Note: Descriptions are shown in the official language in which they were submitted.
CA 02610997 2007-12-06
WO 2006/138112
PCT/US2006/021922
'
APPLICATION FOR PATENT
FOR
METHOD FOR COHERENCE-FILTERING OF ACOUSTIC ARRAY SIGNAL
Inventor: Xiao Ming Tang
ASSIGNEE: BAKER HUGHES INCORPORATED
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BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a method and system of filtering signal data.
More
specifically, the present invention relates to a method and system for
analyzing signal data
collected by an array of receivers, determining the coherence function of the
received data,
and filtering the received raw data with the coherence function.
2. Description of Related Art
Data collection arrays, i.e. a collection of more than one single position
point data
recorders, are used in the collection of a myriad of data. Examples of array
collected data
include radar, seismic, acoustic, sonar, radio waves, to name but a few. Often
the data
received and recorded by such arrays can include unwanted signals that
intermingle with the
desired data and distort the final recordings thereby providing skewed
results. Moreover,
when dealing with arrays of data recording devices, the time lag between
signals of the
individual recorders is especially important. While the recorded data can be
processed and
filtered to remove the noise and to extract information from the time lag,
there still exists
room for significant improvement in processing such data.
In acoustic logging through an earth formation, acoustic signals that travel
along the
formation are often contaminated by other acoustic waves that travel along a
different path.
For example, in the logging-while-drilling measurement, acoustic waves may
travel long the
tool body (drill collar) and significantly interfere with the formation
signals. In cased hole
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logging, acoustic waves transmission along the casing may become significant
if the casing is
poorly bonded with cement. Moreover, this wave transmission may become
overwhelmingly
large if the casing is detached from cement (i.e., the free-pipe situation).
Tubman, K.M.,
Cheng, C.H., and Toksoz, M.N., 1984, Synthetic full-waveform acoustic logs in
cased
borehols, II ¨ Poorly Bonded Casing, Geophysics, 51, 902,913.. In the latter
situation,
processing acoustic signals to obtain formation properties is extremely
difficult because the
formation signals are almost indiscernible in the presence of overwhelming
casing waves.
Because the majority of existing wells are cased and there is often a need to
determine
acoustic properties through casing, acoustic logging in cased borehole is
still routinely made
because formation properties can be measured when casing is well bonded with
formation.
Tang, X. M., and Cheng, C.H., 2004, Quantitative Borehole Acoustic Methods,
Elesevier..
However, the measured data are often abandoned when casing is poorly bonded or
detached
because of the interference caused by the waves passing through the casing.
Because of the need to measure formation acoustic properties through a poorly
bonded/detached casing, various methods have been tested to process acoustic
data under
these conditions. A common practice is to apply the routine semblance method
directly to the
data and to detect the small events on the semblance correlogram that are
associated with the
formation arrivals. This method often fails because the formation signals,
although they
theoretically exist, are small compared to the large casing ringing signals
and are thus difficult
to distinguish from noises in the data. A maximum likelihood method was also
used to
enhance the resolution of the formation signal on the correlogram. Block, L.
V., Cheng, C. H.
and Duckworth, G. L., 1986, Velocity Analysis of Multi-receiver Full Waveform
Acoustic Logging
Data in Open and Cased Holes, 56th Ann. Internat. Mtg.: Soc. of Expl.
Geophys., Session:BHG2.5.
However, due to the amplitude difference between the formation and casing
signals, the
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enhanced resolution is not of much help in resolving the low-coherence
formation signal with
a poor signal-to-noise ratio.
A need exists to suppress the strong casing signal so that the formation
signal
coherence can be enhanced, to accomplish this a waveform subtraction method
was
developed to suppress the casing signals. Valero, H., Skelton, 0., Ahneida,
M., Stammeijer, J.
and Omerod, M., 2003, Processing of Monopole Sonic Waveforms Through Cased
Hole, 73rd Ann.
Internat. Mtg.: Soc. of Expl. Geophys., 285-288. By insolating a portion of
the casing waves
ahead of the formation arrival and subtracting the waves from the data, the
formation signal
coherence is enhanced and the signal can thus be picked from the semblance
processing.
However, as stated in Varelo et al (2003), the method does not work well when
the casing and
formation signals overlap in time. Therefore, there exists a need for a device
and method
capable of processing signal data and successfully filtering away unwanted
portions of the
acquired signal.
