FRACTURE DETECTION AND
CHARACTERIZATION
by
M. Nafi Toksoz and Fatih GuIer
Earth Resources Laboratory
Department of Earth, Atmospheric, and Planetary Sciences
Massachusetts Institute of Technology
Cambridge, MA 02139
ABSTRACT
The effects of fractures on full waveform acoustic logs are studied on the basis of field
observations, available theoretical models, and a series of ultrasonic laboratory experiments. Results from diffusion models applicable to fine microfractures and finite difference models of isolated fractures are reviewed. Laboratory experiments are carried
out with fine microfractures around the borehole in a Lucite model, and isolated single
fractures in aluminum models. Cases of horizontal and inclined (45°) fractures are
studied as a function of fracture aperture and frequency of Stoneley waves. A vertical
fracture model is also studied. Results indicate that the effect of different fractures are
manifested differently on P, S, pseudo-Rayleigh, and Stoneley waves. Micro-fractures
surrounding a borehole attenuate Stoneley waves most strongly. Vertical fractures attenuate Stoneley waves more strongly than other phases in the wave train. Horizontal
and inclined fractures have a greater effect on P and S waves than on Stoneley waves.
INTRODUCTION
An important application of full waveform acoustic logging is the detection of open
fractures and the determination oftheir hydraulic conductivities. Studies based on field
data (Arditty and Staron, 1987; Paillet, 1983; Paillet et a!., 1987; Hardin et a!., 1987),
theoretical modeling (Stephen, 1986; Mathieu and Toksoz, 1984, Tang and Cheng, this
issue), and ultrasonic laboratory models (GuIer and Toksoz, 1987; Lakey, 1985, Poeter, 1987) have been used to relate acoustic log characteristics to fracture properties.
All studies show that full waveform acoustic logs are attenuated by fractures. The
magnitudes of attenuation of different phases, such as the P, S, pseudo-Rayleigh, and
Stoneley, have been different. Even for a given wave type, such as the Stoneley propagating across a fracture, the field results show complete attenuation in some cases and
little attenuation in others. Theoretical results, obtained using different techniques
106
Toksoz and GUIer
and different assumptions in formulating the problem, have yielded different results.
Why are there such differences?
The purpose of this paper is to re-examine these results with the aid of new laboratory studies in order to provide a phenomenological explanation for acoustic wave
attenuation across fractures. In the next section we review some field data and theoretical models. In the third section we present the new ultrasonic laboratory results.
FIELD OBSERVATIONS AND THEORETICAL PREDICTIONS
Field Data
Most field studies of fractures by full waveform acoustic logging have been conducted
in crystalline rocks in the United States and Canada by a U.S.G.S. scientist (Paillet,
1983, Paillet et a!., 1987) and in Europe and other parts of the world by Elf-Aquitaine
investigators using E.V.A. (Arditty and Staron, 1987). The logging tools used in these
two studies are quite different. U.S.G.S. logs were made with relatively high frequency
tools, with frequency responsed peaked at greater than about 10 kHz. E.V.A. has a
broadband response between about 2 and 15 kHz. To our knowledge, no benchmark
field experiment with different full waveform acoustic tools has ever been carried out
in the same borehole.
Figures 1a and 1b show iso-offset (2.1m spacing) plots of full waveform acoustic
logs in Britton well #2 in Hamilton, Massachusetts. The well was drilled in crystalline
rocks that are primarily granitic gneiss. The fracture zones in the borehole are well
documented by conventional logs, temperature logs, a borehole acoustic televiewer,
television and hydrophone surveys (Hardin and Toksiiz, 1985). Some prominent fractures are clearly visible in Figures 1a and 1b at depths of 209,212 and 290m. Compressional and shear head waves and pseudo-Rayleigh waves are significantly or completely
attenuated at open fractures. Stoneley waves are not generated because of the large
diameter (30 cm) of the borehole. Scattering of waves at a 209m fracture is observed,
but at other fractures, significant scattering is not observed.
Another example of acoustic attenuation at fractures is shown in Figure 2. Data
are from a well in crystalline rock in Mirror Lake, New Hampshire (Hardin et a!.,
1987). Various degrees of attenuation are seen at different fractures and identified
by an acoustic televiewer. P and pseudo-Rayleigh waves are significantly attenuated.
Stoneley wave attenuation appears to be less than that of the P wave.
Figure 3 shows an iso-offset section of E.V .A. logs from a borehole in crystalline rock
in France (Mathieu and Toksiiz, 1984). These broadband logs clearly show Stoneley
waves with a frequency of about 2.5 kHz. The fracture completely attenuates P, S,
Fracture Detection and Characterization
107
completely attenuated. This is the clearest evidence that Stoneley waves propagate
across fractures more efficiently than P or pseudo-Rayleigh waves.
