M., T.Marzetta, J.Aron and R.P.Porter, Space-time dependence of
acoustic waves in a borehole: Journal Acoustical Soc. Am., 70, n.5, p.1496,
1981.
Snow, D.T., A Parallel Plate Model of Fractured Permeability Media, Ph.D. dissertation,
University of California, Berkeley, California, 1965.
White, J.E., Underground Sound, Elsevier, Amsterdam, 1983.
Ziegler, T.W., Determination of Rock Mass Permeability, U.S. Army Corps of Engineers,
Waterways Experiment Station, Tech.Report S-76-2, January, 1976 (final
report), Appendix B.
9-9
214
(
Hardin & Toksoz
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610. Tube wave events are generated
at 210m., 290m. and 146m. (apparent
from downgoing tube wave). Upgoing
tube waves from below 41 Om. are
probably caused by reflections from
the hole bottom at ~490m. and a
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9-10
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Tube Wave Generation
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wave generating horizon at 210m.
Hardin & Toksoz
216
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wave generating horizon at 290m.
9-12
217
Tube Wave Generation
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#2, Hamllton, Mass.
9-13
Hardin & Toksoz
218
(uaec/ft)
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I
:~
"-l..!.
I
~
~
1\1
.
i
I
, i._
,
I ..1-
,i
I
't
-! !""'
(em dlL)
1 28
0
i
CAUPI!!R
'1
!
'
;/1
.
,
i
!
200
i
1
,
!
.
:
I
,
250
l"i
lSi
,
:
.
~
-
11i
I'-(
j.
~
I ,!
,
:
,I
i
/
300
,
i
.;
,
I
i
/ - - - - i : f - - - - i f - f . - - - f - - - - f 350
1-'-----'--4H----1 f-..&:~;............-t_...;-;~
(
I
I
I
;~ i i i
I I I,!
jl
r--.......:.LL.....:-.i...---II-..:.'.u'...!..~J....:.-'-.J....l-l400
I,
3~100m gradient
aubtracted
Figure 4(b). Sonic log (partial), caliper and reduced temperature logs from Britton well
#2, Hamilton, Mass. Borehole temperature has been reduced by subtracting a
least squares line which has a slope of 3.0 C ' /100 meters and a surface
(intercept) temperature of RJ9 ' C.
9-14
Tube Wave Generation
810
HYDROPHONES
FRACTURE
ZONE
Figure 5. Schematic of hydrophone VSP survey geometry, depicting observation well
and peripheral shotholes.
9-15
219
Hardin & Toksoz
220
gCOMPOSITE P-WAVE SPECTRA: 3 OFFSETS
...::,---..,...,,.,..,,,-.,,,..,...---.,..-----,-----..,
UJ
o
...
::::l
_l/'l
...I....
0..0
X
a:
(
UJ
>0
a:l/'l
3:0
I
0..
o
UJl/'l
.....'"
~Q
,. . '"'
,
~
t ···
~
···· . · r
.
a:
x
a:
0 0
Zo
9:1.00
20.00
40.00
60.00
FREQUENCY ( HZ)
'<10'
80.00
100.00
Figure 6. Composite amplitude spectra for arriving P-wavelets, for three different
offsets.
9-16
Tube Wave Generation
TIME
em•• c)
221
500
225
250
...
275
'"'
E
....
:t:
300
....0-
W
0
325
350
375·
400
Shotpoint Depth: S8.Sm.
Offset B10
Range: 130.8m.
Bearing: SSoE
Figure 7. Filtered digital section, corresponding to Figure 1 but extending to 500
msec in duration (one of three sections acquired).
9-17
Hardin & Toksoz
222
g 'OBSERVED' T:P RATIO: FRAC AT 290M" 3 0
o
co
_In
..... ,.:
0:
a:
......... ~
,~
.
~
LJ.J
00
:
..... .,; .......................
:::1 0
-
~
.
;
~
"
..J
0.
::l:
0:0
In
.....
0.'
..... '"
.,
~
.
,
~
__________87
;
--+---1
o
o
~+5-0-.0-0--2+-00-.-0-0--2-+5-0-.-00--3+-0-0.-0-0--135-0-.-0-0--l~00. 00
FREQUENCl ( HZ )
o
o
z
.,;-r---....,----,...----.,..-----.-----.
-.....
c
0:0
-'"
>",'
.,
,-
"
.. .. ,- -,
,~
-, ,-
.. -
-,
:
~
LJ.J
:89
~g
• 87
"
:
,-,
.
