Note: Descriptions are shown in the official language in which they were submitted.
1153815
BACKGROUND OF T~E INVENTION
This invention relates to determination of properties of
earth formations surrounding a borehole and, more particularly, to
an apparatus and me-~lod for determining the velocity of propagation
of acoustic wave energy propagating in such formations. Acoustic
well logging is widely used to provide information concerning the
characteristics of earth formations. Generally, measurements are
made of the velocities of acoustic waves to reveal properties, such
as porosity, of the formations surrounding a borebole. An acoustic
well logging tool for measuring the velocity of acoustic waves
typically employs a sonic pulse transmitter and a plurality of sonic
receivers selectively spaced from the transmitter. The sonic
receivers include transducers to convert the incident acoustic wave
to an electrical waveform and suitable amplifiers to transmit the
waveforms to surface located processing equipment.
It is well known that the compressional components of the
acoustic wave energy generally travel at a higher velocity than the
shear components of the acoustic wave energy. It is desirable, at
each depth level, to obtain a reading of both the compressional
velocity and shear velocity of the acoustic wave energy propagating
through the formations since both contribute useful information
concerning the formations. When a plurality of spaced receivers are
employed, a corre~ation technique can be used to determine the
-3- .
~l~53~1.5
desired velocity by correlating the signals obtained at the
different receivers to obtain an output velocity value which
optimally accounts for the difference in arrival times of the
signals at the different receiver locations. Briefly, most
correlation techniques are based on the assumption that
substantially the same signal waveform will arrive at the different
receiver locations at different times, the delay as between
successively further receiver locations depending upon the distance
between receivers and the velocity of propagation of the wave energy
in the formations as between the receiver locations. Thus, a
correlation technique can be employed to compare a delayed version
of a signal arriving at a closer receiver location with a signal
arriving at a more remote receiver location, the amount of delay
(for a given known distance as between the receivers) depending on
an assumed "trial" value of velocity of the acoustic wave energy as
between the receiver locations in question. In simplified terms,
the correlation technique involves trying various trial velocity
values and determining which one provides the best "match".
To visualize a correlation procedure, assume that two
signals to be correlated are plotted one-beneath-another on a common
time axis, with the lower plotted signal being delayed (advanced in
a direction of increasing time on the time axis) with respect to
the upper plotted signal. Assume further that the time differential
as between the signals (resulting from signal propagation time
through formations of unknown nature over a known distance) is
unknown. In performing the correlation, the signals are compared
using a selected slope to account for the relative
~1~38~5
time difference between the signals. The selected slope is representative
of a trial velocity for the particular correlation since, as previously
noted, the time delay as between the two signals (and therefore the slope
as between corresponding points on the two signals plotted on the same
time axis~ is a function of the velocity of propagation of the signals.
The comparison is generally done by multiplying the instantaneous values
of the two signals at each corresponding point thereof and summing all
the products to obtain a single correlation figure. Further correlation
figures may then be determined for different trial velocities (or slopes),
and the correlation figures may be plotted versus velocity. Ideally,
this plot, called a "correlogram" will have a single, well defined peak,
the peak (i.e., the single highest correlation figure~ indicating the true
velocity of propagation of the wave energy. If the wave energy has com-
ponents which travel at different velocities, multiple peaks may be en-
countered. Noise and other complications in hostile borehole environment
will, of course, also introduce difficulties in interpreting correlograms.
In the copending Canadian patent applicatiGn serial number
239,421 of J. Ingram, there is disclosed an acoustic logging technique
wherein a multiple-fold correlation is utilized; that is, the instant-
aneous values of three or more signals are multiplied by each other in
obtaining each correlation figure. This and other techniques set forth
in that application have led to substantial advances in the art, but it
is an ob~ect of the present invention to provide still further improvements
in obtaining accurate values for the velocity of the acoustic wave com-
ponents of sonic waves propagating in formations surrounding a borehole.
1~L53~31S
SUM~lARY OF THE INVENTION
The main aspects of the present inventio]l are concerned with
techniques for obtaining velocity-representative values from the plurality
of received signals, and not Witil any particular technique for obtaining
these signals ;n the first place (the method of obtaining these signals
being known in the art and disclosed, for example, in the above-referenced
copending Canadian patent application Serial No. 239,421). Accordingly, it
will be ullderstood that the principles of the invention to be described
are applicable to the processing of signals obtained directly from a bore-
hole or to derived signals which were previously recorded or communicated
from a remote location. Also, as used herein, the term "signals" is
intended generically to include any waveforms that are in a form suitable
for machine processing.
In accordance with one broad aspect of the invention there is
provided apparatus for acoustic logging of formations surrounding a borehole,
comprising: means positioned in said borehole for establishing acoustic
wave energy in said formations; means for receiving the acoustic wave energy
at a plurality of spaced locations in the borehole; means for deriving, at
each depth level, a plurality of signals respectively representative of the
wave energy received at said plurality of spaced locations in the borehole;
means for correlating, at each depth level, a first portion of the signal
from one of said locations with first portions of signals from the other
locations, the first portions of the signals from the other locations being
determined from an assumed velocity, said correlating being performed for a
number of different assumed velocities to obtain a resultant first pro-
visional velocity at each depth level; means for correlating, at each depth
level, a second portion of the signal from said one of said locations with
second portions of signals from the other locations, the second portions of
signals from the other locations being determined from an assumed velocity,
said correlating of second portions being performed for a number of different
assumed velocities to obtain a resultant second provïsïonal velocity at each
depth level; means for generating an output velocity, at each depth level,
--6--
1~53~ 5
as a function of said first and second provisional velocities; and means
for generating a depth varying recording of said output velocity.