BRIEF SUMMARY OF THE INVENTION
The present method disclosed herein involves a method of waveform processing
technique utilizing signal coherence of the array data for processing signals
having poor
signal-to-noise ratio. Raw waveform data is first transformed into f-k
(frequency-
wavenumber) domain. A coherence function is then calculated and convolved with
the data
in the f-k domain, which effectively suppresses non-coherent signals in the
data. For the
remaining coherent data, the unwanted part is muted and the wanted part is
retained and
inverse-transformed to yield the coherence-filtered array waveform data. After
this
processing, small signals that are hidden in the original data are extracted
with much
enhanced coherence. Subsequent processing of the data yields reliable
information about
formation acoustic property.
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The present invention includes a method of processing signal data comprising,
obtaining signal data, obtaining a coherence function relating to the signal
data, and filtering
the signal data with the coherence function thereby producing coherence
filtered data. The
signal data comprises, among other data, downhole acoustic data. The filtering
of the present
method can be performed in the frequency-wavenumber domain. The method of can
further
comprise suppressing unwanted signals from the coherence filtered wave data as
well as
optionally further comprising converting the coherence filtered wave data into
the time
domain. The step of obtaining signal data comprises, creating a seismic signal
within a
wellbore casing and recording the resulting wave propagating through the
casing. The signal
data may comprise an array of propagating wave signals.
With regard to the present method, the coherence filtered wave data X ou(k,co)
can be
developed with the following equation: X01(k,co)=X(k,co)=coh(k,co).
Wherein coh(km) represents a coherence function of one or more than one wave
mode and
X(k,m) represents signal data.
The present invention disclosed herein may also include a data analysis system
comprising, a transducer array having an array of transducers, and a data
processor in
communication with the array. The array is capable of receiving raw data that
is
communicated to the processor, wherein the processor calculates a coherence
function
relating to the raw data and filters the raw data with the coherence function
to produce
coherence filtered data. Optionally included with data analysis system is a
downhole sonde
on which the array is affixed. The data analysis system may further comprise a
field truck in
communication with the sonde. Further optionally, the processor may be housed
within the
field truck and may be in communication with the field truck. The array of the
data analysis
system can comprise a surface mounted instrument. Optionally, the surface
mounted
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instrument can comprise an accelerometer. Alternatively, the data analysis
system can further
comprise a drilling system comprising a drill string and a drill bit. The
array may be disposed
on the drill string or optionally on the drill bit.
Accordingly, in one aspect there is provided a method of enhancing signal data
comprising:
obtaining signal data having, useful data and non-useful data using a data
collection
system;
transmitting the signal data to a processor;
transforming the signal data into the frequency-wavenumber spectrum with the
processor;
obtaining with the processor a coherence function defined in the frequency-
wavenumber
(f-k) domain that relates to the transformed signal data; and
using the processor to multiply the coherence function and the transformed
signal data
thereby filtering the non-useful data from the signal data.
According to another aspect there is provided a method of enhancing acoustic
signal data
comprising:
obtaining acoustic signal data that has passed through a hydrocarbon bearing
subterranean formation;
transmitting the acoustic signal data to a processor;
using the processor to transforming the acoustic signal data in the frequency
wavenumber spectrum;
providing a coherence function with the processor that is defined in the
frequency
wavenumber (f-k) domain that relates to the transformed acoustic signal data;
and
removing unwanted signal data by filtering the acoustic signal data with the
coherence
function in the processor.
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According to yet another aspect there is provided a data analysis system
comprising:
a source configured to generate a source signal;
a receiver array configured to receive a received signal resulting from the
source signal; and
a data processor in communication with said array;
wherein said processor calculates a coherence function defined in a frequency-
wavenumber
(f-k) domain relating to the received signal and filters the received signal
with the coherence
function.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING
Figure 1 illustrates a flowchart of an embodiment of a method of filtering raw
data.
Figure 2a demonstrates a collection of signal data in the time domain
collected by a recorder
array.
Figure 2b depicts raw data transformed into the f-k plane.
Figure 2c shows filtered data in the f-k plane.
Figure 2d illustrates the convolved f-k data of Figures 2b and 2c.
Figure 2e shows coherence-filtered data in the time domain.