~ l~;;;t~~E==f·;81~O~:E~~
°150.00200.00250.00300.00
FREQUENCY ( HZ )
350.00
~00.00
Figure 8. Composite tube-to-P amplitude ratio spectra with computed standard
deviation, for the three offsets, and the tube wave event identified with the
generating horizon at 290m.
9-18
223
Tube Wave Generation
OBSERVED & FITTED T:P RATIO
. Offsets
B7, B9, B11 B10
2~---"""---""'---""'---""'---'"
~
.
.
r.
~
~
········t··············.. ·······r·············..····
~
::c
..
.
~V~""",..:·J.;B~1~0;....·J.·I=.. ·.=. ·.=. ·.:. j
OB~:
-I
<:t:
.
;
II'l
~.
N
.
.
i..
.
.
.:.
.:.
.:.
;
: B7
:
.
';-----+----+----j.---;-----i
200.
2 O.
300.
350.
~OO.
~ O.
FREQUENCY
(HZ)
Figure 9. Comparison of theoret/al tube-to-P amplitude ratio curves from nonlinear
inversion with the curves generated from the data, for the three offsets, and
the tube wave event originating at 290m.
9-19
(
Hardin & Toksoz
224
-...
o
(I)
( I)
E
~
t-
a.
W
C
294
. :-:,.:~
~;
'.
Figure 10. Borehole televiewer images of the generating horizons at 210 and 290m.
depth.
9-20
Tube Wave Generation
FLUID PAAA"ETERS
FOft"ATION PAAA"ETERS
VP
IH/S!
-5800.
VP
VS
lH/S!
-3300.
AHO
-2700.
VISCo
AHO
lKG/H3!
225
IH/S!
-1500.
IKG/H3!
-1000.
IPLl
I NCOHP.
-0.0010
IGPA! -2.00
P-WAVE/FAACTUAE INCIDENT ANGLE -0.0
P-WAVE/80AEHOLE AXIS ANGLE -0.0
80AEHOLE AAD I US
ICH)
-15.20
CURVES. 80110H- TO- TOP. PEAHEA81 LI TY
g
1.00 - 2.00 - 5.00 -
IDAACrS)
10.00 - 20.00
0.,.--:--.:--:-_.....,.........,.........,....--:-.....,.........,.........,.........,.........,.........,.........,.........,.........,.........,....---:----,
(I')
o
~
~
-~-:-
~:;
"""1 -~. ,-
-f. - , -
==-
10
i!
-;-.,. -i- --:-:- -!- r -!- ~ _·,!_·-t-r- -:-":--1J_l.. _:_.i- _:_ -:. _~ J _ ~ _!_l.. _~_.1 _!_J._.L..J_.L_i_
"4-.
~
-
~
~
i
-: -
;
-; -
!
i
:
t -~~ ;" - i-" i - ;- : _. t -f'-
_....:. -:- -; -;- -:- -:- -:- -:- -<- -..;.-,,:- -;-. .;-.-;.-
N
.
_.-
~
-
. , . . . . . .! ,' ., ,!
~ ~
-
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-:- -!- .. -!-':
-"~ ~'-":'-~-
'
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,-----------.-~-.--------.-
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.
a:o
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LU~
a:
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:
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I
-:-
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-
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- : - - : - '7 - : - '7
-:-
~
-!-
,,
~
-!-,~ -,~~
,,
-j-'~
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-
~
-:-
-r-",'-r -;,.,.
-~~-~~-~_:_--~~-~,-~-
;::l
l
(/')
(/')0
i;
l:
-!-;- -;- t -;,
,
~
-!"-
~-
r-
I
-~-
",;
_._--(---_._;-)--
LUo
a:'
a..~
3:
a..
......
3:0
1-0
<0
3--~...,
-c-~--:--~'~
~._;- -~ - ~ -,- -: - ~ ~ - ~
~ -~~-~_._--
o
-~-------i -
-r -;;;:-: -~::
d'
,
---,--"-
-+- - i- --+ -:- -; - ;- -:-
~+o-•. Lo0--:......:..-1.;..3-0-.0:""0:-':'-2+-'1-=-0~.0:-:0'-'-:-2i:-~O::-.~0::O'---'--:i3'7: 0: -~-=O-: 0 --,-'~lj5 O. 00
FREQUENO'
(HZ)
Figure 11. Theoretical tube-to-P amplitude ratio vs. frequency, for the Britton well
#2, Hamilton, Mass. (Borehole radius: 0.152m. Formation properties used are
ex 5.8 kmjsec, (J 3.3 kmjsec, P 2.7 gmjcc. Fluid properties are txt
1.5
kmjsec, PI = 1.0 gmjcc.)
=
=
=
9-21
=
226
(