1
FULL WAVEFORM ACOUSTIC LOGGING -FROM THEORY TO APPLICATIONS
M.N. Toksoz and C.H. Cheng
Earth Resources Laboratory
Department of Earth, Atmospheric, and Planetary Sciences
Massachusetts Institute of Technology
Cambridge, MA 02139
INTRODUCTION
. This report contains results from the third year of the Full Waveform Acoustic
Logging Consortium and rock physics studies at M.J.T. This year marks the compietion
of the first phase of the project which has been directed primarily to the
understanding of the basic theoretical aspects of acoustic waves in a borehole.
With such a background we are ready to emphasize applications as well as to
undertake special problems which require new and different theoreticai approaches.
As examples of the latter, we can mention uncentered tools, vertical fractures around
borehoies, thinly bedded formations and anisotropy.
The third year studies fall into four general areas: theoretical aspects of wave
propagation in the borehole, applications to the characterization of formations,
integrated log analysis and physical properties of sedimentary rocies relevant to
logging. There are fifteen papers in this report which discuss individual topics in
detail. In this introduction we summarize the major points and also list the potential
applications of full waveform acoustic logs and future directions of our research.
THEORETICAL DEVELOPMENTS
During this year we made major progress in developing thec.etical solutions to
acoustic wave propagation problems in realistic boreholes. Until now our emphasis
had been on developing analytical and numerical techniques to generate synthetic
microseismograms for a variety of borehole conditions: open hole, cased hole with
bonded or unbonded casing, borehole with invaded zone, mudcake, and washout. As a
result of these studies we have acquired an appreciation of the complexity of the
borehole as a waveguide, and the complex manner in which formation and borehole
parameters affect different phases (e.g., p waves, leaking modes, S waves,
pseudo-Rayleigh and Stoneley waves) of the full waveform microseismogram. In
order to understand these effects it is necessary to break the problem into its
components and study each mode IndiVidually.
.
In a fluid-filled, cylindrical borehole with axial symmetry the solution can be
written as
2
Toksoz and Cheng
1
p(r,z,t) = --;;471
~
~
J J__ S(GJ)P(k,GJ)e UcZ eiOJt dkdGJ
(1 )
where p (r ,z ,0 is pressure inside the borehole at radius r and axial distance z, seCJ)
is the source spectrum (complex), P(k,CJ) is the impulse response of the borehole in
the frequency wavenumber domain, k is the wavenumber and CJ is the angular
frequency. Information about different modes is contained in P(k ,CJ), which can be
written as the ratio of two complex functions
P(k ,CJ)
= N(k ,CJ)/ D(k ,GJ)
(2)
D(k ,GJ) contain the singularities -- the poles, branch points and branch cuts. In
integration on the compiex k plane, poles on the real k axis give rise to pseLldoRayleigh waves (normal modes) and to the Stoneley wave. The integration around
CJ2
CJ2
branch cuts due to the square roots of (k 2 - - ) and (k 2 - - ) give rise to P and S
2
v:P
v:s2
head waves. The singularities off the real axes, in the upper and lower Riemann
sheets near the branch points, contribute to the leaky modes. A great problem in full
waveform logging has been the lack of understanding of why small changes in
parameters (tool response, borehole radiUS, formation properties) produce significant
changes in microseismograms. Many investigators have studied this prcblem (Biot,
1952; White and Zechman, 1968; Peterson, 1974; Roever et al., 1974; Rosenbaum,
1974; Tsang and Rader, 1979; Cheng and Toksoz, 1981; Paillet and White, 1982;
Baker, 1984). We have shown in numerous papers in the Full Waveform Acoustic
Logging Consortium Reports volumes I and II that it is possibie to evaluate the
integrals in equation (1) accurately and to calculate the synthetic microseismograms.
We were able to explain many features of the microseismograms and their
dependence on formation and borehole properties. Based on this experience and two
major studies in the past year, we have made significant progress. The recent
studies that contributed to these steps were detailed investigations of head waves
and leaky modes (Paillet and Cheng, 1985, Paper 2 in this volume) and an in-depth
analysis of the finite difference results that were first reported last year (Stephen
et al., 1984). Both of these studies were done without intrinsic attenuation (Q = ~),
As a result, all modes could be seen and resonances in the borehole fluid could be
observed clearly. The compressional and shear head waves are fed energy and
influenced by those resonances. Agure 1 (this is Figure 7 of Paiilet and Cheng)
shows the amplitude response 0'1 the borehole for the P headwaves. Note the
peaked response results from the higher compressional modes. With such a peaked
response, tools with different source spectra would produce headwaves of different
amplitudes. The borehole resonances that contribute to compressional and shear
headwaves have peaks at different frequencies (Figure 2, same as Figure 6 of Pail let
and Cheng) resulting in different spectra for P and S headwaves. With such peaked
response, even tools with flat source spectra would produce headwaves of narrow
spectrum.