In accordance with another broad aspect of the invention, there is
provided apparatus for determining the compressional wave velocity and the
shear wave velocity of acoustic wave energy propagating in formations
surrounding a borehole, comprising: source means positioned in said bore-
hole for establishing acoustic wave energy ïn said formations; means for
receiving the acoustic wave energy at a plurality of at least four spaced
locations in the borehole; means for deriving a plurality of signals respec-
lQ tively representative of the wave energy received at said plurality of spacedlocations in the borehole; means for correlating a first portion of the signal
from the location closest to said source means with a first portion of each of
the signals from the other locations, said first portions of the signals from
the other locations being determined from an assumed compressional wave
velocity, said correlation being performed for a number of different assumed
compressional wave velocities, the assumed velocity which yields substan-
tially the maximum correlation being selected as an output compressional wave
velocity; means for correlating a second later-occurring portion of the
signal from said closest location with second portions of each of the signals
from the other locations, the second portions of the signals from the
other locations being determined from an assumed shear wave velocity, said
correlating of second portions being performed for a number of different
assumed shear wave velocities, the assumed velocity which yields substantially
the maximum correlation of second portions being selected as a first pro-
visional shear wave velocity; means for correlating a third later-occurring
portion of the signal from said closest location with third portions of each
of the signals from the other locations, the third portions of the signals
from the other locations being determined from an assumed shear wave velocity,
said correlation of third portions.~eing performed for a number of different
assumed shear wave velocities~ the assumed velocity which yields substantially
the maximum correlation of third portions being selected as a second pro-
visional shear wave velocity; and means for generating an output shear wave
1~53~
velocity as a function of said first and second provisional shear wave
velocities.
In accordance with another broad aspect of the invention, there is
provided apparatus for determining the velocity of acoustic wave energy
propagating in format;ons surrounding a horehole, comprising: means for
deriving a plurality of signals respectively representative of acoustic wave
energy received at a plurality of locations in the borehole spaced from a
source of acoustic wave energy; means for correlating a first portion of the
signal from one of said locations with first portions of signals from the
other locations, the first portions of the signals from the other locations
being determined from an assumed velocity, said correlating being performed
for a number of different assumed velocities to obtain a resultant first
provisional velocity; means for correlating a second portion of the signal
from said one of said locations with second portions of signals from the
other locationsJ the second portions of the signals from the other locations
being determined from an assumed velocity, said correlating of second
portions being performed for a number of different assumed velocities to
obtain a resultant second provisional velocity; and means for generating
an output velocity as a function of said first and second provisional
velocities.
In accordance with another broad aspect of the invention, there is
provided apparatus for determining the compressional wave velocity and the
shear wave velocity of acoustic wave energy propagating in formations
surrounding a borehole, comprising: means for deriving a plurality of at least
four signals respectively representative of the wave energy received at a
plurality of at least four locations in the borehole spaced from a source of
acoustic wave energy; means for correlating a first portion of the signal from
the location closest to said source with a first portion of each of the
signals from the other lccations, said first portions of the signals: from
the other locations. being determined from an assumed compressional wave
velocity, said correlation being performed for a number of different assumed
compressional wave velocities~, the assumed velocity which yields substantially
--8--
1~53815
the maximum correlation being selected as an output compressional wave
velocity; means for correlating a second later-occurring portion of the
signal from said closest location with second portions of each of the
signals from the other locationsJ the second portions of the signal from
the other locations: being determined from an assumed shear wave velocity,
said correlating of second portions being performed for a number of different
assumed shear wave velocities, the assumed velocity which yields substantially
the maximum correlation of second portions being selected 2S a first pro-
visional shear wave velocity; means for correlating a third later-occurring
portion of the signal from said closest location with third portions of each
of the signals from the other locations, the thïrd portions of the signals
from the other locations being determined from an assumed shear wave velocity,
said correlating of third portions being performed for a number of different
assumed shear wave velocities, the assumed velocity which yields substantially
the maximum correlation of third portions being selected as a second pro-
visional shear wave velocity; and means for generating an output shear
velocity as a function of said first and second provisional output velicities.
In accordance with another broad aspect of the invention, there is
provided a method for acoustic logging the formations surrounding a borehole
wherein acoustic wave energy is established in said formations and received
at a plurality of spaced locations in said borehole, said method converting
a plurality of time varying recordings of signals representative of wave
energy received at said plurality of spaced locations into a depth varying
recording of the velocity of acoustic wave energy propagating in said forma-
tions and comprising the steps of: generating, at each depth level, a
plurality of time varying recordings of signals respectively representative
of the wave energy received at said plurality of spaced locations in the bore-
hole; correlating, at each depth level, a first portion of the signal from one
of said locations. with first portions of sïgnals from the other locations, the
first portions of the signals from the other locations b.eing determined from
an assumed velocity, said correlat;ng being performed for a number of different
as-sumed velocities to obtain a resultant first provisional velocity at each
-8a-
~..
~1531~5
depth level; correlating, at each depth level~ a second portion of the signal
from said one of said locations with second portions of signals from the
other locations, the second portions of the signals from the other locations
being determined from an a.ssumed velocity, said correlating of second
portions being performed for a number of different assumed velocities to
obtain a resultant second provisional velocity at each depth level; generat-
ing an output velocity, at each depth level, as a function of said first and
second provisional velocities; and generating a depth varying recording of
said output velocity.
