1
FUIJ.. WAVEFORM ACOUSTIC LOGGING WHERE WE ARE. WHERE WE ARE GOING
by
.Il. Na1i Toksoz. C.H. Cheng and Gilles Garcia
Earth Resources Laboratory
Department of Earth. Atmospheric. and Planetary Sciences
Massachusetts Institute of Technology
Cambridge• .IlA 02139
INTRODUCTION
We have now completed the second year of the Full Waveform Acoustic
Logging Consortium. During these two years, we have developed a good
understanding of seismic wave propagation in a borehole through both
theoretical modelling and data interpretation. If we were to make a simple
statement about the full waveform acoustic log, it would be that the method has
far greater potential for determining formation properties than we ever had
envisioned. But the problem is complicated and utilizing the data effectively
requires sophisticated theoretical analyses and new approaches to data
acquisition and interpretation.
In this introductory chapter of the second annual report of the
Consortium, we give some examples to illustrate the potential of full waveform
acoustic logs and problems associated with the interpretation of the data.
Based on these assessments, we also identify some topics that will receive
priority in our research in the coming years.
DATA ANALYSES
During this past year, two factors contributed to our better understanding
of full waveform logs: field data sets from different environments, and more
sophisticated theoretical models of realistic borehole problems.
Actual logs are critical in providing direction to our studies. We are
grateful that we received a number of data sets from Consortium members.
These data sets carne from different geologic environments and were collected
using different logging tools. Some examples are shown in Figures 1-3. Figure 1
shows an alternating section of carbonates, evaporates and shales with
relatively high velocities (Vp > 3.0 km/sec). It is an iso-offset (fixed sourcereceiver separation) plot. Different formations and lithologies stand out. They
affect the whole characteristics of the logs. The changes in M or delay times
(or compressional wave velocities) are clear, but not as significant as changes
in the total character of wave trains. An iso-offset section from another
carbonate sequence logged with a different tool is shown in Figure 2. Similar
changes in waveform characteristics can be observed. Another example of an
iso-offset section is shown in Figure 3. In this c·ase the lithology consists of low
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2
Toksoz et al.
velocity shales, sands and sandy shales. Changes in waveform character clearly
define the lithological boundaries. Although P-wave velocity (or arrival time)
changes are small, overall changes in the character of wave trains are
significant. In both Figures 1 and 2, there are sections with pronounced
differences in the overall waveforms, even when compressional wave velocities
are remaining relatively constant. In other words, the waveforms are sensitive
to many lithologic and borehole properties that are difficult to identify on the
basis of compressional wave velocity alone. It has been shown, on the basis of
theoretical calculations (cf. Toksi:iz et al., 1983; Cheng and Toksi:iz, 1981, and
papers in this report), that formation Poisson's ratio, attenuation, density, and
borehole radius can strongly affect the observed waveforms. The true value of
full waveform logging will be realized when all these signatures can be
recognized and interpreted to characterize the formation completely.
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Dependence on Tool Response
Another peculiarity of full waveform logging is its strong dependence on
tool characteristics and response. In a full waveform, there are a number of
wave types - refracted waves, leaky modes, and gUided (pseudo-Rayleigh, and
Stone ley) waves. Their excitation, relative amplitudes, and at times their
presence, depend on the frequency response function of the particular wave.
Differences between examples shown in Figures 1 and 2 (both hard formations)
are due to different tool geometries and frequency responses. Similarly, in
"soft" formations the two waveforms shown in Figure 4 look completely
different because of different tool responses, even though formation
compressional velocities are comparable. Thus, automated interpretation
schemes have to cope with these variations.
Volume of Data
In most new full waveform logging tools the number of sources and
receivers is increasing. Some new tools will produce 48 or 60 traces of different
source-receiver separations at each depth. The trend for an increasing number
of traces will continue just as it did in marine seismic recording. Most of the
methods and algorithms that are used today cannot cope with these data
volumes in the rapid time frames required for field applications, It is necessary
to look for new approaches, before the system comes to a halt.