The leaky modes, as the name implies, leak energy into the formation and
attenuate more rapidly with distance than waves whose singularities lie on the real
axis of the k R' k I plane. Leaking P modes (PL) are significant, especially when
Poisson's ratio is higher than about a = 0.3. A special case is when formation shear
velocity is less than the fluid velocity in the borehole. In this case they control the
shape of the P wave train. Figure 3 (Figure 1 4 of Paillet and Cheng) shows the
1-2
Introduction
change of the microseismogram characteristics with different source frequency
spectra in a low shear velocity formation. Different leaky modes dominate at
different frequencies.
The complexity of the borehole as a waveguide can be illustrated best by
snapshots of finite difference calculations. In Figures 4 and 5 we show two
examples from Stephen et al. (1984) to illustrate the point. These two snapshots
are taken in a simple borehole (Figure 4) and in a borehole with a velocity gradient
(Figure 5).
The preoeding discussion presented a very complicated view of the borehole
waveguide. In general applications, nature helps to simplify some of the problems.
First, intrinsic attenuation damps out the higher frequencies more rapidly
(exponentially) as a function of distance. Thus, the response spectrum of the
borehole becomes somewhat smoothed by the damping of hig;'er frequency iOeaks.
Drilling muds In oil wells generally have low Q (Qf ,,; 20). As a result the resonances
In the borehole fluid are damped out over distances of a few wavelengths. Second,
the source receiver separation in most full waveform acoustic logging tools has
Increased. Since leaking modes attenuate with distance more rapidly than either
head waves or guided waves, their effects become less pronounced with increasing
source-receiver distance.
The complexity of full waveform microseismograms is most critical when
formation velocities are high, fluid damping is low and the sonde length is less than
about 5 to 10 wavelengths•
. DEPTH OF INVESTIGATION OF STONELEY AND PSEUDO-RAYLEIGH WAVES
The depth of investigations of full waveform acoustic logs is of interest both in
open and cased boreholes. In open holes it is important to determine properties of
"virgin" formations beyond the damaged or "invaded" zone as weil as the extent of
such zones. In cased holes the ability to determine formation properties is one of the
most important applications of full waveform acoustic logs.
The depth to which energy penetrates needs to be stUdied using separate
techniques for P and S waves and for pseudo-Rayleigh and Stoneley waves. The P
wave results were studied last year using the finite difference method for damaged
and invaded zones (Stephen et al., 1984). The penetration of guided waves can be
investigated more directly using "partial derivatives" or "energy partition
coefficients". These coefficients are proportional to the fraction of wave energy in
each layer, and they determine the sensitivity of the wave to each layer.
Cheng et al. (1982) derived the partition coefficients for open holes to
investigate effects of attenuation. This has been generalized to layered boreholes
(cased holes, open holes with mudcake and invaded zones) by Burns et al. (Paper 3,
this report). The results show that casing and invasion layers affect pseudoRayleigh and Stoneley waves over a limited frequency range. Formation properties
behind the casing and invaded zones can be obtained by the combinations of the
guided waves at appropriate frequencies. PseUdo-Rayleigh waves can be used in
"hard" formations and Stoneley waves in "soft" (shear velocity is less than fluid
velocity) formations. Figure 6 (Figure 22 of Burns et al.) shows the radial
displacement as a function of radius of a pseudo-Rayleigh wave in the cased hole.
1-3
3
4
Toksoz and Cheng
Note that displacements are high in the formation and the wave is sensitive to
formation properties. Figure 7 (Fig. 27 of Burns et al.) shows the radial displacement
of a low frequency Stoneley wave in a "slow" formation. Again, a considerable
amount of wave energy is in the formation and the wave is very sensitive to shear
velocity of the formation.
These results enable us to interpret the theoretical microseismograms of Tubman
et al. (19a4) and develop an effective method for determining formation properties
behind the casing or beyond the invaded zone.
BOREHOLE RESPONSE TO A NORMAL POINT FORCE
AND SYNTHETIC SHEAR WAVE LOGS
Until now, theoretical calcuiations emphasized models with axiai symmetry.
applicable to acoustic tools currently in use. With the advent of a shear logging tool
(Zemanek et al., 19a4), acoustic sources with directivity have become impa""nt.