In accordance with another broad aspect of the invention there is
provided a method for determining the compressional wave velocity and the
shear wave velocity of acoustic wave energy propagating in formations
surrounding a borehole, comprising the steps of: establishing acoustic wave
energy in said formations; receiving the acoustic wave energy at a plurality
of at least four spaced locations in the borehole; deriving a plurality of
signals respectively representative of the wave energy received at said
plurality of spaced locations in the borehole; correlating a first portion
of the signal from the location closest to said source with a first portion
of each of the signals from the other locations, said first portions of the
signals from the other locations being determined from an assumed compression-
al wave velocity, said correlation being performed for a number of different
assumed compressional wave velocities, the assumed velocity which yields
substantially the maximum correlation being selected as an output com-
pressional wave velocity; correlating a second later-occurring portion of
the signal from-said closest location with second portions of each of the
signals from the other locations, the second portions of the signal from
the other locati.ons being determined from an assumed shear wave velocity,
said correlating of second portions heing performed for a number of
different assumed shear wave velocities., tfie assumed velocity which yields
substantially the maximum correlation of second porti`ons being selected as
a first provisional sfiear wave veloc;ty; correlating a tfi;rd later-occurring
portion of the signal from said clos~est location with th;rd portions of each
-8b-
1~538~5
of the signals from the other locations, the third portions of the signals
from the other locations being determined from an assumed shear wave
velocity, said correlating of third portions being performed for a number
Gf different assumed shear wave velocities, the assumed velocity which
yields substantially the maximum correlation of third portions being
selected as a second provisional shear wave velocity; and generating an
output shear wave velocity as a function of said first and second pro-
visional shear wave velocities.
In accordance with another broad aspect of the invention there is
provided a method for determining the velocity of acoustic wave energy
propagating in formations surrounding a borehole, comprising the steps of:
deriving a plurality of signals respectively representative of acoustic wave
energy received at a plurality of locations in the borehole spaced from a
source of acoustic wave energy; correlat;ng a first portion of the signal
from one of said locations with first portions of signals from the other
locations, the first portions of the signals from the other locations being
determined from an assumed velocity, said correlating being performed for a
number of different assumed velocities to obtain a resultant first provisional
velocity; correlating a second portion of the signal from said one of said
locations with second portions of signals from the other locations, the
second portions of the signals from the other locations being determined
from an assumed velocity, said correlating of second portions being performed
for a number of different assumed velocities to obtain a resultant second
provisional velocity; and generating an output velocity as a function of
said first and second provisional velocities.
In accordance with another broad aspect of the invention there is
provided a method for determining the compressional wave velocity and shear
wave velocity of acoustic wave energy propagating in formations surrounding
a borehole, comprising the steps of: providing an coustic source in said
borehole to establish acoustic wave energy in the formations surround;ng the
borehole; receiving the acoustic wave energy at a plurality of at least four
spaced locations in the borehole; deriving a plurality of signals respectively
-8c-
8~5
representat;ve of the wave energy received at said plurality of locations;
correlating a first portion of the signal from one of said locations with
first portions of signals from the other locations, the first portions of the
signals from the other locations being determined from an assumed velocity,
the correlating being performed for a number of different assumed velocities
to obtain a resultant output compressional wave velocity; correlating a
second substantially later-occurring portion of the signal from said one
o:E said locations with second portions of the signals from the other
locations, the second portions of the signals from the other locations being
determined from an assumed velocity, the correlating being perfolmed for a
number of different assumed velocities to obtain a resultant first pro-
visional shear wave velocity; correlating a third portion of the signal
from said one of said locations with third portions of the signals from
the other locations, the third portions of the signals from the other
locations being determined from an assumed velocity, and the correlating
being performed for a number of different assumed velocities to obtain a
resultant second provisional shear wave velocity; generating an output
shear wave velocity as a function of the first and second provisional shear
wave velocities.
In accordance with another broad aspect of the invention there is
provided apparatus for determining the velocities of different modes of
propagation of acoustic wave energy propagating in formations surrounding
a borehole, comprising: means positioned in said borehole for establishing
acoustic wave energy in said formations; means for receiving the acoustic
wave energy at a plurality of spaced locations in the borehole; means for
deriving a plurality of signals respectively representative of the wave
energy received at said plurality of spaced locations in the borehole;
means for identifying the location and duration of a first characteristic
portion of the s gnal from one of said locations; means for correlating
said first portion of the signal from said one of said locations with first
portions of signals from the other locati`ons, the first portions of the
-8d-
1~5381S
signals from the other locations being determined from an assumed velocity,
said correlating being performed for a number of different assumed velocities
to obtain a resultant first provisional velocity; means for identifying
subsequent characteristic portions of the si.gnal from said one of said
locations; means for correlating said subsequent portions of the signal
from said one of said locations with subsequent portions of signals from
the other locations, the subsequent portions of the signals from the other
locations being determined from assumed velocities, said correlating of each
of said subsequent port;.ons being performed for a number of different
assumed velocities to obtain resultant further provisional velocities; and
means for generating cutput velocities of said different modes of propagation
as a function of said first provisional velocity and said subsequent
provisional velocities.
In accordance with another broad aspect of the invention there is
provided apparatus for determining the compressional wave velocity and the
shear wave velocity of acoustic wave energy propagating in formations
surrounding a borehole; comprising: source means positioned in said bore-
hole for establishing acoustic wave energy in said formations; means for
receiving the acoustic wave energy at a plurality of at least four ;spaced
locations in the borehole; means for deriving a plurality of signals
respectively representative of the wave energy received at said plurality
of spaced locations in the borehole; means for identifying the location
and duration of a first characteristic portion of the signal from the loca- -
tion closest to said source means; means for correlating said first portion
of the signal from said closest location with a first portion of each of
the signais from the other locations, said first portions of the signals
from the other locations b.eing de*ermined from an assumed compressional wave
velocity, said correlation being performed for a number of different assumed
compressional wave velocitieS,the assumed velocity which yields substantially
the maximum correlation being selected as: an output compressional wave
velocity; means for identifying subsequent characteristic portions of the
-8e-
,~
~1538~5
signal from said closest location; means for correlating said subsequent
portions of the signal from said closest location with subsequent portions
of each of the signals from the other locations, the subsequent portions of
the signals from the other locations being determined from assumed shear
wave velocities, said correlating of each of said subsequent portions being
performed for a number of different assumed shear wave velocities, the
assumed velocities which yields substantially the maximum correlations of
said subsequent portions being selected as provisional shear wave velocities;
and means for generating an output shear wave velocity as a function of said
provisional shear wave velocities.