Theoretical Studies
There are three different studies of wave attenuation across fractures. The first is
by Mathieu and Toksoz (1984). It treats the problem of Stoneley wave attenuation
across a horizontal fracture as a function of fracture, aperture, frequency, formation
and fluid properties. The problem is formulated with the assumption that attenuation
results from reflection at a borehole-fracture intersection and as a result of fluid flow
into the fracture. Scattering of Stoneley waves into other wave types are ignored.
The attenuation mechanisms are schematically shown in Figure 4. The Stoneley wave
attenuation A is defined by
(0.1)
where PI and PT are incident and transmitted pressure amplitudes at a given frequency,
respectively.
Attenuation as a function of fracture aperture, at three frequencies, is shown in
Figure 5a, for a borehole with 3.8 cm radius. For the "slim" borehole, the frequency
dependence is small, but the dependence on fracture aperture is strong. The theoretical
curves for borehole radii of 5, 10 and 15 cm are shown in Figure 5b. Attenuation
decreases with increasing borehole radius. The formation properties correspond to
those of a crystalline rock with "If" = 5850 m/sec, V. = 3350 m/sec, and P = 2.65
g/sec. The fluid is water. Note that although the figures show attenuation as a
function of fracture aperture, the important parameter is the hydraulic conductivity
or transmissivity (T) which is related to permeability (E) and fracture aperture (L)
by
(0.2)
T=E·L.
Furthermore, it is assumed that flow is laminar and governed by Darcy's Law; cubic
law for flow in fractures applies (Snow, 1965; Van Golf-Racht, 1982). With these
assumptions, transmissivity (T), fracture aperture (L) and fluid parameters are related
by (Paillet et aI., 1987)
L3
T = Pi' 9
(0.3)
12JL
where Pi = fluid density, 9 = acceleration of gravity, and JL = fluid viscosity. Thus, in
Figures 5a and 5b the fracture aperture can be converted to equivalent transmissivity
or permeability.
It is important to keep in mind that the nature of assumptions limit the application
of attenuation curves given in Figures 5a and 5b to cases where Darcy flow apply-small
(
108
Toksoz and Giiler
aperture fractures. In addition, since wave scattering is neglected, the model cannot
be applied to large fractures. Paillet and Hess (1986) and Paillet et al. (1987) found
that the Mathieu model gave good results when applied to multiple and fine fractures.
Figure 6 shows the theoretical attenuation curves as a function offracture permeability,
in a model where the fractured zone contains 100 to 2,000 fine fractures per meter. In
this case the assumptions involved in theoretical formulations are satisfied. The curves
show that if permeability of the zone is 10 darcy, the high frequency tube waves are
almost completely attenuated over a 2-foot interval.
A more complete model of Stoneley wave attenuation across a horizontal fracture
is presented in a paper by Tang and Cheng in this report. The basic assumptions are
similar to those of Mathieu and Toksoz, except propagation effects along the fracture
are taken into account along with the viscous flow effects. The result is a model that
is similar to the Mathieu and Toksoz model at low frequencies and high viscosities,
but have larger dependence on frequency, fracture aperture, and viscosity. Tang and
Cheng were able to fit the model to the data of Poeter (1987).
The attenuation of full waveforms crossing an isolated horizontal fracture was calculated by Stephen (1986) using the finite difference approach. The model is perfectly
elastic, without intrinsic attenuation. Neither Biot nor Darcy type flow is included in
the calculations. Figures 7a and 7b show synthetic full waveform acoustic logs for a
vertically homogeneous sandstone and for the same sandstone with 1 cm thick horizontal fracture. The fracture attenuates P, pseudo-Rayleigh, and Stoneley waves at
15 kHz by about a factor of 2; Stoneley attenuation is less that that of P. There is an
observable Stoneley wave reflected from the fracture. Frequency dependence of attenuation and complex scattering can be observed by comparing Figures 7a and 7b. Clearly
in the case of isolated major fractures, numerical solutions are required to understand
scattering and attenuation. At the present time, these calculations can be done only
for horizontal fractures. Also, numerical codes for very thin fractures and those that
incorporate fluid flow, need to be developed. The laboratory models discussed in the
next section provide a physical insight into such cases.