There is much that can be learned from the seismic processing experience,
Unfortunately, logging is more complicated because of the multiplicity of modes
and wave types,
Cased Boreholes
A significant application of full waveform acoustic logs will be for the
determination of formation properties in cased boreholes. In the past year we
completed the theoretical formulation and associated computer programs for
wave propagation in a radially layered borehole, These programs can model a
well-bonded cased hole as well as a borehole in which the casing is free (casing
to cement unbonded) or in which the cement is bonded to the casing but not to
the formation. The theory of wave propagation in a cased hole is discussed in
details in two papers by Tubman et al. in this report (Papers 2 and 3). Our
initial study of the limited field data available to us shows: 1) Formation
1-2
Introduction
3
properties can be determined reliably in cases where the casing is well-bonded
(casing-cement-formation bonds are good). 2) In a well where the cementing is
poor or the casing is free, it may be possible to determine the formation
properties provided there is an adequate array of receivers and data for
frequency-wavenumber analysis and filtering. 3) Full waveform logs can be
used quantitatively for "bond log" interpretation. The quality of cementing or
the nature of free fluid layers can be identified on the basis of wide-band data
and theoretical analysis.
THEORETICAL FORWARD MODELS
In order to understand and interpret fully the observed full waveform
acoustic logging data, we must understand the wave propagation in a borehole
in a realistic formation. In the past year, we have modelled complicated
borehole geometries using the finite difference and discrete wavenumber
integration techniques. Furthermore, we have isolated and studied individual
phases by the method of contour integration. The discrete wavenumber
integration was applied to the situation of bonded and unbonded cased
boreholes, as described above.
Finite DitIerence Models
The finite difference modelling technique was discussed in details by
Stephen et at., (1983). In this report, Pardo-Casas et at. (Paper 5) and Stephen
and Pardo-Casas (Paper 6) show examples of finite difference synthetic
microseismograms in formations with an invaded or damaged zone, with a
horizontal fracture, and with a washout. In each case, the amplitude and
character of the waveform are significantly affected. More studies are needed
to fully quantify these results.
It is clear that the finite difference method is extremely useful for studying
complicated borehole environments. However, there are two disadvantages to
the method at present. One is computational time. At present it takes up to a
few hours on a medium size machine, such as a VAX 111780, to do a single
model. making it impractical for detail modelling purposes. The other
disadvantage is the difficulty in applying in situ attenuation to the model. This
latter problem can be solved by going to the frequency domaIn and using
complex velocities to model attenuation (Cheng et at., 1982). Because of the
band-limited nature of the full waveform acoustic logs, a frequency domain
approach could also cut down the computational time significantly. This
approach will be tested in the coming year.
Head Waves
The amplitudes of the P and S head waves as a function of formation and
borehole parameters are very important in the determination of in situ
attenuation. In this report, Zhang and Cheng (Paper 4) studied the variations
of the amplitudes of the head waves with formation, borehole and tool
parameters using contour integration. It is found that in addition to the
variations of amplitudes with formation and fluid velocities, the geometric
spreading factors of the head waves vary with both source-receiver separation
and frequency. Thus, it appears that a simple analysis based on the slope of
1-3
Toksiiz eta!.
4
the Fourier amplitude ratio will not give correct values of in situ attenuation.
The exact geometry, frequency and velocities must be known to properly
correct for the geometric spreading factor. It appears that a full waveform
inversion is necessary for the determination of attenuation.
The necessity for full waveform inversion, either in simple or in complex
boreholes, requIres a fast forward modelling technique. For boreholes with
axial geometry, such as a simple borehole or a cased borehole, the discrete
wavenumber integration method is a possible candidate. For isolated phases,
contour integration is the proper approach. In either case, the computer
programs, as they exist now, are not fast enough. However, there are ways of
speeding up the calculations significantly. One such method is to use a table
lookup algorithm for the complex Bessel functions. It is estimated that this
alone will lead to a factor 3 to 6 improvement in computer time. This will be
pursued in the coming year in conjunction with full waveform inversion.
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COMPARISON OF LOG VELOCITIES
Two questions generally asked about log velocities are: 1) how well do they
refiect the true formation velocity because of possible effects of well damage,
mud cake, and invaded zones? and 2) are the log velocities (generally measured
at 10-20 kHz) the same as the seismic velocities measured at 100 Hz? In other
words, is there a significant dispersion over two decades of frequency?