The first and second portions of the signals may be compressional
wave components thereof, and the output velocity will then be an output
compressional wave velocity. Alternatively, the first and second portions
of the signals may be shear wave components thereof, in which case the
output velocity will be an output shear wave velocity. Of course, the
technique may be utilized on both the compressional wave components and
shear wave components of the signals to obtain both an output compressional
wave velocity and an output shear wave velocity. The first and second
portions preferably each have a duration of an integral number of half-
cycles, not exceeding two full cycles, of the signal from said one location.
~1538~5
Generally, the output veloc:Lty (compressional and/or shear)
is determined for each of a number of adjacent depth levels.
In a disclosed embodiment, the generated output velocity, in
addition to being a function of the previously mentioned pro-
visional velocities, is selected taking into account the outputvelocity that had been generated at an adjacent depth level.
The technique of the present invention of determining
provisional wave velocities by correlating, over a limited range
of velocities (e.g., a range of about fifty microseconds per
foot), relatively small portions of the different receiver
waveforms, tends to reduce prior art problems associated with
multiple correlation peaks that could occur when longer portions
of the signals are correlated. Also, individual portions of the
signals containing spurious information have less tendency to
upset the selection of accurate output values since, in an
embodiment to be described, selection is from a plurality of
provisional values and an individual spurious value is likely
to be discarded without affecting the output values.
Further features and advantages of the invention will
become more readily apparent from the following detailed description
when taken in conjunction with the accompanying drawings.
1~538~5
BRIEF DESCRIPTION OF THE DRA~INGS
FIG. l is a block diagram of an apparatus in accordance
with an embodiment of the invention, and includes a recording or log
of acoustic velocity versus depth that can be set forth using the
invention.
FIG. 2 is a graph which illustrates the nature of the
signals or wavefonns received at the four receivers of the logging
device in FIG. l.
10FIG. 3 is another recording or log of acoustic velocity
versus depth that can be set forth using the invention.
FIG.s 4A, 4B, 4C and 4D, when placed one-below-another,
illustrate a flow chart suitable for programming the processor 40 of
15FIG. l to perform operations in accordance with the invention.
FIG. 5 illustrates the manner in which an initial estimate
of slope is obtained from a pair of waveforms.
20FIG. 6 illustrates the manner in which the correlation
window is initially positioned with respect to the Rl waveform.
--10--
1153~15
FIG. 7 is a flow chart representative of the functions of
the block 120 of FIG. 4 and sets forth a technique of fourEold
correlation.
FIG.s 8A and 8B illustrate the manner in which a fourfold
correlation is performed, with the correlations of FIG.s aA and 8B
each utilizing different slopes.
FIG. 9 illustrates a technique for obtaining the slope or
velocity which yields a maximum correlation.
FIG. 10 is a plot of provisional compressional velocity
values and provisional shear velocity values at a particular depth
level.
--11--
1~5~8~'~
DESCRIPTION OF THE PREF~RRED EMBODLMENT
Referring to FIG. 1, a sonic borehole logging tool 10, with
centering elements not shown, is illustrated as being suspended from
a cable 12 in a borehole 14. The tool 10 includes a transmitter 16
located at the bottom of the tool and preferably four or more
selectively spaced sonic receivers lB.l, 18.2, 18.3 and 18.4. The
cable 12 is shown fed over a pulley 20 from a cable supply 22 and is
electrically connected to a panel 24. The panel 24 includes
suitable amplifiers, switching circuits and electrical supplies for
tool 10 and the firing of sonic transmitter 16. The tool 10
includes suitable amplifiers and controls needed to enable receivers
18 to sequentially detect sonic waves and provide panel 24 with
waveforms representative of the acoustic waves incident upon
transducers in receivers 18.
In the operation of the sonic logging tool 10, the
transmitter 16 is regularly energized (about ten times per second)
to produce sonic pulses such as 26 in FIG. 2 while the tool is moved
upwardly at a speed of the order of one foot per second. Each pulse
26 is directed at the formation in which an acoustic wave such as 28
is launched. The acoustic wave 28 has components which travel
through the formation towards the receivers 18 and in turn produce
wave components 29 which are incident upon the receivers 18 to
produce a set of signals or waveforms such as 30.1, 30.2, 30.3 and
-12-
~538~LS
30~4 shown in FIG. 2. Waveforms 30 may also include those sonic
waves which, after travel through the borehole, are incident upon
receivers 18.
The transmitter is periodically activated, and the
receivers 18 preferably are alternately enabled to generate
waveforms in the sequence as sho~l by waveforms 30.1 - 30.4. In
this manner, waveforms which are of several milliseconds duration
can be analyzed to detect velocity in a manner to be described. In
addition, the sequential enabling of receivers 18 allows their
outputs to be multiplexed onto a common line towards panel 24. This
is an advantage when the analog form of the outputs of receivers 18
is to be conducted to panel 24 since the analog waveforms 30 are all
exposed to the same electronic amplification and cable attenuation
to enable amplitude comparisons. rrhe advance of the tool 10 during
the time needed to generate one complete set of waveforms 30 can be
controlled and is not sufficient to appreciably affect velocity
measu~ements.
The receivers 18 each typically but not necessarily bear a
known spacing "d" from each other (i.e. dl = dz = d3 = d in
FIG. 1) while the distance "S" between receiver 18.1 and transmitter
16 is known to further accurately locate all the receivers from
transmitter 16. Thus, for example, if the arrival of the
compressional wave could be precisely detected at each receiver,
then the time between respective receiver arrivals would provide an
accurate determination of the velocity of the compressional wave.
As described in the copending U.S. application Serial No. 581,381 of
J. Ingram (file 60.327), employing a multiple number of receivers
-13-
1 lS3815
18, such as four, allows a generally more accurate and reliable
determination of wave velocities, although increased distance of the far
receiver from the transmitter results in a substantially attenuated
waveform at this receiver.