LABORATORY MODELS OF FRACTURES
Laboratory modeling of acoustic wave propagation in a borehole complements the
theoretical studies for the understanding and interpretation of field data. In this section we describe the ultrasonic laboratory results of the effects of fractures on full
waveform acoustic logs. There are few papers on laboratory studies of full waveform
acoustic logs in a borehole (Chen, 1982; Lakey, 1985; Shortt, 1986; Giiler and Toksoz,
1987, Poeter, 1987). Except for Giiler and Toksoz (1987), none of these addresses
the problem of vertical fractures. One difficulty of laboratory work is the complexity
of experiments, particularly adequate scaling of physical dimensions and wavelengths.
(
(
(
Fracture Detection and Characterization
109
The second problem arises from the complexity of waveform microseismograms which
require sophisticated analysis for the identification of wave types and interpretation of
the results.
Two separate experiments are carried out. The first studies the effects of microcracks around the borehole. The second studies the isolated single fractures that are
horizontal, inclined (45°), or vertical. Wavelength scaling is used to determine the
physical dimensions of the model, including the borehole radius. The frequency response of the source-receiver transducers covers a range of 30 kHz to 600 kHz. The
modeling materials are Lucite and aluminum. The borehole diameter is 1 em. With
these specifications, the aluminum model corresponds to a 2 to 30 kHz frequency band
in the field with a 20 em (8") diameter borehole. The data are collected with a fixed
source and a moving receiver.
Lucite and aluminum with a diameter of 20 em (8") and a length of 30 em (12")
are used for the experiments. Each cylinder is center drilled and reamed to produce
a smooth 1 em diameter borehole. Full waveform experiments are performed before
fractures are introduced, and repeated with fractures. The experimental set-up and
procedures are described in detail in an earlier paper (GuIer and Toksoz, 1987).
Microfractures Around the Borehole
The first set of experiments investigate the effects of microfractures on the attenuation
of full waveform acoustic logs. Lucite cylinder was used for the experiments. After
the borehole was drilled, the first data set was collected. In the following weeks small
microcracks developed around the borehole due to stress relaxation. There were horizontal, vertical, and inclined fractures with characteristic dimensions of millimeters.
Fracture density decreased away from the borehole and no fractures extended more
than 10 mm beyond the borehole wall. In one region there was a predominant vertical fracture. In others, orientations appeared to be random. The borehole remained
smooth and intact, and no material fell from the wall. A schematic diagram of the
cylinders is shown in Figure 8, before the fractures formed and after.
The full waveform microseismograms are shown in Figure 9 for the crack-free and
cracked cases. To the left (Figures 9a and 9c) are broadband microseismograms, and
to the right (Figures 9b and 9d) are the filtered waveforms showing the Stoneley waves.
The P velocity in Lucite is 2.4 km/sec and the S velocity is 1.4 km/sec, slightly less
than sound velocity in water. In Figure 9a, P waves, P leaky modes, and Stoneley
waves are visible. The small pulse at about 80 J1 / sec is the P wave reflected from the
outer surface of the cylinder.
To separate the Stoneley waves, we use a pie-slice or fan filter in the f-k domain.
Especially in the later experiments, where there is an overlap in time between Stoneley
110
Toksoz and Giiler
and pseudo-Rayleigh, the fan filtering is more effective than low-pass or band-pass
filtering. In the f-k domain, both the individual modes and the frequency band where
a given mode has adequate power, is separated. To look at different frequency bands,
both fan- and band-pass filtering are used.
The Stoneley waveS shown in Figure 9b are attenuated. The Q value calculated is
25 and close to the shear wave Q of Lucite. The group velocity of Stoneley waves is
about 1.0 km/sec and there is no significant dispersion in this frequency range.
Figures 9c and 9d show the results from a model with microcracks. Crack density
IS not uniform along the borehole. In the 10 to 30 mm distance range, there is a
prominent vertical fracture. Randomly oriented fractures dominate a 30 to 80 mm
distance range. The attenuation of all phases are clearly shown. The Stoneley waves
are dispersed and strongly attenuated. Since we could not measure fracture apertures
or permeability, we cannot determine how much of the attenuation is due to fluid flow
versus increased shear wave attenuation in microfractured zone. Note that P waves
and high frequency P leaky modes are visible, and they are attenuated less than the
low-frequency Stoneley waves. We judge that fluid flow plays a major role in the
Stoneley wave attenuation.
Isolated Fractures
Three types of single fractures-horizontal, inclined at 45°, and vertical-were studied.
Geometries are shown schematically in Figure 10. Aluminum cylinders, 20 em in
diameter and 30 em long, with 1 em diameter borehole were used. For horizontal
and inclined fracture cases, the block was sawn in two after the initial measurements.
For vertical fractures, a 1 mm sew-cut was make parallel to the axis, dissecting the
borehole and the block. The vertical extent of the fracture was 15 em.