The first question has been investigated extensively using theoretical
models of multi-layer boreholes (Baker, 1981; Tubman et al, 1984), and
heterogeneous formations (Stephen et at., 1983; Pardo-Casas et al., Paper 5,
this report; Stephen and Pardo-Casas, Paper 6, this report). For long spaced
acoustic tools, where source-receiver separation is more than about 2 meters,
invaded zone effects are minimal on measured compressional velocities and
these represent true formation velocities (Figure 5a). For shear waves the
problem is more critical. The shear head wave is more closely confined to the
fiuid borehole interface (Figure 5b). However, since shear wave velocity is
essentially determined from the first cycle of the pseudo-Rayleigh waves, going
to lower frequencies increases the depth of penetration and minimizes any bias,
provided the frequency still remains above the cut-off frequency of the first
mode of the pseudo-Rayleigh wave.
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Comparison with Laboratory Data
Another test commonly used is to compare log velocities and laboratory
measured core velocities as shown in Figures 6 and 7. In these comparisons
some measurements differ more than one would expect, given the precision of
log or laboratory data. We believe these differences are primarily due to the
fact that the core represents only a small sample (usually 2-5 cm) of the
formation, and that the log measures velocity averaged over 50 cm or more of
the formation. Invasion or borehole damage effects would be apparent as a
consistent bias, which is generally. not observed.
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Introduction
5
Comparison with VSP Velocities
Check shot and vertical seismic profiling (VSP) surveys provide excellent
data to determine the accuracy of log velocities and the possible effects of
dispersion. This comparison can be done using integrated sonic times and
seismic travel times. Stewart (1983) has carried out a detailed study of this
problem. Figures 7a and 7b show curves of observed differences between VSP
and integrated sonic travel times, normally called the "drift" curves. From
these o.gures, there is a strong suggestion that the sonic log velocities are
faster than seismic velocities. Stewart (1983) shows that the primary factor
contributing to the bias was attenuation due to multiples and resulting group
delay. Figure 8 shows that without multiples the integrated sonic times and
seismic times agree closely.
DETECTION AND CHARACTERIZATION OF FRACTURES
The detection and characterization of fractures are emerging as important
applications of full waveform acoustic logs and other borehole seismic
measurements. Figure 9 shows an example of the strong signature of a
hydrofrac on a full waveform log section. The fracture causes strong
attenuation of P and S, pseudo-Rayleigh and Stoneley waves. In addition, very
strong scattering of the Stoneley waves is clearly visible. The paper by Paillet
(Paper 9, this report). contains examples of logs showing fractures and fracture
zones. and discusses their characteristics.
Unquestionably, in all the cases where fractures can be verified
independently, full waveform acoustic logs have been sensitive to fractures.
Two aspects of this application need to be developed further. First, ail the tests
so far have been in crystalline rocks. It is necessary to investigate the
applicability of the technique to sedimentary rocks. We expect that in
dolomites. limestones, and other "hard" sedimentary rocks the technique will
work. Tests are needed in "softer" rocks such as high porosity sandstones and
shales. The second point is the quantitative characterization of fractures. As
will be discussed in the next section, this work has begun. However, much more
data and additional theoretical developments are needed. The detection' and
characterization of fractures using full waveform acoustic logs will be among
the major research topics in the coming year.
A related study is the identification and mapping of major fractures by the
use of low frequency tube (Stoneley) waves. These waves are generated by
compressional waves from surface sources impinging on a fracture. As the
fracture is compressed, the fiuid inside is "squirted" into the borehole,
generating up- and down-going tube waves. The tube waves are generally
recorded by a hydrophone array in the borehole. The generating mechanism of
these field waves and an example of field data are shown in Figure 10.
The relative amplitude of tube waves depends on the hydraUlic
conductivity of the fracture. The theoretical treatment of this problem is
discussed in detail by Beydoun at al. (Paper 11. this report). For a o.xed
amplitUde of compression, tube wave amplitudes increase with the hydraUlic
conductivity of the fracture. and with the period of the wave. Figure 11 shows
theoretical curves and a set of data obtained from measurements in deep water
1-5
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6
Toksi:iz et aL
wells in New England. The technique is relatively simple and is suitable for field
applications. We are investigating opportunities to test it in oil fields.