The signals 30 may arrive at the panel 24 either in analog form
or sampled form or may be digitized downhole. For example, the tool 10
may be provided with an analog to digital (A/D) converter (not shown) to
sample waveforms 30. The samples would then be transmitted along cable 12
to panel 24 for further processing. The waveforms 30 may be derived from
a previously obtained record, communicated from another location, or
derived directly from receivers 18. In the system depicted in FIG. 1, the
waveforms 30 arrive in analog form at panel 24 where they may be coupled
to a cathode ray tube 32 for real-time display and to a magnetic tape
recorder 34 to provide an analog record. In order to utilize a sampled
form of waveforms 30 they are shown coupled along a line 35 to an analog
to digital converter 36 which generates samples of the waveforms at a high
sampling rate on an output line 38.
Although not specifically illustrated in FIG. 1, panel 24 also
provides depth signals frQm a depth sensor operatively coupled to the
cable 12. The depth signals preferably are presented on line 37 in a
format which is compatible with the format employed for the samples on line
-14-
~153~5
38. The generation of depth signals is well known in the art of well
logging and shall not be further described. The output from waveform
sampler 36 is applied to an apparatus 40 which processes the samples to
produce velocity-representative values from waveforms 30. The apparatus
40 preferably is a general purpose digital computer, but may be any gener-
al purpose or special purpose digital or analog processor or special
purpose circuitry. Also, with a recording capability present, processing
need not necessarily be performed in real time. The output of apparatus
40 may be, for example, a plot 42 of the velocity of the compressional
and shear wave components of the sonic wave as a function of well depth
in feet. Curve 43 shows the velocity of the compressional wave, desig-
nated ~ T , and curve 44 shows the velocity of the shear wave, designated
~\Ts. The plot 42 is made by moving suitable logging paper in the direct-
ion indicated by arrow 45 while the tool is raised as reflected by the
indicated depth values. (It is conventional in acoustic logging to present
velocity in terms of microseconds per foot, which is actually the inverse
of true velocity. Thus convention will be followed herein.)
As described in the abovereferenced copending Canadian appli-
cation serial no. 239,421, and as illustrated in FIG. 2, the receivers
18 are sequentially enabled for successive firings of the transmitter 16.
A portion of the electronics in device 10 provides waveform identification
signals, which may be coded pulses such as a two bit code word, and which
determine the particular receiver that is
-15-
~'~
1~53E~
enabled. Such receiver waveform identification code, together with a
pulse to identify the firing time of the transmitter 16 are delivered
along cable 12 to panel 24. A magnetic recorder 47 is provided to
record the waveform samples produced by A/D converter 36 as well as
the waveform identification code transmitted along cable 12. As
described in the referenced copending application, the panel 24 may be
provided with a conversion control network 46 which selectively delays
initiation of A/D converter 36, depending upon which receiver waveform
is to be sampled. Fbr example, if receiver waveforms 30 are each
sampled by starting the same amount of time after the firing of
transmitter 16 (or upon occurrence of its output pulse 26), the amount
of useful information obtained varies as a result of receiver spacings
"d". In order to preserve greater portions of the waveforms for
subsequent analysis, a conversion control network can be used, but
will not be treated herein.
A/D converter 36 commences conversion at the end of a
delay ~ which is a function of the distance between receiver 18 and
transmitter 16 and the fastest expected velocity of the acoustic
wave. The conversion process continues for a sufficient time period
to provide samples of the waveforms of interest. A sampling rate of
ten microseconds, for example, may be employed, and a total of 512
samples, or about five milliseconds, of sampled waveform duration will
be obtained and be sufficient in most cases to determine the
compressional and shear velocities of the sonic waves, as will be
described hereinafter. However, it will be understood that the number
-16-
~1538~C;
of samples used in any one group may be varied with 512 being
generally used herein as an illustrative example. A/D converter 36 is
provided with a suitable counter (not shown) which terminates the
conversion process when the desired number of samples 60 (see FIG. 2)
have been generated. The A/D conversion of each waveform 30 results
in the generation of a group identified at 62 in FIG. 2 of 512 samples.
Since each sample 60 occurs at a known sampling rate, any one
sample has an index value which can be directly related to the time
interval measured from the time of occurrence of the sonic pulse 26
which resulted in the sampled waveform. Thus the first sample 60.1 in
group 62.1 occurs at a time equal to ~ + (NxSR), where N is the index
position value (N = 0 for the first sample) and SR is the sampling
rate in microseconds. In a similar manner, each sample 60 in the
other groups 62.2, 62.3 and 62.4 can be precisely related in time to
their associated transmitted sonic pulse 26.2, 26.3 and 26.4.
An example of how these index values can be used is as
follows: Assume a given reference (e.g. "first motion") on the
compressional wave is detected for the sample in group 62.1 at an
index value Nl, and the same given reference is detected in group
62.2 at index value N2. The time a T for that wave to travel the
distance between receivers 18.1 and 18.3 would then be equal to
(N2 - Nl) SR. At a ten microsecond sampling rate, the velocity of the
compressional wave in microseconds per foot would be determined as
(Na - Nl) x 10.
1~538~L5
The samples applied to processor 40 are assembled in groups
of 512 samples with each group coded to identify a waveform from a
particular receiver. The processor 40 is provided with a buffer to
enable accummulation of a pair of sets of waveforms, wherein each set
represents waveforms from all four receivers during a full operational
cycle of the transmitter-receiver. Access to the buffer is under
control of A/D converter 36 to enable transfer of the samples as they
are produced.