Figure 3a demonstrates a free pipe model.
Figure 3b is a depiction of modeled data.
Figure 3c shows a plot of the results of a direct semblance calculation as
performed on the
data of Figure 3b.
Figure 3d illustrates the coherence-filtered formation signal f-k spectrum of
the P-wave
slowness range of Figure 3b.
Figure 3e are plots of an inverse f-k transformation of the data of Figure 3d.
Figure 3f is a plot of the semblance calculation of the filtered data of
Figure 3e.
Figure 4 demonstrates a comparison of raw versus filtered cased hole acoustic
data.
Figure 5 compares raw data to filtered data in combination with a correlogram.
Figure 6 depicts an embodiment of a data collection system for use with the
present method.
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Figure 7 illustrates an alternative embodiment of a data collection system for
use with
the present method.
DETAILED DESCRIPTION OF THE INVENTION
Disclosed herein is a method of processing signals that may have poor signal-
to-noise
ratio. This is required so that useful information can be extracted from the
signals that would
otherwise be deemed unusable by conventional means. While this may be present
itself in
multiple situations, poor signal-to-noise ratio scenarios are frequently
encountered in acoustic
logging practice. For example, cased-hole acoustic data logged in free-pipe
are often
abandoned because the formation signals are usually untraceable due to the
presence of
predominant casing signals. The disclosed method is not limited to acoustic
logging
applications; it can generally be applied to any array data that comprise
propagation wave
signals. The wave signal array data, for example, may comprise seismic waves
recorded at
different depth levels in a Vertical Seismic Profiling (VSP) survey, or the
seismic waves
recorded by a geophone array in a surface seismic survey. In earthquake
seismology, the
signals may be the earthquake-generated seismic waves recoded at different
stations/observatories. Apart from the elastic/seismic waves, the wave signals
may also be the
electromagnetic waves recorded by a sensor array, for example, radar waves
recorded by an
array of antennas.
The coherence-filtering technique disclosed herein significantly improves the
situation
of a poor signal-to-noise ratio. Application of this technique to various
difficult conditions,
especially cased-hole acoustic logging, has been remarkably successful. In the
cased-hole
scenario, coherence-filtering outperforms other currently known techniques.
The processing
technique described herein allows for the acquisition of formation properties
through poorly
bonded well casing that are unobtainable by conventional techniques. The
technique
disclosed herein has produced several important applications in acoustic
logging data
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processing. For example, it has been applied to process cased-hole acoustic
data in the free-
pipe situation with remarkable success and also been proven effective in
suppressing tool-
wave effects in the logging-while-drilling (LWD) acoustic data processing.
The present disclosure describes a coherence-filtering technique to
significantly
enhance the coherence of signal events. When the signals are recorded by the
receiver array
of an acoustic tool, this technique is especially advantageous when the
signals are masked by
other overwhelming waves or noises and thus have a poor signal-to-noise ratio.
The filtering
process is performed in the frequency-wavenumber (commonly known as f-k)
domain. The
technique employs a coherence filter constructed from the coherence function
of the array
wave data. After filtering the data with the filter, non-coherent noises are
suppressed and the
coherence of the wanted signal(s) is enhanced and can further be separated by
either muting
the unwanted (coherent) signals or passing the wanted signal(s) in the f-k
domain.
The flowchart of figure 1 illustrates an embodiment of the present invention
directed
to signal processing of acoustic signals received downhole. In modern acoustic
logging in a
borehole, the acoustic wave time series X(t), where t represents time, is
recorded by an array
of receivers equally spaced along the borehole z-axis (step 100). The wave
data in essence
are a two-dimensional function of z and t, denoted as X(z, t) . The two-
dimensional Fourier
transform, known as the f-k transform, of the data is:
X (k, co) = ffX(z,t)e0)t)dzdt , (1)
where co = 27-cf is the angular frequency and k is the axial wavenumber.
A very useful property of the f-k transform is that a linear moveout of
slowness s for a
wave signal in the z-t domain corresponds to a linear trend of the wave energy
that can be
traced to the center of the f-k plane, where k and f are respectively the
horizontal and vertical
coordinate of the rectangular coordinate system in the f-k plane. This
property allows for
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delineating the moveout and dispersion (i.e., change of wave slowness or
velocity with
frequency) characteristics of the waveform data in a receiver array.