PERMEABIIJTY
The determination of formation permeability from logs still remains one of
the most important topics in borehole research. Many techniques, mostly
empirical, have been tried using acoustic logs (Bamber and Evans, 1971; Staal
and Robinson. 1977; Lebreton st cU., 1978). There is a correlation between the
attenuation of some phases of the full waveform and permeability. However, the
quantitative relationship has been elusive. The Biot (1956a,b) fluid flow
approach, incorporated by Rosenbaum (1974), assigns all attenuation to
permeability and flow. Yet the drilling mud in the borehole could be the largest
factor contributing to the attenuation of some phases, while bulk fluld flow is
only one component of in situ attenuation of the formation. While it is clear
that attenuation is the seismic property most sensitive to permeability, in
practice it is necessary to determine the contribution of permeable flow to the
attenuation of different phases of the full waveform.
The Stoneley wave is the simplest phase to use as the initial test case. It
has no geometric spreading and its attenuation due to borehole fluid and
formation properties (Qp-I, Q.-I, Qi 1) are well studied (Cheng st al., 1982; Toksoz
st al., 1983). The attenuation due to permeability can be calculated with
reasonable assumptions about the fluid flow from the borehole into the
formation. As discussed in detail in this report, Mathieu and Toksoz (Paper 10)
calculated Stoneley wave attenuation due to a fracture, a finely fractured zone
(fracture permeability), and a zone with standard permeability due to porosity.
This study investigated the dependence of attenuation on borehole radius and
wave frequency as well as on permeability. Figure 12 shows the attenuation due
to porous permeability as a function of frequency. Note that attenuation
increases rapidly with increasing permeability but is also dependent on
porosity.
In one case, where both full waveform and packer tests were available,
attenuation derived permeability (or fracture density) compared favorably
(generally within a factor of two) with the packer test results.
We feel qUite optimistic about the prospect of determining permeability
from full waveform logs.
FULL WAVEFORM INTERPRETATION
The primary features of full waveform acoustic log data are: 1) data
contain significant amounts of information; 2) data volume is very large: 3)
waveforms vary depending on formation and borehole properties; 4) relative
amplitudes of wave types are affected by the logging sonde and its frequency
response, and 5) effective analyses require sophisticated algorithms and a good
deai of expertise.
The last point can best be demonstrated with the aigorithms currently
used for determining the two simplest and most important quantities:
1-6
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Introduction
7
compressional and shear waves velocities. Compressional wave velocities can be
determined using anyone of a number of techniques that are well tested (Willis
and Toksoz, 1983, provides a good review). The major areas for improvement in
these algorithms are speed, accuracy, and robustness.
The determination of formation shear wave velocities, however, poses a
different problem. The shear wave velocities can be obtained with a
straightforward approach as long as they are higher than borehole l1.uld
velocity. If shear wave velocity is lower than l1.uid velocity, one must revert to
various complicated techniques: 1) determine the Stoneley wave phase and/or
group velocity and invert these to determine shear velocity. In low velocity
formations Stoneley waves are generated efficiently only at lower frequencies,
and this technique would work well only if data was acquired with a tool that
has low frequency response. 2) Use the complete waveform inversion to obtain
the shear velocity as is suggested in the paper by Toksoz et al. (Paper 8) in this
volume. This procedure is slow and fast techniques have to be developed to
automate it for routine analysis.
We conclude from this background that any effective shear wave velocity
analysis system will require some degree of "expert" input. This could be an
experienced human analyst, or a computer-based system relying on "Artificial
Intelligence" (A.I.) principles. At the least, an "expert system" can determine
the appropriate analysis technique for each section of the data. Ultimately
such a technique could derive complete information about the formations by
analyzing the data set, including full waveform inversion when appropriate, and
integrating the seismic properties with other log information such as resistivity
and gamma ray. A brief description of such a system is given below.
Interpretation-guided inversion
In the last decade considerable progress has been made in applying
Artificial Intelligence to real-world problems including applications In geology
(Duda, 1982; Campbell et al., 1982; Agterberg, 1979; Kerzner, 1983). Domainspecific techniques have been developed and several systems, embodying a high
level of expertise, have been successfully built, (PROSPECTOR, MYCIN, DENDRAL,
and CENTAUR, to mention just a few). Knowledge Engineering methods are also
currently being developed to help transfer expertise from humans to programs
and build knowledge bases. In the area of full waveform acoustic logging,
interpretation problems are numerous and inherently difficult and A.I.
approaches in this area have not yet been considered, mainly because the
science is still evolving, although there is a lot of experience that remains
largely untapped.