The description set forth in conjunction with FIG.s 1-3, and
the specific technique of sampling and using index numbers as
described in the copending Ingram application, are intended to
illustrate a manner in which a plurality of signals or waveforms can
be obtained from a plurality of spaced acoustic receivers and loaded
into a processor at known sampling times. It will become understood,
however, that the novel aspects of this invention deal with apparatus
and method for obtaining useful information, such as
velocity-representative signals or graphs, from the plurality of
signals or waveforms 30 which are loaded into processor 40, and any
suitable technique can be employed to obtain the signals or waveforms
30 (the terms "signals" and "waveforms" being utilized interchangeably
herein in this context). For example, all four receiver signals may
be digitized, after a single transmitter firing, by a downhole A/D
converter. A buffer memory and data transmission system may also be
provided downhole. Also, the described indexing system sets forth an
example of how timing registration between the sampled waveforms is
-18-
~53~5i
established; but it will be understoocl that alternate methods may be
employed. In this respect, and for clarity of explanation, the index
number system set forth above will not be referred to each time timing
registration considerations are set described below, although it will
be understood that this index number technique can be utilized in each
instance to keep track of the timing registration as between samples
from the different receiver waveforms.
Referring to FIG. 4, there is shown a flow diagram suitable
for programming the processor 40 to obtain output values at ~Tc
and ~ Ts at each depth level; e.g. the values shown in the graphs
43 and 44 of FIG. 1. The block 105 represents the initiation of
processing for the next depth level. Block 110 is then entered, this
block representing the determination of the "first motion" of each of
the four receiver waveforms. As is known in the art, first motion can
be determined by detecting when each waveform exceeds a predetermined
threshold level. Block 110 represents the determination of an initial
estimate of compressional velocity or slope, designated ~ TCe,
obtained by averaging the slopes as between the first motion of the
close receiver (Rl) waveform and the first motion of each of the
other waveforms. (The term "slope", as used in this context,
represents a time difference as between waveform sample points
received at different receivers that are a known fixed distance
apart. Since this characteristic time difference is proportional to
the inverse of velocity, slope determinations are equivalent to
determinations of velocity. Accordingly, the terms "slope" and
-19-
~53~3~5
"vel w ity" are, in this context, used interchangeably herein.) The
signal received at the closest receiver, Rl, is generally the
strongest and "cleanest" signal and it is therefore used as a main
reference for obtaining the slopes from which the initial estimate of
compressional velocity is determined. In particular, L~TCe is
computed as:
( 2 fml)/d + (fm3 - fml)/2d + (fm4 - fml)/3d tl)
~T
where fml through fm4 are the times of the first motions
respectively detected in the waveforms of Rl through R4,
respectively. The three numerator terms are seen to be the three
slopes which are averaged to obtain ~ TCe. FIG. 5 illustrates, in
simplified form, how one of the slopes, in particular
(fm2 - fml)/d, is obtained.
Returning to FIG. 4, bl w k 115 is next entered, this block
representing the establishment of a correlation window whose end
points are selected as respectively being at the zero crossing which
precedes the first motion fml and at the second zero crossing
thereafter; i.e. a window substantially corresponding to the first
full cycle of the compressional wave received at Rl. This may be
readily done by scanning the samples of the Rl waveform from point
fml until the appropriate zero crossings are obtained. FIG.6
illustrates the correlation window on the Rl waveform.
Two indices, r and m ( to be utilized later ), are next
set equal to unity (block 116) . A fourfold correlation
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~,'
~15~5
is then performed, as represented by the block 120, to determine a pro-
visional compressional velocity or slope, designated ~ T'. (The basic
concept of a fourfold correlation is described in the abovereferenced
copending Canadian patent application Serial No. 239,421.) The present
technique of fourfold correlation is set forth in FIG. 7 which is a flow
chart representative of the functions of block 120 of FIG. 4, and can be
referred to during the present description of the fourfold correlation.
An initial assumed slope is first selected (block 701) as being the
estimated compressional wave velocity or slope, ~ T . The value of each
sample point of the Rl signal within the correlation window is then multi-
plied by the value of a sample point on each of the other waveforms, the
location of the sample point on the other waveforms being determined
using the assumed slope (block 702 and loop 703). For example, the value
at the leftmost point of the Rl waveform within the correlation window is
multiplied by the value of a point on the R2 waveform that is diSplaced
in time from the point on the Rl waveform by ~ TCe(d); i-e- the time that
it would have taken the wave energy to travel the distance d between re-
ceivers Rl and R2 (FIG. 1) at an (inverse) velocity ~ T e (with dl = d2 =
d3 = d for assumed equal spacings). The resultant partial product is
then again multiplied by the value of a point on the R3 waveform that is
displaced in time from the point on the Rl waveform by ~ T (2d~ and then
again multiplied by the value of a point on the R4
1~538~L5
waveform that is displaced in time from the point on the Rl waveform
by aTCe(3d). The resultant product, designated ~R, is multiplied
by weighting function which is utilized to ~ake account of the signs
of the values multiplied together. A convenient weighting function is
simply unity when the four multiplicands have the same sign and is
otherwise zero. The use of the weighting function avoids making a
positive contribution to the correlation when two of the signals are
positive and two are negative; i.e., the worst possible mismatch. The
determination of the product PR is represented by block 704 of FIG.
7. In the simplified illustration of FIG. 8A, this first product is
PRl. The same procedure is then performed with respect to the next
point of the Rl waveform within the correlation window (diamond 705
and block 706 of FIG. 7) to obtain a product designated as PR2, also
shown in the simplified FIG. 8A. This procedure is then repeated for
each point of the correlation window to obtain products PR3,
PR4....pRn, where n is the number of points in the correlation
window. The summation, designated as ~, of all the products is then
determined (block 707 of FIG. 7) as:
El = PRl + PR2 + .. PRn
where the subscript 1 designates that this summation is a correlation
figure associated with the first estimated slope. FIG. 8A is again
referred to for an understanding of how El iS generated.