It should be pointed out that the f-k technique, although extensively used in
seismic
data processing has some serious limitations in the acoustic log data
processing practice.
Yilmaz, 0., 1987, Seismic Data Processing, Soc. of Expl. Geophys. 526. For
conventional
wireline and LWD array acoustic data, this technique is rarely used because
the data are over
sampled in time but sparsely sampled in space. The number of receivers in
array, N, is
typically eight or fewer. (For LWD acoustic tools, N is usually four or six).
The sparse spatial
sampling and short array length causes problems for the array acoustic data in
the f-k domain.
Firstly, in the f-k plane, the energy density of various wave modes may be
closely clustered
and smeared by noise, making it difficult to distinguish data trends of the
wave modes. (An
example of this is given in Figure 2b.) This happens because the receiver
array length
(typically 3.5 ft or 1.07 m) is usually not long enough to allow waves of
different moveouts to
separate in time and space.
Another problem with the f-k technique is that strong spatial aliasing effects
may exist
in the f-k data of an acoustic array. The Nyquist wavenumber beyond which the
aliasing
effect occurs is given by:
27r
kNyquist = d (2)
where d is receiver spacing. For a typical receiver spacing of d=0.5 ft
(0.1524 m), kNyqõ,s, is
only 6.28/ft. For this low value of kNyquiõ , aliasing usually occurs at
higher frequencies. For
example, a 10-kHz compressional wave with an 8000 ft/s velocity has a
wavenumber of k =
7.85/ft (>6.28/ft), resulting in the aliasing of the wave data, that is, the
data beyond k = 6.28/ft
will wrap around from k = -6.28/ft in the f-k plane. The aliased data may
overlay with the
clustered/noise-smeared f-k data, aggravating the problem.
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time shifts in the array data of the wave mode (step 102). For a wave signal
with a moveout
slowness s, we use this slowness to shift or advance the wave time series of
the nth receiver
in array by an amount:
At = s(n ¨1)d, (n =1, 2,L , N) , (3)
The shifted wave signal will then have almost no moveout in the array and, by
applying the f-
k transform to the data (step 106), its trend (or energy density contour) in
the f-k plane will
have an infinite slope. In other words, the data trend will lie on, or very
close to, the
frequency axis, and will therefore not be aliased in the f-k plane.
With regard to coherence filtering, this technique has been developed to
better
delineate data trends in the f-k domain than the straightforward f-k
transform. The
mathematical basis of the coherence-filtering technique is to approximate the
spectral array
data, as obtained by Fourier-transforming the acoustic wave traces, by a
number of
propagation wave modes,
Xõ (co) E A (co) eik,(n--1)d
(n =1,L , N), (4)
P
P=1
where M 1) is the total of wave modes in array; Ap , kp= amp, and sp are
respectively the
spectral amplitude, wavenumber, and slowness of the pth wave mode. This
approximation is
a quite accurate description for acoustic logging data that primarily consist
of guided wave
modes in the borehole, such as pseudo-Rayleigh and Stoneley waves in monopole
logging,
flexural wave in dipole logging, and screw wave in quadrupole logging, and the
like. Even
for refracted (compressional and shear, or P and S) head waves along the
borehole, the
propagation-mode approximation is still valid because the receiver array is
typically several
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wavelengths away from the source such that the wave amplitude 4, of the waves
does not
vary significantly across the array.
In step 104, the question is posed if the data is comprised of a single wave
mode or
multiple wave mode. If the array data is comprised primarily of a single wave
mode (e.g., in
dipole acoustic logging, the dipole-flexural wave is the only mode that
dominates the data.),
then a single-mode coherence function can be constructed in the f-k domain
(step 110), as
given by (Tang and Cheng, 2004):
Z.X:;(0)eik(11-1)d
n=i _____________________________________
coh(k, co) = _______________________________________ (5)
NEX:(co) X õ(co)
\ n=1
where * denotes taking the complex conjugate of the data and denotes taking
the modulus
of the complex quantity inside. For the data described by equation (4), we see
that if the
wavenumber variable k attains the value of kp , the wavenumber the propagation
mode, then
the phase of Xõ*(co)eiko-i)d Ape[i(k-k p)(n-1)(1]
in equation (5) will be canceled and the
coherence function value will be maximized (the value will approach 1 if the
data are noise-
free). Equation (5) is essentially a semblance/coherence stacking of the array
data in the f-k
domain. A property of the coherence function defined in equation (5) is that
it is mainly
applicable for single-mode data. If the data consist of more than one mode,
then the
coherence will be biased toward the dominant wave mode that has the highest
amplitude or
coherence, resulting in underestimating the contribution from other wave
modes.