Several investigators (Roever et aI., 1974; White, 1967; Kitsunezaki. 1 9aO; Kurkjian,
1984, Winbow and Rice, 19a4) have formulated muitipoiar or directivG sour<::es.
Zhang and Cheng (Paper 4, this report) treated this problem using the multipolar
formulation and calculated both dispersion curves and synthetic microseismcgrams.
The asymmetric modes (flexural waves) are found to be highly dispersive both in hard
and soft formations. In both cases, there Is a cut-off frequency (generally about 2
kHz for the lowest mode) at which the phase velocity is equal to formation shear
velocity. Figures 8 and 9 (Figures 3 and 4 in Zhang and Cheng) show calculated
synthetic microseismograms for radially symmetric (monopole) and asymmetric (dipole
and quadrupole) sources. An important aspect of flexural waves is that although the
phase velocity is equal to shear velocity at cut-off, at higher frequencies both phase
and group velocities fall below the shear velocity. In order to obtain formation shear
velocity, it is necessary to use the phase velocity (the move out between receivers)
and to make corrections for dispersion at frequencies higher than the cut-eft
frequency.
APPLICATIONS
A major effort is now being directed to utilization of full waveform acoustic d6.ta
for determining formation properties. Until now the primary use of acoustic iogs was
to determine formation compressional and shear wave velocities. Attenuation
determination (Qp-1, Qs-l) has proved to be more difficult than anticipated at the
beginning. However, with the waveform inversion, attenuation can be derived as an
inversion parameter. Full waveform envelopes and other characteristics have been
used for lithology identification in conjunction with pattern recognition algorithms
(Hoard, 1983).
Encouraged by such successful applications and a better understanding of the
theoretical wave propagation problems, we have expanded the domain for full
waveform acoustics to general log analysis. We looked at probl8ms whe,.·) full
waveform logs are the primary data and problems where full waveform logs can serve
as part of a suite of logso The latter has been directing us to broaden scm8wh<1t into
general log interpretation.
1-4
Introduction
In the discussion below, we cover a few such examples.
FORMATION PERMEABILITY
Determination of flow properties from full waveform logs has been one of our
primary goals. Biot (1952), Rosenbaum (1974), and White (1983) have shown that
wave attenuation in a borehole would depend on formation permeability. A number of
empirical studies have shown that there is some correlation between wave
attenuation and formation permeability (Bamber and Evans, 1967; Paillet, 1983;
Williams' et al., 1984). The difficulty of determining permeability from full wavefcrms
comes from the fact that wave attenuation depends on several other factors in
addition to permeability (papers in ToksDz and Johnston (1981) discuss these
prcblems in detail). In the borehcle, viscosity of borehole fluid and intrinsic
an elasticity of the formation generally contribute much more than permeability tc the
attenuaticn of full waveform acoustic waves.
In cases where borehole fluid was relatively unattenuating (e.g., water Instead
of mud) and formation attenuation was low (crystalline rocks or dense carbonates),
permeability of fractures and fractured zones could be determined from the
attenuation of Stoneley waves (Mathieu and Toksoz, 1984). This study showed that
Stoneley wave attenuation was highly sensitive to fluid loss into the formation.
Furthermore, for a given permeability, attenuation increased with decreasing
frequency. Formation anelasticity generally gives a constant Q.
We could combine all of these efforts, relying on high frequency P and S waves
for determining anelastic effects and on low frequency Stoneley waves for
attenuation due to fluid flow. The preliminary results of such a study are given by
Hsui et al. (Paper 8) in this repdrt. The problem is solved by two approaches: first,
for the Stoneley wave only and then for a Biot type model with an anelastic rock
frame. Both of these approaches give similar results. Theoretical values are
compared with core measurements given by Williams et al. (1984). As shown in
Figures 10 and 11 (Figures 5 and 6 in Hsui et al.), theoretical and measured values
show goed agreement both at low and high permeabilities. It is important tc reemphasize that these are recent results. We are confident that we are on the rignt
track and permeability determination from full waveform acoustic logs is an attainable
goal. Another development is the determination of permeability and other properties
of fractures in hard (crystalline) rocks using VSP, full waveform acoustic, televiewer
and other logs as discussed by Hardin and ToksDz (Paper 9) in this report. This stUdy
extends the work of Beydoun et al. (1984) for characterizing the fractures. Figure
12 (Figure 1 in Hardin) shows tUbe waves generated at open fractures at 210m and
290 m depths by an incident P wave. Figures 13 and 14 (Agures 2 and 3 in Hardin
and Toksoz) show the strong attenuation of acoustic waves at these fractures.