A different estimated slope is next assumed (diamond 708 and
block 709 of FIG. 7), and the procedure for obtaining ~ (in this case
designated ~2) is repeated for the new assumed slope. FIG 8B
illustrates the manner in which E2 is obtained using a slope which
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~53815
is different than that of FIG. 7A. The number of different slopes
which are tried is a matter of choice and, in the present embodiment,
five different slopes are used to obtain five values of ~, e.g. ~1
through E5. The five slopes utilized are: ~TCe (the originally
assumed slope, rounded off to the nearest multiple of the sampling
rate); ~Tce+lO~s; ~Tce-lO~s; aTce+20~us; and ~Tce-20~s, the ten
microsecond multiples being multiples of the sampling rate. rme
optimum slope can then be determined as a slope at which E is a
maximum. In the present embodiment, an interpolation technique is
preferably utilized to obtain the optimum slope, designated as
~ Tc (block 710 of FIG. 7). This may be done by fitting a second
order polynomial through the largest value of E and the two adjacent
values of ~. An example of the technique is illustrated in FIG. 9
wherein the maximum of the polynomial curve, selected as qTc~ is
determined, in a given case, to be between ~Tce-lOus and ~TCe,
as shown by the dashed line. In the event that the maximum value of E
is found to be at one of the assumed slope extremes (viz., at either
~Tce-20~us or ~ Tce+20~s), diamond 711 of FIG. 7 causes block 712
to be entered via diamond 712. The slope is then incremented toward
the direction of the extreme and the same procedure is followed.
Eventually, either an appropriate maximum is obtained (called ~Tc
in this case) or a "no" answer to decision diamond 712 indicates that
the attempt at obtaining ~Tc has been unsuccessful.
Referring again to FIG. 4, decision diamond 130 is next
entered and, if a value of ~Tc has been successfully obtained
(routine of block 120), diamond 130 causes entry to another decision
~538~5
diamond 135. If, however, a value oL ~ Tc was not successfully
obtained the block 160 is entered. In accordance with the criterion
of diamond 135, ~ Tc is tested as against the value of ~Tc
obtained at the previous depth level (except, of course, where this is
the first depth level being processed whereupon suitable provision is
made for bypassing diamond 135), to determine if the value of ~Tc at
the present depth level is within a particular range, for example
lO~s, of the value of ~Tc which had been obtained at the previous
depth level. If the test result is affirmative, the block 140 is
entered, this block representing the acceptance of the value aTC,
the accepted value being an output value designated as ~Tc (e.g.
curve 43 of FIG. 1). If, however, the answer to the inquiry of
diamond 135 is negative, diamond 145 is entered and inquiry is made as
to whether ~Tc has been rejected (in accordance with the criterion
of diamond 135) for five depth levels in a row. If not, block 160 is
entered, this block representing the adoption of a ~rc for this
depth level which is the same as the one from the previous depth
level. The block 160, it is seen, is also directly entered from the
negative output line of decision diamond 130; i.e. the situation where
the attempted determination at 4Tc was unsuccessful.
Having established an output value of dIc for this
particular depth level, an initial estimate is next made of the shear
wave velocity or slope, this estimated value being designated as
~TSe. In the present embodiment, the initial estimated slope or
velocity of the shear wave is computed as:
~TSe = 1.35 ~Tc+3 (sampling rate)
-24-
~15;~8~'i
as indicated by block 150 of FIG. 4. Thus, if, as above, the sampling
rate is selected as 10 ~usec the estimated velocity or slope of the
shear wave would be:
~ TSe = 1.35 ~TC+30 ~sec/ft.
Block 156 is then entered and a lower limit of the shear wave velocity
or slope, designated ~TSLL, is computed. In the present
embodiment, this lower limit, to be used in a manner described below
in rejecting any values of shear wave velocity below the lower limit,
is selected as being 1.5 ~Tc, as indicated by the block 156.
The next portion of the flow chart is, in the present
embodiment, concerned with movement along the time scale of the Rl
waveform until such time when useful information concerning the shear
wave velocit~ or slope can be expected. The portion of the Rl
waveform used in the previously described correlation is stripped away
(block 165); i.e., the time reference is moved forward to the
rightmost end point of the previously utilized correlation window.
From this point in time, a "first tion" detection is again performed
(as described above), as represented by the block 170. The nearest
zero crossing is then detected, and the beginning of the correlation
window is moved to the time of zero crossing detection, as represented
by the block 175. The correlation window size is then adjusted to
encompass one full cycle of the waveformr e.g. by setting the far end
thereof at the second zero crossing past the beginning thereof. The
time of occurrence of the latest first motion detection is next
compared (diamond 180) against a maximum allowable time, designated
Tw, which represents the approximate expected arrival time of the
1~5;~E~15
water or mud waves the value Tw being selected based on the
transmitter-receiver spacing and an assumed water velocity of about
200 ~s per foot. If Tw is exceeded (of course, it is unlikely that
it will be exceeded during an early pass through the loop being
described), a meaningful value of shear velocity is wnlikely to be
obtained at this depth level, and diamond 240, described below, is
entered. ~ecision diamond 190 is next entered and the index r
(originally set to unity -- block 116 above) is tested to see if it is
greater than or equal to K, where K is the number of waveform cycles
to be skipped, for example five cycles, from the original cycle which
had been used to determine the compressional velocity or slope. Thi$
inquiry is represented by the diamond 190. If the answer is in the
negative, block 195 is entered, this block representing essentially
the same function as the block 165 above; viz., of stripping away the
Rl waveform within the present correlation window. Block 170 is
then re-entered and, by action of the fwnctions of blocks 170 and 175,
the beginning of the correlation window is then moved to the zero
crossing closest to the next first motion, and the size of the
correlation window is readjusted, as previously described. This
action continues, in the loop designated by reference numeral 199,
until the requisite number of cycles (e.g. five cycles) have been
skipped over. The primary purpose of loop 199, in the present
embodiment, is to save processing time since it is not generally
expected that meaningful shear arrivals will occur within five cycles
of the first strong compressional cycle. However, it will be
wlderstood that, if desired, the technique to be subsequently
described for determination of shear wave velocity or slope could be
-26-
~S;~8~5i
initiated directly after the output value of compressional velocity or
slope is determined.