Nevertheless, this property, if properly used, can significantly enhance the
coherence of a
designated wave mode.
If the wave data consist of multiple wave modes, such as the compressional,
shear,
and Stoneley waves in a typical monopole logging data set acquired in a fast
formation, then a
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multiple-mode coherence function should be used (step 108). Here the
construction of this
function is briefly described. The M propagation exponentials epd, (p 1,L ,M)
in
equation (4) satisfy the following characteristic polynomial equation (Tang
and Cheng, 2004):
ikilld (M -1)d
aoe P + ,L ,+ am .0, (p =1,L ,M) (6)
where aõ =1; other coefficients a p (p =1,L ,M) (note these coefficients are
dimensionless)
need to be solved from the array data. By combining equations (4) and (6), it
is easily shown
(see Tang and Cheng, 2004) that data at receiver n, as described by equation
(4), can be
predicted by a linear combination of the data from other receivers, as given
by:
Xõ (co) = ¨E apxõ_p(w), (M + 11 N) (7)
p=1
Equation (7) is called forward prediction because the receiver whose data is
being
predicted is ahead of the receiver(s) whose data are used to predict. To
increase data
redundancy, the complex conjugate of equation (4) is taken and then combined
with equation
(6) to yield another prediction: X:(co) = ¨E apx (c)) , (1 _< n N ¨ M)
P=1
(8)
Equation (8) is called backward prediction because the receiver whose data is
being predicted
is behind the receiver(s) whose data are used to predict. Equations (7) and
(8) are then
combined and simultaneously solved using the Kumaresan/Tufts (known as the KT)
method
to yield the coefficients a, (p =1,L ,M) . Tufts, D. W., and Kumaresan, R.,
1982,
Estimation of Frequencies of Multiple Sinusoids: Making Linear Prediction
Perform Like
Maximum Likelihood, Proc. IEEE, 70, 75-89. With the coefficients known in
equation (6),
we replace the wave mode wavenumber k p with the wavenumber variable k in this
equation
and use it to construct a multiple-mode coherence function:
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IkMd 12
coh(k, co) = exp aoe + eik(M -1)d , +am (9)
Since the polynomial function in equation (9) has the same functional form as
that in equation
(6), the function approaches zero when the k variable hits one of the roots k
, (p =1,L , M)
of equation (6); the coherence function in equation (9) will then approach a
maximum value
of 1. For other values of k, the (dimensionless) modulus of the function
inside 11.11 is large and
the coherence function value is low; the function approaches zero if k is far
away from kp .
Therefore, the high-value region of the coherence function effectively
delineates the
trajectories/trends of the coherent part of the data in the f-k plane,
especially when the data
contain several propagation modes.
It is worthwhile to comment on the data coherence function, as computed from
equation (5) (single mode) or equation (9) (multiple mode), versus the data
energy density, as
obtained from the direct f-k transform (equation (1)). The f-k data density
reflects the wave
energy distribution in the f-k plane. However, a region with high energy
density may not
necessarily mean that the data there is coherent. In comparison, the coherence
function is a
measure of data coherence in the f-k plane. Even in regions where the data
energy density is
low, the coherence function value can still be quite significant as long as
the data are coherent
in these regions. (An example of comparing the wave energy density and
coherence is given
in Figure 2b and Figure 2c.) Therefore, the data coherence function, compared
to the data
energy density, can better delineate data trends in the f-k domain.
Using the given coherence function (single mode: equation (5); multiple-mode:
equation (9)) as a coherence filter (step 112), a coherence-filtering
processing can be
performed (step 114). According to a property of (two-dimensional) Fourier
transform,
filtering or convolving the data X(z, t) in the z-t domain with a filter (the
coherence filter) is
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equivalent to multiplying the f-k transformed data X(k, co) with the filter's
f-k spectrum in
the f-k domain. Therefore, the coherence-filtered wave data in f-k domain,
designated as
Xcill (k, a)) , is simply
X01(k,a)). X(k, a)). coh(k,co) (10)
Because the coherence function coh(k, co) delineates the trajectory/region of
the
propagation modes (the coherent data) in the f-k plane, multiplying the f-k
data X(k, a)) with
the function retains the data in the coherent region and reduces/mutes the
data outside the
region, thus suppressing the non-coherent (or noise) part of the data.