Figure 15 (Figure 4 of Hardin and ToksDz) is a complementary set of logs showing
decreased resistivity and increased SP values at the open fractures where fresh
water is entering the borehole.
Using tube "'lave amplitudes from surface sources on different azimuths around
the borehole, Hardin and ToksDz were able to determine the attitude (strike and dip)
of the fracture planes. These compared well with values from televiewer data.
1-5
5
6
Toksoz and Cheng
DIP DETERMINATION FROM FULL WAVEFORM LOGS
Refracted P and S waves propagating In the formation around the borehole are
reflected from and transmitted across the bed boundaries. When the bed boundary is
not normal to the borehole axis, an incident P wave can produce reflected P and S
and transmitted P and S waves. These reflected and converted waves can be seen
in an iso-offset (fixed source-receiver spacing) full waveform section as oblique
arrivals. Such arrivals have been observed and identified in a number of cases
(Serra, 1984; Arditty et al., 1984). The apparent velocities of these arrivals depend
on the formation velocities as well as the angle between bed boundary and borehole
axis, and hence the dip. Examples of such arrivals can be found in Paternoster and
Larrere (Paper 7, this report). In an extensive study of such events, Paternoster and
Larrere have· established a comprehensive set of criteria for identifying and
enhancing such events. Although at first sight these "oblique events" appear to be
generated only at interfaces with very strong impedance contrasts, processing by
velocity filtering shows that they' are observable at most interfaces.
The dips that have been determined from apparent velocities of oblique events
agree reasonably well with dip meter data. It is important to mention that in full
waveform logging, acoustic waves penetrate about one meter into the formation and
measure dips averaged over such distances and at bed boundaries. Thus, they
complement the conventional dipmeter data in a significant way.
SOURCE ROCK LOGGING
An extensive study was carried out to determine how the organic content of
shales affects the log responses and whether acoustic logs contribute significantly
to source rock problems (Mendelson, Paper 11, this report). The investigation
consisted of several steps: model log response dependencies on kerogen content,
develop bivariate and multivariate correlation and non-linear regression methods,
compare log data with laboratory data measured from the cores. It was found that
the logs most sensitive to kerogen content are: sonic, gamma density and neutron
porosity. The resistivity logs are strongly controlled by water and shale resistivities
and kerogen effects are small. There were no full waveform logs available in the
data set. Had there been information on shear wave velocity and attenuation, some
uncertainties could have been removed and source rock potential could have been
more clearly defined.
ROCK PHYSICS STUDIES
The physical properties of porous rocks and their dependence on matrix
minerals, porosity and pore shapes, shaliness and distribution of clay minerals, pore
fluids and degree of saturation are essential for effective formation evaluation based
on well log data. In this report, detailed studies of the matrix and pore geometries of
sandstones and their' effects (Wilkens et al., Paper 14); the feasibility of
determination of pore shapes from seismic P and S velocities (Burns et al., Paper 15);
the comparison of effects of water, benzene and gas (nitrogen) saturation on seismic
velocities (Coyner and Cheng, Paper 12), and attenuations (Gonguet et al., Paper 13)
are investigated. Lo et al. (Paper 16) study the seismic anisotropy of selected
rocks, its pressure dependence and physical interpretation.
1-6
.
{
Introduction
The emphasis of all of the rock physics measurements is on the elastic and
anelastic properties. Full waveform data can best be utilized for formation evaluation
with a good understanding of the seismic properties of porous and permeable rocks
under different saturation conditions.
A SUMMARY OF POTENTIAL APPLICATIONS OF FULL WAVEFORM ACOUSTIC LOGS
There is a tremendous amount of information in the full waveform acoustic log.
Interpreted properly, with good physical understanding and laboratory data or used
jointly with other logs, full waveform acoustic logs can contribute greatly tu formation
analysis. Some applications of full waveform acoustic logs are listed below.
(1) Determination of formation velocity and attenustion: Format;cn P 'Jv'uve
velocity can be determined accurately using any number of available techniques.
Formation S wave velocity is more elusive, especially In "soft" fer!'1ations where
the shear wave velocity is lower than the fluid velocity. When a logging tee! has
adequate low-frequency response, good Stoneley waves are gener"ted. The
Stoneley wave phase velocity is inverted directly to obtain the shear wave
velocity. When high-frequency, narrow-band tools with limited dynamic range
are used, Stoneley waves are either not recorded or clipped. Even in such
cases, full waveform logs can be used to determine formation S wave velocity
by waveform inversion. The determination of attenuation is more difficult. In
general it requires the synthesis of full waveform logs or the inversion of the
waveform.