For horizontal and inclined fractures, measurements were made with different fracture apertures, ranging from 0.2 mm to 4.5 mm. The source-receiver spacing was
increased from 2 to 86 mm, at 2 mm increments. The fracture was centered at about
38 mm. In each case the broadband microseismograms were recordered. Different wave
types were identified in the f-k domain. Stoneley waves were separated by fan filtering. Attenuation at different frequency bands was determined from band-passed and
fan-filtered microseismograms. Frequency bands were determined from the f-k spectra.
For vertical fractures, measurements were made for one aperture equal to 1.00 mm.
The results for each case are discussed below.
Fracture Detection and Characterization
111
Horizontal Fractures
Measurements were made with fracture apertures of 0.2, 0.5, 1.0, 2.5, and 4.5 mm.
The thinnest fracture case corresponds to aluminum blocks sitting on top of each
other held apart by the roughness of the polished surfaces and a layer of water. In
other cases the blocks were separated by shims to obtain the desired aperture. The
broadband microseismograms are shown in Figure 11, for four apertures. In addition to
P, S, and Stoneley, several modes of pseudo-Rayleigh waves are recorded. Attenuation
and scattering of different waves, as a function of fracture aperture are indicated.
The Stoneley waves, separated by f-k filtering, are shown in Figure 12. As fracture
aperture increases, so does the reflection from the fracture. Broadband and filtered
microseismograms for the 0.5 mm wide fracture case are shown in Figure 13. Note
that the Stoneley attenuation is substantial in this case.
To analyze the effects of fracture on Stoneley waves, the rms amplitude is plotted
as a function of source receiver separation for three frequency bands centered at 50,
85, and 135 kHz. Since there is no geometric spreading and insignificant attenuation
in water and aluminum, if it were not for the fracture, Stoneley amplitudes would be
constant as a function of distance. Figure 14 shows the amplitude plots. There are
three major observations:
1. Attenuation is greatest at lowest frequency and least at highest frequency.
2. At low and intermediate frequencies, attenuation increases from 0.2 mm to 0.5 mm
fracture aperture, decreases at 1.0 mm, and then increases again at 2.5 mm and
4.5 mm.
3. As the fracture is approached, the Stoneley amplitudes oscillate and generally
increase before the fracture. This last observation can be explained by the interference of the incident and reflected waves as the receiver approaches the fracture.
The first observation is consistent with the model of Mathieu and Toksoz and
that of Tang and Cheng. The second observation points out the fact that Stoneley
wave attenuation across a fracture cannot be explained by fluid flow alone. Scattering
from the fracture has to be taken into account. At large apertures and relatively
high frequencies, the viscous effect becomes minimal and attenuation across a fracture
is due primarily to the scattering from the fracture and wave propagation along the
fracture away from the borehole. Comparing the microseismograms (Figure 13) and
amplitudes (Figure 14) with the finite difference synthetics (Figure 7b) shows similar
amplitude decrease across the fracture, although the latter ignores viscous effects. In
experiments, P wave amplitudes decrease more than those of model calculations, and
this may be due to greater impedance contrast between aluminum and water than
between the sandstone and water used in finite difference models.
112
Toksoz and Giiler
The decrease of attenuation as a function of increasing frequency of Stoneley waves
can be attributed to the borehole diameter to wavelength ratio. At a short wavelength
the borehole acts like a finite piston. The Stoneley pulse propagates across the aperture
with little or no disturbance and couples to the borehole on the other side. At long
wavelengths, the end of the borehole acts like a point source. Although these arguments
are qualitative, physically they are consistent with observations.
Inclined Fractures
The broadband microseismograms for 45°inclined fractures are shown in Figure 15 for
four fracture apertures-O.O, 1.0,2.5, and 4.5 mm. Attenuation increases with increasing fracture aperture. Also, the zone of attenuation is broadened because of the fracture
inclination. The f-k filtered Stoneley waves are shown in Figure 16. No reflections are
observed from the attenuation appear to be more significant than the horizontal fracture case. The Stoneley amplitudes as a function of distnace, at three frequency bands
are shown in Figure 17. There is no attenuation across the 0.0 mm fracture. In this
case the surfaces were machined and polished to obtain greater smoothness than the
horizontal case. Attenuation is greater at low and intermediate frequencies than at
high frequencies. Amplitude decrease is spread to a wider depth zone than the horizontal fracture case. There is a decrease in attenuation as fracture aperture increases
from 1.0 mm to 2.5 mm.