For the remaining coherent part of the data, further processing can be done to
reject/suppress unwanted signals (step 116). For example, in cased-hole
acoustic logging, the
dominant ringing casing waves are very coherent and should be suppressed in
order to pick
the formation signal of much smaller amplitude. The condition for separating
the wanted
from unwanted signals is that they should have distinctively different
propagation velocity (or
slowness) values. For formations with intermediate and slow velocities, this
condition is
satisfied. For instance, if the formation slowness is greater than 80 pts/ft,
as compared to the
typical casing slowness 57 gs/ft, then the casing waves can be effectively
suppressed (step
118).
There are at least two ways to suppress the unwanted wave signals. The first
is a data
rejection method that uses a known fan-filtering technique in the f-k plane
(e.g., Yilmaz,
1987) (step 120). The fan-shaped region is bounded by two (left and right)
lines originating
from the center of the f-k plane. This region should cover the data trend of
the unwanted
signal (step 124). For filtering the casing wave with a 57 lis/ft slowness,
the corresponding
slowness of the left line of the fan can be set to 57-20 = 37 [ts/ft and that
of the right line, to
57+20=77 gs/ft. If the waveform data have been shifted using equation (3) (the
data trend
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now lies on the frequency axis), then the slowness value can be set to -20
s/ft for the left
line, and 20 s/ft for the right line. Then, rejecting the data by muting the
value of Xcfii(k, co)
within the fan suppresses the unwanted casing signal.
The second method to suppress the unwanted wave signals is a data passing
method
(step 122). This method needs to have a rough estimate of the propagation
slowness of the
wanted wave signal. To avoid possible aliasing of the wanted signal in f-k
domain, the
slowness in equation (3) is used to shift the data and then transform the data
to f-k domain.
The data trend of the wanted signal should now lie in the vicinity of the
frequency axis.
Because now only one signal is involved, the single-mode coherence function
(equation (5))
can be used to filter the data in a fan-shaped region surrounding the
frequency axis. Using the
same cased hole situation as an example with a casing wave slowness of 57
s/ft and a
formation wave slowness of 100 s/ft (this slowness is used in equation (3) to
shift the data),
the slowness corresponding to the left and right lines of the fan can be set
to -30 us/ft and 30
us/ft, respectively. After the operation using equation (10), the Xefii (k,
co) data in the fan
primarily contains only one signal and the signal coherence should be much
enhanced. Then
passing the data in the fan and muting the data outside the fan yields the
wanted signal.
The coherence-filtered f-k spectral data X1 (k, co), either with or without
the fan-
filtering, are inverse-transformed back in to z-t domain to obtain the
coherence-filtered array
waveform data, as given by (step 126):
X cin(Z ,t) = (k,co)eiu'dkdco (11)
If time shifts, as given in equation (3), were applied to advance the receiver
waveform data
prior to transforming the data to f-k domain, the same time shifts should now
be applied to
delay the filtered data so as to restore the original time position of the
wave data (step 128).
The resulting array data for one array location in depth can then be output
(step 130) for being
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processed/analyzed to extract formation acoustic properties for that depth.
The same
processing is then performed for all depths of interest (steps 132, 134). The
above-described
processing procedures are summarized by the flow chart in Figure 1. The
results of applying
the coherence-filtering technique to acoustic data processing will be
demonstrated in the
following non-limiting examples of the method of the present disclosure.
Example 1: A real data example to demonstrate the coherence-filtering
procedure
Figures 2a ¨ 2e demonstrate the coherence filtering procedure using a field
dipole data
example. Here the data were recorded by a wireline dipole acoustic logging
tool. The tool
consists of a dipole transmitter and an array of receivers that are located
about 10 ft above the
transmitter and aligned longitudinally along the tool. Figure 2a is a
graphical depiction of
raw low-frequency dipole array acoustic data recorded by an array of equally
spaced acoustic
receivers. This data can also be referred to as received data or a received
signal. The ordinate
represents time and the abscissa represents the distance between the dipole
source transmitter
and the receivers. Significant noise contamination can be seen from the wave
reverberations
in the raw data of the near receivers.