(2)
Cased borehole logging: Waveform inversion is also a reliabie method to obtein
formation properties in cased boreholes. Forward modelling shows that formation
properties can be determined with good accuracy in well-bonded cased hoies.
Even in cases where the casing is pooriy bonded to the cement or th" cement is
poorly bonded to the formation, the formation properties significantly affect the
full waveform iog.
(3) Invaded zone and complicated borehole conditions: Using analytical and finite
difference calculations, it is possible to simulate an invaded or damaged zone
around the borehole. Using wav~forms from different receivers with increasing
source-receiver separation, the damaged or invaded zone effects can be
identified and removed. Long-spaced full waveforms complement electrical logs
in this respect.
(4) Formation permeability: The attenuation of Stoneley waves is a good indicator
of the relative permeability of a formation. To obtain absolute values of in situ
permeability, it is necessary to correct for the attenuation due to anelastic
effects. The permeability determined from the attenuation of Stoneley waves in
porous formations compares well with field and laboratory measurements.
(5) Source rock analysis: P wave velocity, P to S wave velocity ratio, ar.d
attenuation in shales appear to be dependent on kerogen content and relative
maturity. A promising study is the combined interpretation of gamma (including
NGT), sonic, density, neutron and resistivity logs for determining source rock
properties and comparing the results with geochemical measurements from
cores. Formation elastic properties determined from full waveform acoustic logs
1-7
7
Toksoz and Cheng
8
in combination with other logs enhance the characterization of source and
reservoir properties of the formation.
(6) Fracture detection and characterization: Full waveform accustic logs are
sensitive detectors of fractures and can determine the fracture permeabiiity or
hydraulic conductivity. Since acoustic waves penetrate deeper into the
formation, full waveform logs complement televiewer resuits nicely.
(7)
Dip determination: A recent discovery from full waveform acoustic·data analysis
has been the identification of reflected and transmitted converted waves at
dipping bed boundaries. The apparent velocities of these secondary waves are
highly sensitive to the dip of the interface. Dip angles determined by this
method correlate well with dipmeter results. Since full wavefcrm logs :::snetrate
deeper into the formation and measure structural dips, they compiement
standard dipmeter data and have the potential for measuring the magnitude (not
the direction unless modified tools are used) of the dip in cased holes and open
holes with oil base mud.
(8) Quantitative bond logging: Detailed theoretical calculations show tr.at fuJi
waveform acoustic logs can be interpreted to determine whether casing is well
bonded. If poorly bonded, the logs can differentiate between free casing,
casing bonded to cement, and cement bonded to the formation.
(9) Resolution of thin beds: In order to penetrate deep into a formation, acoustic
logs have a large source-receiver separation. To accurately measure time
deiays, the receiver-to-receiver distances must also be large. In thinly bedded
formations this gives good average velocity but poor resolution of the velocities
of individual beds. Acoustic logs have dense spatial sampling. These data can
be inverted to resolve the velocities of individual thin beds.
(10) Acoustic log interpretation using expert systems: Rapid analysis of massive
amounts of fuii waveform data is necessary for on-line decisions at the well
head. New LISP machines have the potential for very rapid interpretations, with
the aid of AI techniques. The characteristics of full waveform iogs change
significantiy with lithology. Even a small change in shallness affects the
waveforms.
(11) Borehole tomography: With a number of sources and an array of receiVers, full
waveform logging can generate as many as 60 traces at every few centimeters
of depth. With such data density and a wide spectrum of frequencies, one can
obtain a tomographic image of the formation around the borehole. Transmitted
(refracted) as well as reflected and scattered waves can be enhanced and
interpreted by tomographic reconstruction algorithms.
1-8
Introduction
REFERENCES
Arditty, P.C., Arens, G., and Staron, P., 1984, Improvement of formation properties
evaluation through the processing and interpretation results of the EVA tool
recordings: 54th Annual International SEG Meeting Expanded Abstracts, Atianta.
Baker, LJ., 1984, The effect of the invaded zone on full wave train acoustic logs:
Geophysics, 49, 796-809.
Bamber, C.L and Evans, J.R., 1967, SO-k log (permeability definition from acoustic
amplitude and porosity logs): AIME, Midway USA Oil and Gas Symp., Paper SPE
1971.
Beydoun, W.B., C.H. Cheng and M.N. Toksoz, 1984, Detection of open fractures with
vertical seismic profiling: J. Geophys. Res., In press.