A long-standing goal of full waveform acoustic logging research is to
extract and interpret parameters such as Vp , Vs , Qp, Qs, and p for the layers
surrounding the borehole directly from the full waveform. So far, emphasis has
been on the identification of the different wave types and the determination of
their respective velocities and attenuation using travel time information, phase
moveouts, and amplitudes. The results thus obtained are then used as inputs in
some synthetic seismogram algorithm (such as discrete wavenumber
integration and finite difference wave propagation) and the resultant synthetic
waveforms generated are compared visually with the observed data.
1-7
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Toksoz et al.
However, automating these analysis-by-synthesis methods is impractical
today, even on large machines, and real time full waveform inversion using
standard numerical techniques is stili unthinkable on current minicomputers.
There are two main reasons for this:
First, there is the computing time factor. A classical numerical inversion
method would, presumably, attempt to minimize some measure of the distance
between synthetic and actual data as a function of the formation and borehole
parameters of interest. The synthetic waveform generation procedure would
usually be inside an iterative loop and invoked repeatedlY as the algorithm
progressed. Owing to the compute-intensive nature of synthetic data
generation, this type of iterative and "blind" numerical search in the
parameter space would be too time consuming to be practical.
Second, given the narrow-band nature of the signals and the inherent
complexity of the physical phenomena involved, this kind of brute force
approach is likely to be plagued with problems stemming from the existence of
local minima, large residuals, unknown and variable model uncertainties,
sensitivity to noise in the data, ill conditioning, etc ... It is certainly necessary,
at some point to, invoke the mathematical machinery, but since mathematics
do not provide any globa.l optimization algorithm, and systematic initialization
searches in n-dimensional spaces are prohibitively time-consuming, it is natural
to turn towards A.I. to explore what, if anything, can be inferred from simple
primitives extracted from the waveforms. The main idea is not to compete with
numerical software techniques, but to recognize that geophysicists do not look
at waveforms as arrays of floating point numbers. For example, the initial work
of interpretation-guided segmentation of pictorial features, performed by a log
analyst looking at a section of a full waveform acoustic log, is very powerful but
of a totally different nature from the work performed by an optimization
algorithm. The initial conclusions of the log analyst are perhaps rougher than
those of the program, but they are much broader and have sorted through a
very considerable volume of data. Software technology today can exploit and
"store" this kind of experience, so that in turn it can be used to gUide the
numerical inversion procedure, in other words, to perform a "smart inversion."
In looking at the possibility of using Artificial Intelligence methods to help
solve the fUll waveform inversion problem, one sees two key components:
1. Before there ca.n be ArtijicialIntelligence, there must be Intelligence.
There is a large body of knowledge concerning the interpretation of the
full waveform acoustic log that would be useful in guiding a numerical inversion
program. It is possible, for instance, to make an educated guess on the causes
of the disappearance of an S wave or of a Stoneley wave, or to detect the effect
of a damaged zone on the P wave amplitude, and there is certainly a lot of
material to start a sizable knowledge base. However, this base is stili expanding
rapidly and it is important to conceive it as a part of an incremental system,
where additional results could gradually be incorporated. One would even want
to design a system that could suggest experiments (Le. execution of a new
theoretical model) to refine rules such as in the SEEK system (Politakis and
Weiss, 1984) and to assist the interpreter in the smooth transfer of this
expertise. This brings forth the second key component:
1-8
(
Introduction
2. It is not the lcind
expressive structures.
of knowledge that
is critical, but the careful choice
9
of
One of the most critical aspects in the development of an intelligent
inversion program will be the choice of the structures which are to represent
knowledge about a set of waveforms, including information coming from other
logs. A combination of Production rules and of F'rames seems. the most
promising approach at this time. The notion of Prototype developed by Atkins
(1983) embodies both rules and frames and is a structure which is well suited
for the object-level representation of groups of geophysical waveforms. One of
the advantages of the Prototype Is that it allows the representation of
knowledge as expected patterns of data.