The corresponding f-k spectrum is shown in Figure 2b where several closely
clustered
events are exhibited. Since the aliasing effect does not occur for this low-
frequency data, no
time-shifts were applied to the waveform data before the f-k transform. Figure
2c shows the
resulting plot by applying the coherence function to single-mode scenario of
the raw data
(equation (5)). As can be seen by comparing the plots of Figure 2b and 2c, the
f-k coherence
plot shows a defined data trend unlike the rawf-k data. Figure 2d, illustrates
the convolved f-
k data of Figures 2b and 2c. Converting the f-k data of Figure 2d back into
the time domain
produces the coherence-filtered data of Figure 2e. The filtered f-k data, as
obtained by
multiplying the raw data with the coherence function, shows a dominant trend
for the dipole-
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flexural mode in the f-k plane. Inverse-transforming the data gives the
filtered array data with
much improved waveform coherence across the array.
Example 2: Extracting formation P wave from free pipe (synthetic) acoustic
data
Figure 3 uses simulated array acoustic data to demonstrate the ability of
coherence
filtering to extract formation signals through an unbonded casing. This is a
free pipe situation
with a 0.25-cm thick fluid annulus behind the casing. Figure 3a illustrates a
free-pipe model
used to create the array acoustic data and Figure 3b contains the
corresponding modeled data.
As with Figure 2a, the data of Figure 3b is in the time domain, with the
ordinate in time units
and the abscissa in distance units. The data shows strong ringing casing waves
with almost
no discernible formation arrivals. A direct semblance calculation was
performed on the data
of Figure 3b and plotted in Figure 3c. The plot of Figure 3c on the data
(right) shows a
dominant casing peak (slowness = 57 s/ft) and a weak formation arrival
(slowness = 102
pts/ft) with a low semblance/coherent value. Figure 3d illustrates the
coherence-filtered
formation signal f-k spectrum for the P-wave slowness range of Figure 3b. The
wave data
were shifted using its slowness (102 ps/ft) so that the data almost lie on the
frequency axis.
Note the bottom event of Figure 3d represents the Stoneley-wave energy that
falls into the
data pass region (the fan filter) and the upper two events belong to the
formation P wave. The
plots of Figure 3e are obtained by inverse f-k transforming the data of Figure
3d. These plots
depict formation P wave plus a low-frequency Stoneley.
As shown in Figure 3f, subsequent semblance calculation of the filtered data
of Figure
3e shows a well-defined formation arrival at 102 s/ft. The semblance of the
formation wave
is much enhanced compared to that of the unfiltered data. Note the
disappearance of the
casing event from the correlogram. This result points out a useful property of
the f-k
coherence-filtering technique. Although the unwanted casing wave may not be
completely
removed from the data of Figure 3d due to short array and sparse spatial
sampling, the
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coherence of the unwanted wave is largely eliminated. It is eliminated from
both from the f-k
data spectrum and from the space-time domain semblance correlogram.
Example 3: Application to cased-hole acoustic data to extract formation P-wave
slowness
Figure 4 uses a field data example to demonstrate the ability of the coherence-
filtering
technique to extract formation slowness from cased hole acoustic data, even in
the free-pipe
situation. The acoustic data, shown in the Raw Data track, include several
scenarios: good
cement bond (middle), poor cement bond (lower), and poor bond/free pipe
(upper). The data
in the upper free-pipe sections are dominated by casing signals, resulting in
inability to pick
formation slowness from the semblance correlogram, which is shown in the
Correlogram
(raw data) track. As seen in the Filtered Data track, coherence filtering the
data suppresses
the casing signals and enhances the formation wave coherence. The enhanced
coherence
enables picking the formation slowness with high confidence even in the free
pipe situation
(Correlogram (filtered data)).