Biot, M.A., 1952, Propagation of elastic waves in a cylindrical bore containing a fluid:
J. Appl. Phys., 23, 997-1009.
Cheng, C.H., and Toksoz, M.N., 1981, Elastic wave propagation in a flUid-filled
borehole and synthetic acoustic logs: Geophysics, 46, 1042-2053.
Cheng, C.H., Toksoz, M.N., and Willis, M.E., 1982, Determination of in situ attenuation
from full waveform acoustic logs: J. Geophy. Res., 87, 5477-5484.
Hoard, R.E., 1983, Sonic waveform logging: a new way to obtain subsurface geologic
information: Trans. SPWLA 24th Ann. Logging Symposium, Paper XX.
Kitsunezaki, C., 1980, A new method for shear-wave logging: Geophysics, 45, 14891506.
Kurkjian, A.L., 1 984, Radiation from a low frequency horizontal aCOustic point force in
. a flUid-filled borehole: 54th Annual International SEG Meeting Expanded
Abstracts, Atlanta.
Mathieu, F. and Toksoz, M.N., 1984, Determination of fracture permeability using
acoustic logs: S.A.I.D. Ninth Int. Formation Evaluation Trans., Paper 47.
Paillet, F.L, 1983, Acoustic characterization of fracture permeability at Chalk River,
Ontario, Canada: Can. Geotech. J., 20, 468-476.
Paillet, F.L, and White, J.E., 1982, Acoustic modes of propagation in the borehole and
their relationship to rock properties: Geophysics, 47, 1215-1228.
Peterson, E.W., 1974, Acoustic wave propagation along a fluid-filled cylinder: J. Appl.
Phys., 45, 3340-3350.
Rosenbaum, J.H., 1974, Synthetic microseismograms: logging in porous formations:
Geophysics, 39, 14-32.
Roever, W.L, J.H. Rosenbaum and T.F. Vining, 1974, Acoustic waves from an impulsive
source in a fluid-filled borehole: J. Acoust. Soc. Am., 55, 11 44-11 55.
Serra, 0., 1984, Fundamentals of Well-Logging Interpretation, vol. 1, The Acquisition
1-9
9
10
Toksoz and Cheng
of Logging Data, chap. 15,247-250, Elsevier.
Stephen, R.A., F. Pardo-Casas and C.H. Cheng, 1984, Finite difference synthetic
acoustic logs: Geophysics, in press.
Toksoz, M.N. and Johnston, D.H., (editors), 1981, Seismic Wave Attenuation: S.E.G.
Geophys. Reprint Ser., 2, Tulsa, OK.
Tsang, L., and Rader, D., 1979, Numerical evaluation of the transient acoustic
waveform due to a point source in a fluid-filled borehole: Geophysics, 44, 17061720
Tubman, K.M., Cheng, C.H., and ToksDz, M.N., 1984, Synthetic full waveform acoustic
logs in cased boreholes: Geophysics, 49, 1051-1059.
White, J.E., 1967, The hula log: A proposed acoustic tool: Trans. SPWLA 8th Annual
Logging Symp., paper I.
White, J.E., and Zechman, R.E., 1968, Computer response of an acoustic 10gginO tool:
Geophysics, 33, 302-310.
White, J.E., 1983, Underground Sound: Elsevier, Holland.
Williams, D.M., Zemanek, J., Angona, F.A., Dennis, C.L., and Caldwell, R.L., 1984, The
long space acoustic logging tool: Trans. SPWLA 25th Ann. Logging Symp., Paper T.
Willis, M.E., and Toksoz, M.N., 1983, Automatic P and S veiocity determination from full
waveform digital acoustic logs: Geophysics, 48, 1631-1644.
Winbow, G.A. and J.A. Rice, 1984, Theoretical performance of multipole sonic jogging
tools: 54th Annual SEG Meeting Expanded Abstracts, Atlanta.
Zemanek, J., FA Angona, D.M. Williams and R.L. Caldwell, 1984, Continuous shear
wave logging: Trans. 25th SPWLA Ann Logging Symp., Paper U.
1-10
Introduction
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1-11
11
Toksoz and Cheng
12
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1-12
Introduction
13
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20 kHz.
1-13
Toksoz and Cheng
14
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-'-'...=..
16
Figure 4: The complete picture of wave interaction around the borehole for the sharp
interface model is shown in the snapshot format of vertical displacement. The
first eight frames show the amplitude distribution of the vertical displacement
field in radius-depth space. Each frame is 0.6 m wide by 3.0 m deep. Time
progresses from 0.2 msec to 1.6 msec. The ninth frame is a representation of
the compressional wave velocity model.