The Stoneley attenuation as a function of fracture width and frequency is shown
in Figure 18 for horizontal and inclined fractures. In both cases attenuation is greater
at lower frequencies. The increase of attenuation with increasing fracture width is
similar in both cases. At the lowest frequency, the horizontal fracture attenuates the
Stoneley waves more than the inclined fracture. Both sets of measurements suggest
a dual mechanism for attenuation. In the case of very thin fractures (L ::; 1.0 mm),
fluid flow may playa significant role. In the case of thicker fractures, scattering is the
primary mechanism of attenuation.
Vertical Fractures
Broadband and f-k filtered microseismograms for a borehole with a vertical fracture
1 mm wide are shown in Figures 19a and 19b, respectively. The broadband microseismograms show the attenuation and scattering of waves. P wave attenuation is slight.
There is an S to P scattering at the fracture tip. The high frequency components
of pseudo-Rayleigh waves are not attenuated significantly. In fact, they may increase
due to Stoneley to pseudo-Rayleigh scattering. The Stoneley waves attenuate slowly
once they encounter the fracture and propagate in the fractured section. There are no
observable reflections.
Fracture Detection and Characterization
113
Amplitudes of P, S, pseudo-Rayleigh, and Stoneley waves as a function of increasing
distance are shown in Figure 20. Stoneley attenuation in the fractured zone is significant. The S attenuation increases in the fractured zone, most likely due to scattering.
P wave attenuation is slight; pseudo-Rayleigh shows no attenuation. In fact, its rms
amplitude increases possibly due to energy scattering into this mode.
The frequency dependence of Stoneley attenuation along the vertical fracture is
shown in Figure 21. Attenuation is greatest at the lowest and decreases with increasing
frequency.
CONCLUSIONS
The detection and characterization of fractures by full waveform acoustic logs requires
a multifaceted approach, including field data, theoretical modeling and laboratory
studies. Based on the available theoretical models and ultraosnic laboratory studies, we
conclude that the effects of fractures on full waveform logs depend upon: (1) whether
fractures are single, isolated with apertures of millimeters or greater, or a series of
microfractures that intersect the borehole; (2) on the attitude (horizontal, inclined,
or vertical) of the fracture plane; (3) on the wave type (P, S, pseudo-Rayleigh, or
Stoneley); and (4) on frequency. Fluid flow and wave scattering play major roles in
affecting the full waveform logs.
In the case of microfractures, Stoneley waves are strongly attenuated while other
phases in the wave train are less attenuated. In the cases of horizontal or inclined
isolate fractures, P and S waves are attenuated more strongly by the fracture. Stoneley attenuation decreases with increasing frequency. In the case of vertical fractures,
Stoneley waves are attenuated more strongly than P or pseudo-Rayleigh waves. Again,
Stoneley attenuation is greater at lower frequencies.
ACKNOWLEDGEMENTS
This research was supported by the Full Waveform Acoustic Logging Consortium at
M.LT.
114
Toksoz and Giiler
REFERENCES
Arditty, P.C. and Staron, P., Lithologic analysis and fracture detection for EVA data:
Examples in open and cased holes, Sonic Fullwave Research Workshop, Soc. Expl.
Geophys. 57th Ann. Mtg., New Orleans, 1987.
Chen, S.T., the full acoustic wave train in a laboratory model of a borehole, geophysics,
47, 1512-1520, 1982.
GUIer, F. and Toksoz, M.N., Ultrasonic laboratory study of full waveform acoustic logs
in boreholes with fractures, M.l. T. Full Waveform Acoustic Logging Consortium
Annual Report, 511-530, 1987.
Hardin, E.L. and Toksoz, M.N., Detection and characterization of fractures from generation of tube waves, Trans. SPWLA 26th Ann. Logging Symp., Paper II, 1985.
Hardin, E.L., Cheng, C.H., Paillet, F.L., and Mendelson, J.D. Fracture characterization
by means of attenuation and generation of tube waves in fractured crystalline rock
at Mirror Lake, New Hampshire, J. Geophys. Res., 92, 7989-8006, 1987.
Lakey, K.G., Physical modeling of the full acoustic wave train in a borehole with a
perpendicular fracture, M.S. thesis, Washington State University, Pullman, Washington, 1985.
Mathieu, F. and Toksoz, M.N., Application of full waveform acoustic logging data to
the estimation of reservoir permeability, Proc. Soc. Expl. Geophys., 54th Ann. Int.
Mtg., Atlanta, Georgia, 9-12, 1984.
Paillet, F.L., Acoustic characterization of fracture permeability at Chalk River, Ontario, Canada, Geotech. J., 20, 468-476, 1983.