Example 4: LWD (APX) data processing to suppress tool-wave effects
Figure 5 demonstrates the advantages of coherence filtering for logging while
drilling
(LWD) acoustic data for suppressing tool-wave effects. LWD acoustic data is
often
contaminated by tool waves that travel along an associated drill collar. As
seen in the
Correlogram (raw data) track of Figure 5, the tool waves generate a
significant semblance
value and interfere with the picking of formation slowness. This example may
seem trivial
because the tool waves are small relative to the formation waves, as compared
to the cased
hole example in Figure 4 where formation waves are almost indistinguishable in
the free-pipe
section. However, one should note that the f-k data from LWD tools are even
more hampered
compared to those from wireline tools, due to a fewer number of receivers
(six, versus eight,
the typical number of receivers of a wireline tool) and sparser sampling
(0.75ft, versus 0.5 ft;
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the Nyquist wavenumber kNAõ;õ is now even lower, which is only 4.2/ft, versus
6.28/ft of the
wireline case). However, the example in Figure 5 shows that the coherence-
filtering
technique is still effective despite the increased adversities. The Raw Data
track of Figure 5
displays the LWD data (receiver 1) in VDL, which shows that the data are
contaminated by
tool waves. The tool waves produce a strong semblance in the Correlogram (raw
data) track
and interfere with the picking of formation slowness. As shown in the Filtered
Data
(normalized) track coherence filtering suppresses the tool wave and removes
its semblance
from the Correlogram (filtered data) track. The enhanced formation signal
coherence allows
for picking the formation slowness in areas dominated by tool waves as can be
seen from the
agreement between the picked LWD slowness (curve) and the wireline-measured
slowness
(markers).
A data collection system 4 utilizing an embodiment of the method of the
present
disclosure is illustrated in Figure 6. The data collection system 4 as shown
comprises a sonde
10 connect by wireline 8 to a field truck 6. Signal data is collected by a
sonde 10 disposed
within a wellbore 14, where the wellbore 14 pierces a formation 16. An array
of transducers
12 is disposed on the sonde 10, the transducers 12 are capable of receiving
and recording
downhole signals transmitted to the receivers from within the formation 16.
The transducers
12 can be capable of transmitting a signal in addition to receiving a signal.
The raw recorded data received by the transducers 12 can be stored within the
sonde
10 for later retrieval or processing, or can be transmitted to the field truck
6 via the wireline 8
or telemetry. The method of coherence filtering can be performed within the
sonde 10, field
truck 6, or the associated processor 18. The processor 18 may be a computer,
or
microprocessor, with memory capable of running programmed instructions. The
processor 18
may also have permanent data storage and hard copy output capabilities. The
processor 18
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may be a separate unit or may be located in an enclosure attached to the field
truck 6 or any
other suitable enclosure commonly used in the art. Combining the data
collection system 4
with a processor 18 or other means of processing the signal data, such as
manually, comprises
a data analysis system.
Figure 7 illustrates an alternative data collection system 4a for use in
logging while
drilling operations. Here the embodiment of the data collection system 4a is
shown coupled
with a drilling system 25. The drilling system 25 comprises a drill string 26
having multiple
elements and terminating on its lower end at a drill bit 27. Transducers 28
for receiving
signal data are shown on the drill string 26 and on the drill bit 27. The
transducers 28 can be
any type of device capable of receiving signal data while being disposed
within the confines
of a wellbore 14. Similar to the data collection system 4 of Figure 6, the
signal data collected
by the drilling string transducers 28 can be transferred to the processor 18
or to data recording
devices (not shown) within the field truck 6. Optionally, processing means can
also be
included within the drill string 26 for storing the collected signal data
and/or processing the
data in accordance with the method described herein.
Optionally, a surface mounted transducer 20, such as an accelerometer, can be
mounted in mechanical cooperation with the Earth's surface for recording raw
seismic signals
for storage and subsequent analysis. An example of such an accelerometer can
be found in
U.S. Patent No. 6,062,081, issued to Schendel on May 16, 2000. In the
embodiment of
Figure 6, the surface transducer 20 communicates with the processor 18 wherein
coherence
filtering is accomplished. Alternatively, the filtering process can also take
place within the
immediate confines of the surface transducer 20.
The present invention described herein, therefore, is well adapted to carry
out the
objects and attain the ends and advantages mentioned, as well as others
inherent therein.
While a presently preferred embodiment of the invention has been given for
purposes of
CA 02610997 2012-03-12
disclosure, numerous changes exist in the details of procedures for
accomplishing the desired
results. These and other similar modifications will readily suggest themselves
to those skilled in
the art, and are intended to be encompassed within the scope of the appended
claims.
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