The kind and nature of patterns that can be easily extracted from the
waveform are certainly some of the most important questions to address, since
it is the manipulation and reasoning about prototypical patterns that will guide
the inversion.
We are just starting to investigate this approach. We expect it to be one of
the major research topics we will pursue in the coming years.
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Toksoz et aI.
REFERENCES
Agterberg, F.P., 1979, Statistics applied to facts and concepts in geoscience; in:
F'izism, Mobilism or Rela.tivism: Va.n Bemmelen s Sea.rch for Ha.rmony,
W.J.M. van der Linden (ed), GeoL Mining, 201-208.
Atkins, J.S., 1983, Prototypical knowledge
intelligence, 20, 163-210.
for
expert systems; Artijicia.l
Baker, L.J., 1981, The effect of the invaded zone in full waveform acoustic
logging; 51st Annua.linterna.tiona.l SEG Meeting, Los Angeles, CA.
Bamber, C.L. and Evans, J,R, 1976, 'I' - K log, permeability definition from
acoustic amplitude and porosity logs; SPEpa.per P171, Nov.
(
Biot. M.A., 1956a. Theory of propagation of elastic waves In a fluid-saturated
porous solid: I. low frequency range; J. Acous. Soc. Am., 28, 168-178.
Biot, M.A., 1956b, Theory of propagation of elastic waves in a fluid-saturated
porous solid: II. higher frequency range; J. Acous. Soc. Am., 28, 179-191.
Campbell, A.N., Hollister. V.F., Duda, RD., and Hart, P.E., 1982, Recognition of a
hidden mineral deposit by an artificial intelligence program; Science, 217,
927-928.
Cheng, C.H. and Toksoz, M.N., 1981, Elastic wave propagation in a flUid-filled
borehole and synthetic acoustic logs; Geophysics, 46, 1042-1053.
Cheng, C.H., Toksoz, M.N., and Willis, M.E., 1982, Determination of in situ
attenuation from full waveform acoustic logs; J. Geophys. Res., 87, 54775484.
Duda, RD., 1982, An overview of rule-based expert systems; AAPG Bulletin, 66,
1704.
Goetz, J.F., Dupal. L., and Bowles, J., 1979, An investigtion into the discrepancies
between sonic log and seismic check shot velocities; Austra.lia.n Petrol
Explor. Assoc. Jour., 19, 131-141.
Kerzner, M.G., 1983, Formation dip determination: An artificial intelligence
approach; The Log Ana.lyst, 24, 10-22.
Koerperich, EA. 1980, Shear wave velocities determined from long and short
spaced borehole acoustic devices; Soc. Pet. mgr. Jour., 317-326.
Lebreton, F., Sarda, J.P., Trocqueme, F., and Molier, P., 1978, Logging tests in
porous media to evaluate the influence of their permeability on acoustic
waveforms: 'I'ra.ns. 19th SPWLA Ann. Logging Symp., Fa.per Q.
Politakis, P. and Weiss, S.M., 1984, Using empirical analysis to refine expert
system knowledge bases: Artijicia.llntelligence, 22, 23-48.
Rosenbaum, J.H., 1974, Synthetic microseismograms:
formations; Geophysics, 39, 14-32.
1-10
Logging
in
porous
<-
Introduction
11
Staal, J.J., and Robinson, J.D., 1977, Permeability profiles from acoustic iogging:
S.P.E. pape-r no. 8821 presented at the 52nd Ann. Fall Tech. Conf. and Exh.
oj the Soc. oj Pet. Elng. oj AIME, Denver, CO.
Stephen, RA., Pardo-Casas, F., and Cheng, C.H., 1983, Finite difference synthetic
acoustic logs: M.l T Pull WaveJorm Acoustic Logging Consortium Annual
Report, Paper 4.
Stewart, RR, 1983, Ve-rtical seismic profiling: the one-dimensional forward and
inverse problems; Ph. D. thesis. M.LT., Cambridge, MA.
Toksoz, M.N., Cheng, C.H., and Willis, M.E., 1983, Seismic waves in a borehole - a
review; M.I.T. Pull WaveJorm Acoustic Logging Consortium Annual Report,
Paper 1.