Paillet, F.L. and Hess, A.E., Geophysical well log analysis of fractured crystalline
rocks at East Bull Lake, Ontario, Canada, U.S. Geological Survey Water Resources
Investigations Report 86-4052, 1986.
Paillet, F.L., Hess, A.E., Cheng, C.H., and Hardin, E.L., Characterization of fracture permeability with high-resolution vertical flow measurements during borehole
pumping, Ground Water, 25, 28-40, 1987.
Poeter, E.P., Characterizing fractures at potential nuclear waste repository sites with
acoustic waveform logs, The Log Analyst, 28, 453-461, 1987.
Shortt, E.R., Laboratory borehole model, M.l.T. Full Waveform Acoustic Logging Consortium Annual Report, 461-470, 1986.
Snow, D.T., A parallel plate model of fractured permeable media, Ph.D. thesis, Uni-
Fracture Detection and Characterization
115
versity of California, Berkeley, 1965.
Stephen, R.A., Synthetic acoustic logs over bed boundaries and horizontal fissures,
M.LT. Full Waveform Acoustic Logging Consortium Annual Report, 365-414, 1986.
Tang, X.M. and Cheng, C.H., A dynamic model for fluid flow in a borehole fracture,
M.I.T. Full Waveform Acoustic Logging Consortium Annual Report, 87-104, 1988.
Van Golf-Racht, T.D., Fundamentals of fractured reservoir engineering, Elsevier, Holland, 1982.
116
Toksoz and Giiler
TIME (lJsec)
490
890
12pO
16pO
2000
285
.....
....e
~ 290
c.
w
Q
295
Britton Well 2
TX - Rx Spacing 2.1 m
Figure 1a: Full waveform acoustic log traces from an interval encompassing the tube
wave generating horizon at 210m.
\.
Fracture Detection and Characterization
117
TIME (lJsec)
Q
.490-
890· .12pO_
1SPO
2000
J:
IQ.
W
C
Britton Well 2
Tx - Rx Spacing 2.1 m
Figure Ib: Full waveform acoustic log traces from an interval encompassing the tube
wave generating horizon at 290m.
118
Toksoz and Giiler
Fractured Zone
!
Time
Depth
(
Time
Figure 2: Full waveform acoustic data recorded after a hydrofracturing experiment.
Fracture Detection and Characterization
119
Full Wav.farm Acauatlc ~all
TIMI (IIISIC)
o
0.4
D.•
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!
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;n.i••
,
i-I'("
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to 60 meters containing tube wave generating horizon at 44 meters. Separation:
0.91 meters, approx. source band center frequency: 15 kHz. Stoneley packet can
be distinguished from pseudo-Rayleigh, although not at every depth.
Toksoz and Giiler
120
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I
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fracture.
121
Fracture Detection and Characterization
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~-t-~i-~+-~~-~-l-+-~'~-~~-~-i-
!
:
!;:
20. 00
ijO. 00
FRACTURE WIDTH
:
60.00
(H I CRI)NSJ
:
80.00
100.00
'<10 '
Figure 5a: Frequency effect on attenuation in the case of a single fracture.
Toksoz and Giiler
122
FORHRTION PARAHETERS
VP IH/SI
-saso.
VS IH/S)
-3350.
RHO IKO/H31 -2650.
FLUID PARRHETERS
VP IH/SI
RHO IKO/H31
-1500.
-1000.
VI5C.
-0.0010
IPLI'
INCOHP.
IOPRI -2.00
FREQUENCY IKHZI -3q.
aOT - TOP aOREHOLE RAD II
ICH):
15.00 - 10.00 - 5.00
o
co
o
o
N
o
o
c+-~::::"':"-+-':"'-':"'-:""-~~~-;-":-":---:''''';'-':''--'---'---i
C;J.OO
20.00
qo.OO
FRACTURE WIDTH
60.00
(MICRONS)
ao.oo
100.00
><10'
Figure 5b: Borehole radius effect on attenuation in the case of a single fracture.
123
Fracture Detection and Characterization
FORMRTION PRRRMETERS
FLUID PRRAMETERS
1M IS)
VP
IM/S)
-5a50.
VP
VS
IM/S)
-3350.
RHO
RHO
IKG/H3) -2650.
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ICM)
1KHZ)
-0.0010
IGPRI-2.00
-3.ao
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FREOUENCT
-1000.
IPLI
INCOMP.
aOREHOLE RADIUS
-ISDO.
IKG/M3)
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-3~.
aOT-TOp ISO-OENSITIES.