1-14
-
",~
Introduction
15
i
I
i
~
,
.,
'i
I
:1
ii
,I
Ii
r
,
6
e
1
~D.I[
J2 1 4
\rlS)
16
Figure 5: The snapshots of vertical displacement for the Gradient model are shown.
The dimensions are the same as for Figure 4.
1-15
Toksoz and Cheng
16
...
8.128
r-------r------r-----.....-----,
C
lD
e 8._
lD
o
-
CIS
0.
'tI
.~
e
_
8.868
-
<U
'tI
<U
...
e
9.ll3lI
0
11
_.
::Ii
-I'
I.
9.
9.
I
saa._
1_.98
radius/Rbhoie
1598.98
2988.98
x100
Figure 6: Radial displacement of a low frequency component (12.643 kHz) of the
pseudo-Rayleigh wave in a cased borehole.
..
1-16
Introduction
17
t .200 ..--~---r-----""-----"-T------'
eu
0.
0.
250.ooe
se0.aee
750.aoo
1000.00
radlua I R bhole X 100
Figure 7: Radial displacement pf a component (1.073 kHz) of the Stoneley wave
in a cased borehole with a slow formation.
1-17
Toksoz and Cheng
18
X19~
2
.l
- .
•-r--
r\
•I
-, +,
I
-2
I
"I
Z0<la
bl
Ieee
--
J\
•
i
i
I
\j'v
V
-Ieae -
\
,
-2000
\
.u
,.
ol
Ii 1\ I :\
I
•--
'i I
--J\I\ II'
ill/III
t ,I
IJ!;r i
-2.
IV
\~"
v
"Ii !, ~
,
I
a
,
00.?
a aa3
TIME (sec)
Figure 8: Synthetic microseismograms for the sandstone formation generated using
a) a monopole (n = 0) source; b) a dipole (n = 1) source; and c) a quadrupole (n
= 2) source. The source used is a Ricker wavelet centered at 3 kHz and the
source-receiver separation is 3 meters.
1-18
Introduction
19
xle~
5
a)
e-- -
a
5- -
a a-
-a
-
'v
\
s-
I
a
.aa
- I
I
I
I
b)
a- -
I-
-,
-
..
t
-
...
T
la
I
,
I
I
I
c)
5
- -
I
l-
-5
0v
\)
V
•I
-
-Ia
a ""a
V
I
(I
081
,
,
I
I
I
e al;l3
I
fa eS4
a eS2
a eas
TIME (sec)
Figure 9: Same as Figure 8 for the soft formation. The center frequency of the
source is 2 kHz.
1-19
Toksoz and Cheng
20
t·
13
-r========---------i
13.8
o
I<
a:
-
13.6
w
• • ••
•
•
•
no intrinsic Q
c::)
I::::;
13 . 4
Q.
:E
<
13.2
Well 1
(Williams et al.. 1984)
13 . 13 -+-nrrrt-,-T1-rh-.,....,-r+-r""T""r-r+r-r--r-r-+-T""T'..,....-+-~~.,--/
13.5
1.13
1.5
2.13
2.5
3.13
3.5
13.13
LOG PERMEABILITY (millidarcies)
Agure 10: Theoretical (Blot model) and observed amplitude ratio for two receivers 5
ft (1.53 m) apart versus permeability. The data (points) are from well 1 in Williams et al. (1984). The top line is the theoretical result without intrinsic attenuation. The bottom line is with Qp = 100, Q. = 50, and QJ = 30.
1-20
Introduction
21
1.13
no intrinsic a
medium a
13.8
0
-
l-
e(
a:
13.6
Iowa
W
0
::J
l-
-
.~
•
0.4
•
C.
:E
e(
0.2
Well 3
(Williams et aI., 1984)
0.0
2
0
3
4
LOG PERMEABILITY (millidarcies)
Figure 11: Same as Figure 10 for well 3 in Williams et al. (1 984). The top line is the
theoretical result without intrinsic attenuation. The middle line is with Qp = 100,
Q. 50, and Q/ 20. The bottom line is with Qp 30, Q. 15, and Q/ 1O.
=
=
=
1-21
=
=
22
Toksoz and Cheng
TIME (ms)
o
200
i5§i=:=::=
200--'....,,1...:...'..,;;1"',' - - - - ..
A"
\'
•
..... *\' '
•
... 'fi
250::::'::::J~==::::
,;'
J~
~'
Ie
1".
, · Pt:. '0'
t.
l\l
en
a:
w
IW
!