Tubman, K.M., Cheng, C.H., and Toksoz, M.N., 1984, Synthetic full waveform
acoustic logs in cased boreholes: G<lophysics, in press.
Willis. M.E., 1983, Seismic velocity and attenuation Jrom Jull waveform acoustic
logs; Ph. D. thesis, M.LT., Cambridge, MA.
Willis, M.E. and Toksoz, M.N., 1983, Automatic P and S velocity determination
from full waveform digital acoustic logs: G<lophysics, 48, 1631-1644.
1-11
Toksoz et al.
12
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Figure 1: Variable area plot of an iso-oft'set section in a formation with alternating sections of carbonates, evaporates and shale. The data was logged
with E.V.A.. the Ell Aqultaine full waveform acoustic logging tool.
1-12
Introduction
13
-J:
l-
e.
w
c
0·5
TIME (ms)
Figure 2: Variable density plot of an iso-offset section in a carbonate sequence.
The logging tool used was from Welex, a Halliburton Co.
1-13
Toksoz et aL
14
(
-... - -
100
o
m
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-i
I
200
o
s
2
a
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TIME (msec)
Figure 3: Bit plot of an iso-offset section in a sand-shale sequence. The data
was logged with the Mobil Long Space Acoustic Logging tool.
1-14
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15
Introduction
.
(a)
-
,
1.50
2.70
7.50
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Figure 4: Comparison of full wave acoustic log microseismograms obtained in
similar (but not identical) "soft" formations using (a) Mobil LSAL tool; (b)
Schlumberger SLS-TA tool.
1-15
(
Toksoz et al.
16
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20
30
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Figure 5a: Ray trace in a borehole with a damaged or invaded zone with a constant velocity gradient. The depth of investigation of a particular ray
corresponding to a specific source-receiver separation is the depth at
which the ray turns back towards the borehole.
1-16
Introduction
o
17
O.7m
o
2.5m
O.97ms
0.42ms
Figure 5b: "Snapshot" of the displacements calculated by the finite difference
method in a borehole with a damaged or invaded zone.
1-17
Toksoz et al.
18
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-1.
1.+--i'f--+--l..,,=-f.--i--4--+--1--+--~
".M .,...L.
...,!<O.
(
SHe SONIC (klt/s)
I.M
1.--+--f---+--+---f.--i---1--+--'i---+
so~~t
25
_
DEPTH (Ill
Figure 6a: Comparison of log and core velocities.
1-18
19
Introduction
...
'"
.....
"' ... 5
tp
~.!:
>-
_ Coma.to55'0 n al To ......
(Flt'lo Rtocarotool
:
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J' -S SHe
•• ··10' • 12' LS~
Co Q
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60'
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140
80 80
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ts
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<J>C>~
<-;,;.;;..
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:=:;:
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Figure 6b: Comparison of log and core velocities (from Koerperich, 1980),
1,19
•
Toksoz et al.
20
(
I
10 -8
-2
o
2
4
-
10
ms 11000 ft
Figure 7a: Histogram of drift between integrated log and VSP traveltimes from
159 wells (from Geotz et at., 1979).
1-20
Introduction
2000 f3000 f4000 -
--
5000 f-
e..
6000-
J:
l-
w
I
I
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..11,
.,
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8000 f-
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9000-
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c
7000 -
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!
-10.0
t vsp
21
-
!
o
•
•
:.
••
••.,
• ••
. ••
,....
i
10.0
(ms)
tiNT SONIC
Figure 7b: Example of a drift curve 01 the difference in integrated log and VSP
traveltimes. The VSP was collected using a vertical vibrator source with a
1000 It offset (from Stewart, 1983).
1-21
Toksoz et al.
22
_---------------,L()
-en
~
()
(
Z
0
0
0
.
(/')
f-
Z
(
of-'
a.
(/')
>
of-'
(
(
L.-_...L-_....l...._.....jL!(
l..-_J...._...L..._....J..._--I._ _
o
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<0
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o
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CO
o
o
o0')
(1::J) H1d30
Figure 8: Synthetic drift curves with and without mUltiples for the well shown in
Figure 7b (from Stewart, 1983).
1-22
Introduction
23
Depth
·
·
E
,...'"