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o
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9:1.00
1.20
PERMERB I LI TY
2.40
3.60
~.ao
6.00
(LClG I 0 (M I LLI DRRCYS) )
Figure 6: Attenuation versus permeability in the case of a fractured zone.
Toksoz and GiiIer
124
TIM E (msee)
o
1 50 -\-
2.0
1.0
1.0
0
2.0
.L..-'_--,
--L;-:--
I---+---Iv'«
\"Mllt-I----~
\' \11'
.•1.
a
x1
0.0
x10
b
10.5 em
0.0
(
mud1
sandstone
(
15 kHz
e
Figure 7a: Synthetic full waveform acoustic log for a vertically homogeneous sandstone.
125
Fracture Detection and Characterization
TIM E (msee)
o
1.0
2.0
150
.. ,
.1.
"iV'
::I:
I-
.!l
20 0
" Vi"
-.
.,!.
"VI
a..
••1.
LU
Cl
2.0
.nAI
'Vi'
E
£.
1.0
0
,
·'v'-
25o·
.1.
'Y\'
.AI
.'V"
,1ft.
30 0
VV'
a
x1
0.0
x10
b
10.5 em
0.0
mud1
sandstone
215 em
1 em
sandstone
15 kHz
e
Figure 7b: Synthetic full waveform acoustic log for a 1 cm thick horizontal fissure.
126
Toksoz and Giiler
(
Figure 8: Schematic diagrams of borehole in Lucite: intact (left) and microfractured
(right).
127
Fracture Detection and Characterization
'Y~
"
'Ii'"
~
', - - ',
~
r---""'"
,
S
2
~
~
r:
.-
/0:
/0:
E
~
:,..-
40
"F 40
•=
~
•
;...::::
-:;:::::
'6
r:-::::::=
80
80
j
0
2
time(l'sec)
time(l'sec)
60
a
120
•
120
b
2
:.....-,..' N
,:-~f.
80:
80 :
time (I'sec)
time(l'sec)
o
60
60
c
120
a
60
120
d
Figure 9: Broadband microseismograms (left) and Stoneley waves (right) recorded in a
borehole in Lucite. Top: without microcracks around the borehole, Bottom: with
microcracks around the borehole.
128
Toksoz and Guier
Figure 10: Schematic diagrams of aluminum models with single isolated fractures. Left:
horizontal fracture. Middle: fracture inclined at 45°. Right: vertical fracture.
129
Fracture Detection and Characterization
2 =:::""
:~
R'i'~~
~-~\
!
4
r,~~
~
~
~
;:r:;;
=
~
$
80
time(l'Uc)
time(l'Uc)
o
2
120
60
a
".
::::::I,~
=,'
-'
2
v..c
~
=:::::.J,~
120
b
~
~
60
0
~
NL~
~
II
'~~
'M
40
;.:r .v
\
'Ji
,.
t
80
~
~
80
time(l'8oc)
o
60
C
120
o
60
120
d
Figure 11: Broadband microseismograms of full waveform acoustic logs as a function
of increasing source-receiver distance. A horizontal fracture intersects the borehole
as indicated on the vertical axis. Fracture width: (a) 0.2 mm; (b) 1.0 mm; (c)
2.5 mm; (d) 4.5 mm.
Toksoz and Giiler
130
2~
~
~
~
~
f'
.'
4 -;
80 :
80 :
j
o
l
~
time(!"ec)
time(!',ec)
120
60
o
B:
~g:
=
80 '
80 :
o
60
~
c
120
o
I
\
~:
time(!"ec)
time (!,'ec)
60
d
!
120
60
b
I
~
120
Figure 12: Stoneley waves, obtained from broadband microseismograms by f-k filtering, crossing a horizontal fracture. Fracture is indicated on the left vertical axis.
Fracture width: (a) 0.2 mm; (b) 1.0 mm; (c) 2.5 mm; (d) 4.5 mm.
Fracture Detection and Characterization
131
~
'-..l-J"I
· >:f~~
~
:~'\i0~
-;fj '" ..
:
~~, ~
,
-
=::/'
.)
w
:.A
i
~
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~
;
,
-----'
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"7i~
~
~
::::.;:
ev:--
80
"
I
time(~8eC)
o
60
120
•
'iii
I
! 40~
U!
80.
~:
~:
:; :
~
~
---..
..r---
-v---..r-
time(Jlsec)
0
60
b
~
I
120
Figure 13: Broadband microseismogram and filtered Stoneley waves in a borehole with
a 0.5 mm horizontal fracture.