300-....JI:,------·
::
$
Q
Figure 12. Field record of unfiltered traces
acquired using source offset/shothole
810. Tube wave events are generated
at 210m., 290m. and 146m. (apparent
from downgolng tube wave). Upgoing
tube
waves
from by
below
41 Om. are
probably
caused
reflections
from
the hole bottom at ~490m. and a
possible generating horizon at 450m.
1-22
350
====t======
~~~~~~~~~~~
23
Introduction
TIME (J.Isec)
Q
. 400,
,
. 890 '. 12pO_
1600
!
2000
-E
J:
IQ.
IJJ
C
220
Britton Well 2
Tx - Rx Spacing 2.1 m
Figure 13. Full waveform acoustic log traces from an intervai encompassing the tube
wave generating horizon at 210m.
.
1-23
Toksoz and Cheng
24
TIMECIJsec)
400
,
890
1290
16pO
2000
-e
J:
I-
a.
w
c
295
300
Britton Well 2
Tx - Ax Spacing 2.1 m
Figure 14. Full waveform acoustic log traces from an interval encompassing the tube
wave generating horizon at 290m.
1-24
Introduction
SP
l't1l"'TlV'TY
~
(kOhrn-m)
,, ....
,
i
I
f'
,
r--
I
,
,-''''1
, I
;
!
,
,
-
(f
<
,j ,,
,
I
!
!
"" '-,
3
V
: .=:"
~
i
"
i
ii
v
,
I
I
,
:
,
!
I
I
,
i
!
1
,
I
i
!
I
i
i
! i
i
i
I
,
,
~
I
I
!
j
i
,
i
::;.. ,
~
/i
-ra'
l-:
!
,
i
~;
,.!: '
~
r
4i
,
,,
Fl ,,
I
,i
,
,
'.
I
;
I
!
~!
I
I
, , 300
,
i
;
i,
,
,
,
!
!
,
\
,
, , ,
,
'
L.s:!
i
i
250
, , ,
!
, I , ,
,
i
:,
:
200
!
IoC
~
I : i
i
!
:[:
i
II
I
,
i~
!
,I
II
>
,, ,
! ,i
150m
i
i ...
,
~ 1...
)
I
I
I
I
j
~:
:
i
,
::S'
l
i
~
:
,
J,
.r.
! t.1 i
......1
2-
+-..
i
<:
........,
,
i
,
-?
.7
;.
,,>,
\
'-1 ,
I I
I
.~
-.
,
I
i,
.....:
~,
I
,
200
(c/••c)
,
;1P,
'
I
i~
i
bZ:
)
:...J
1
,
!
So
'
,
I
i i
,
,, ,
,
,
,
1
i
.c,
iL-
,
,
.<.J
~
---
!
~:
~
!
[..>i ,, I
;
?
.....
,
,
250 0
!
,
Natural GAMMA
(illY)
4 150
, ,
25
350
,,
!
:
,,
:,i:" , i
r-I
I i
i
! i
!
,I
400
Figure 15(a). Natural gamma, self potential (SP) and resistivity logs from Britton well
#2, Hamilton, Mass.
1-25
Toksoz and Cheng
26
SOMe (ulee/ft)
10
"educed Temp. (Cl
o
11C1
CAW'!!"
(om dle.>
1 28
I-~!~,~,~,r"'"Ir"'"I--"TI,-,-H.-,---,"'l/~-,--:-i1-..,..;-,- i-I"".......; -j.....,'-i-115Oftt
'/
!
)
j!
. 1 ;
f
; !
I
,
)
l
1 :
!
l
,
,,
,
'L'
i
'f "
,.1
'"
)
i .-i-..!-
-;
I
\ ii-~
00:-
I
I----:lt-+-----ll---=:t.ot-\-"-,---II-,~--..:.!- !-""';'I"":'"--I
I----=~
200
1
/:
f.--:--..-;,~f----i I - - -I
M"<..'-:'- '- - l
~~
1\
17:
/1:
-n
r~~'='±::+' ~i
._,
I'
!'
1
I
250
,
J
I
1----..J..---II-----+rJI"-,---I1-..,L.---!--------l300
;
\ !
,
,
1----+---1 H ' - - + - - - - I 3 5 0
~
;
,
; \! '
'~I i
! iii
) \
; i ~
: t! i
,r"
!!: I i
1---.;......i.J.-.;....--H·,.;""j,,;,...:._..J---'.....I.~ 400
;"..; , !
1
3~100m
gradient
aubtracted
Figure 15(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 '"9 C.
°
1-26