<D
I-
w
<J)
u.
u.
·
-
,~ ·
0
0
-
-
. . .
Zone
. .
. . . .
Time
-
Depth
,
~,
...
J
l"'·
Time
Figure 9: Iso-offset section of a full waveform acoustic log in a formation with a
hydrofrac. The attenuation of the waveform crossing the fracture is
clearly seen.
1-23
(
Toksoz et al.
24
(
P
SOURCE
/.
TIME (SECONDS)
0.2
(
X
",- '- f-
• •-; ~ .' "< -
~
><
__ /'
/
SENSORS
..... - •• '- • •
FRACTURE ZONE
TUBE WAVES
Figure 10: Schematic diagram showing the mechanism for tube wave generation
from incident P waves impinging on a fracture in a VSP.
1-24
Introduction
25
GRANITE FClRMATIClN
FORHRTION PRRAHETERS
VP IHISI
-5800.
VS IHISI
-3300.
RHO IKG/H31 -2700.
o
FLUIO PRRAHETERS
VP IHISI
-1500.
RHO IKG/H31
-1000.
VISC. IPLl
-0.0010
INCOHP. IGPAI =2.00
BOREHOLE RAOIUS ICHI -7.60
HIN-HAX TUBE WRVE VELOC. IH/SI -1446. - 1446.
BOT-TOP ISO-PERHER8ILITlES IOARCYI:
0.10 - 0.20 - 0.50 - 1.00 - 2.00
o
~ . ....,---,.......,.-.:-,-,----;--:-...,-.."..-..,.-,.-,--"7".-,..-,--.--,.--,
,
:- -i-"t
"
-i--~
,
- r- -i -
r- -i-
C'l
(JJ
(JJ
'to
<
<ll
:::l:
3:
-
<5
<ll
a:
CIl
0
Cl
Z
Cl
c:
0
c:
c:
l-
e.:>
1Il
(JJ
o
o
>-
<D
.....
CIl
0:0
0:0
...... ......
r--
W~
r-x
r-x
C'l
~
..;
Q;
<ll
"':
0:
:::>
if)
if)
<ll
... ...
3: 3:
.c
.c
..... .....
WO
0: 0
0....
""
0
CIl
0
-.... ... ...CIl
"<t
...
C'l
lO
C\J
•
Figure H: Data versus theoretical tube to P wave pressure ratios as functions
of frequency and permeability. The data were collected in crystalline
rocks in Massachusetts.
1-25
Toksoz et al.
26
FORHRTION PRRRHETERS
FLUIO PARAHETERS
VP
IH/SI
-5850.
VP
VS
IH/S)
-3350.
RHO
-2650.
VISCo
RHO
IKG/H3)
IH/SI
IPLl
INCOHP.
80REHOLE RAOIUS
ICHI
POROUS ZONE WrOTH
FREOUENCY
-1000.
-0.0010
IGPAI.2.00
-3.80
IHI
IKHZI
_1500.
IKG/H31
-0.60
-34.
BOT-TOP ISO-POROSITIES
,(
IPERCENTJ:
0.1 - 1.0 - 10.0
o
'"o
-:- t -i- -i- -:- -:-:-!- T·-i- +-1-~ - ~ ~ - ~ -f~
\- -i-·
-~-
t -;.-.; -\- -i - \-....; -;,...
- r- -; - ;- -;- "'i
o(\J
~
-!-
-'i- -; - ;- -: - :- -i-
~_L_i_L_!_~_~~_~~_L_l_
o
:
i
~
!
i i : : i
.
~4-r4-t~-t-!-1-~~-r-!-
J _ L _i _ 1- _:_ .i. _ i_ J _ L. J _ L _:_
!
i
: i ! i
o
.!- i - :- -1 - i- -j - i- -i - i - i- -f - r --i - i- -io~:::="';~.i'
L'~,:.....Li.-W-~
<
"b.00
_
~
1.20
PERMERB III TY
+'...'-'-'-'
2.40
3.60
4.BO
6.00
(LOG 10 (M I LLI DRRClSJ J
Figure 12: Theoretical Stoneley wave attenuation versus permeablllty in a
porous formation. For details, see Mathieu and Toksoz (Paper 10, this report) .
1-26
(