132
Toksoz and Giiler
~,
,
is
•
.••
0.2 rom
1l
&
=
/
l.Omm
/
0.5
0
mm
2.5 mm
4.5 mm
,
a
O.~mm
-
"---
~
O.§.mm
~".
l.Omm
~
2.5 mm _______
4.5 mm
b
O.5mm
1.0
m
2.5... mm
4.5"ln.m
60
10
distance(mm)
Figure 14: Amplitudes of Stoneley waves as a function of distance along the borehole
with a horizontal fracture. Fracture widths are shown on each curve. The curves
are shifted vertically to separate them. The amplitude axis is on the left. The
fracture is shown at the bottom axis. The three figures are for three different
frequency bands centered at: (a) Ie = 35 kHz; (b) Ie = 85 kHz; (c) Ie = 135 kHz.
133
Fracture Detection and Characterization
80 :
80
time(ll·ec)
o
60
time(ll.ec)
120
0
•
60
b
i
120
2~,::
~
""
~ 4
E=
••
."
80 :
80
time (,usee)
time{,usec}
o
60
c
120
o
60
120
d
Figure 15: Broadband microseismograms of full waveform acoustic logs in a borehole
intersected by a 45°inclined fracture. Fracture width: (a) 0.01 mm; (b) 1.0 mm;
(c) 2.5 mm; (d) 4.5 mm.
Toksoz and Giiler
134
~
80
'3::
i
o
60
a
120
~?si2
§:
I~I
I
80 :
l
60
120
I
:
;:---.J
time(~sec)
c
120
I
4cl
~
o
60
b
0
5'
~
80 '
time (,usee)
:
time(,usec)
o
60
d
~
120
Figure 16: Stoneley waves separated from microseismograms in Figure 15 by f-k filtering. Inclined fracture with thickness (a) 0.01 mm; (b) 1.0 mm; (c) 2.5 mm; (d)
4.5 mm.
Fracture Detection and Characterization
.....Dmm
,
v
'"
135
.~
Q.
E
•
..'"
1.0mm
.~
/
E
"
=
/
0
2.5 mm
0
4.5 rnm
•
/
1111
mm
• ,
'"E
/
:aE
l.Omm
/
•
..
'"
.~
/
"
=
0
rom
2.5
E
0
4.5 rom
/
b
"'"
11111
•
']
'""E
•
11
:.;"
/
§
=
/-
2.5 rnm
0
4.5 mm
,
20
.111101.....111111111111111
50
distance(mm)
Figure 17: Stoneley amplitudes as a function of distance at three frequency bands for
an inclined fracture. (a) j, = 35 kHz; (b) j, = 85 kHz; (c) j, = 137.5 kHz.
136
Toksoz and Giiler
'~
~
•
"
.~
]~
.••
~
1.0.·
:\
1'=135 KH•
/
~
1,=35 KH.
o
o
5.0
fracture width (rom)
•
'~
•
"
~
E
'-c;
•
"•••
1.0
1,=135 KH.
/
~
~
o
o
fracture width (mm)
5.0
b
Figure 18: Normalized amplitudes of Stoneley waves as a function of fracture width.
Center frequencies are 35, 85,and 135 kHz. (a) horizontal fracture; (b) inclined
fracture.
Fracture Detection and Characterization
-/~
-'i:~
.:;:..~~~""
.
~.;"';t·r\~
137
:=::=
....."
'--./
./
""":;;~,
"
~
I3
~
/1!tJ.:[
i0;~~
:~~
.
:;:;-
"'>-
8
I
!
o
time(,usec)
60
120
•
80
time{psec)
o
60
12C
b
Figure 19: Broadband (top) and Stoneley waves (bottom) microseismograms of full
waveform acoustic logs in a borehole with a vertical fracture. Fracture is indicated
along the vertical axis on the left.
138
Toksoz and Giiler
51
•
40
80
Distance (mm)
Figure 20: Actual amplitudes of the waves versus source-receiver separation in a vertical fracture extending from 38 mm to 86 mm indicated on the right-hand axis.
The fracture width is 1.0 mm. Amplitudes are peak-to-peak maximum amplitudes
except for the pseudo-Rayleigh waves, which are RMS amplitudes. Note that the
major differences in amplitudes occur in the Stoneley waves (St) which decrease
along the fracture. The pseudo-Rayleigh wave (pR) amplitudes increase in the
fractured zone due to energy scattering from the Stoneley waves.
Fracture Detection and Characterization
139
Ic=35 KHz
1.0
/'
--
Ic=135 KHz
o
60
10
distance(mm)
Figure 21: Stoneley wave amplitude in a borehole with vertical fracture at three frequency bands. The fracture is indicated by hatch marks along the x-axis.
140
Toksoz and GuIer