When the requisite number of cycles have been skipped, block
200 is entered and a fourfold correlation is performed with respect to
the present correlation window The fourfold correlation was
described above in conjunction with block 120 of FIG. 4 and, in
further detail, in conjunction with the flow chart of FIG. 7. In the
case of block 200, the initial estimated value of shear wave velocity
or slope, designated ~TSe, is as derived above in conjunction with
block 150. In other respects, the correlation may be the same as
described with reference to FIG. 7, with ~ values being obtained at
10 ~s spacings of slope and an interpolation being utilized to obtain
a resultant provisional velocity or slope. In this case, the result
is a provisional value for shear wave velocity or slope, designated as
~Tsm. Since m had been initially set at unity (block 116), this is
a first provisional value of shear velocity or slope, i.e. ~TSm.
Decision diamond 205 is next entered and the provisional
value of shear wave velocity or slope (the first provisional value for
the first pass through) is tested against the lower limit for shear
wave velocity or slope (established above -- block 156) as represented
by the decision diamond 205. If ~TSm is not below this lower limit,
decision diamond 210 is entered and ~TSm is tested as against the
expected velocity of the mud or water waves, ~Tw, which is typically
about 200 ~seconds. If ~TSm does not exceed ~Tw, block 215 is
entered, this block representing the acceptance of ~TSm as an
acceptable provisional value of shear wave velocity or slope,
-27-
~7
~538~ S~
designated ~TSm. In other words, removal of the prime from ~TSm
designates that it is within a range which makes it a feasible value
for further consideration. rhe diamond 220 is then entered and ~TSm
is tested as against the value of shear wave velocity or slope which
had been determined at the previous depth level. In the present
embodiment, if ~rsm is within 5 ~s of the previously stored value of
shear wave velocity or slope, then the value ~TSm is accepted (block
225) as the output shear wave velocity or slope at this depth level,
designated as ~Ts. If, however, TSm is not within 51us of the
output value at the previous depth level, diamond 230 is entered and
inquiry is made as to whetller a particular number of values of TSm
have now been obtained at the current depth level. In the present
embodiment, the particular number utilized is four. rhus, if four
provisional values, Tsm,have not yet been obtained, block 235 is
entered, this block also being entered, as can be seen from the
diagram, when the tests of diamonds 205 or 210 had indicated that
Tsm was outside the acceptable range (as previously described).
In accordance with the function represented by the block 235,
the beginning cycle of the R1 waveform used in the most recent
correlation is stripped away. Block 170 is then re-entered, via block
171, which represents the incrementing of index m, and operation of
blocks 170 and 175 establish the new position of the correlation
window with respect to the Rl waveform. rrhis effectively means that
both ends of the correlation window are advanced to the next zero
crossing and the new correlation window overlaps the previous
correlation window by one-half cycle. Testing against Tw is then
-28-
~153~3~5i
performed (diamond 18n), but the loop l99 skipping routine is now
ineffective since index r exceeds the rnaximum (diamond l90). Block
200 is then entered with a resultant fourfold correlation which yields
the next provisional value of shear wave velocity or slope, L~r
which is ~TS2 in this example. The criteria of blocks 205 through
230 are next applied as previously set forth.
The described procedure continues until either an output
value of ~Ts is obtained by operation of the block 225, until four
provisional values ~TSm have been obtained (an affirmative answer to
the inquiry of diamond 230), or until the water arrival time Tw is
exceeded (diamond 180). In each case, diamond 240 is entered and
inquiry is made as to whether or not there is an accepted value
~Ts~ If not, block 245 is entered, this block representing the
selection of ~Ts as the value of 4TSm which is nearest to the
value of ~Ts that had been determined at the previous depth level.
Block 250 is then entered (block 250 also being entered from the
affirmative answer branch of diamond 240), this block representing the
recording of the predetermined values of ~Tc and ~Ts for the
present depth level. Block llO, at the beginning, is then re-entered
and the technique is repeated for the next depth level.
In the embodiment set forth in conjunction with FIG. 4, a
plurality of provisional shear wave velocities are developed and an
output shear wave velocity is determined as a function of the
provisional shear wave velocities. (An exception in this ernbodiment
is when a particular provisional shear wave velocity is sufficiently
close to the value at the previous depth level whereupon it is
-29-
l~LS38~5
immediately accepted.) Each of these provisional shear wave
velocities is determined by correlating relatively small portions of
the waveforms over a limited range of slopes (of the order of 50 ~s),
so prior art problems associated with multiple correlation peaks, that
might occur using longer waveforms and wider slope ranges, are
minimized. Also, individual portions of the waveform containing
spurious information have less tendency to upset the selection of
accurate output values since, in the described embodiment, selection
is from among a plurality of provisional values and an individual
spurious value is likely to be discarded without affecting the output
values. The comparison of provisional velocity values (both shear and
compressional) to the values obtained at the previous depth level
provides a degree of protection against spurious perturbations in the
output graphs, but genuine abrupt changes in formation characteristics
(such as at a bed boundary) will be properly indicated within a few
depth level increments since the technique allows for abrupt
modifications which appear genuine (e.g. diamonds 145 and 220, 230).
It will be understood that the technique of the invention of
obtaining an output shear wave velocity from among individual
provisional shear wave velocities obtained by correlating individual
relatively short portions of the waveforms can be applied equally well
to determination of an output compressional wave velocity.
The invention has been described with reference to a
particular embodiment, but variations within the spirit and scope of
the invention will occur to those skilled in the art. For example,
the provisional velocity values can be utilized, in the case of both
-30-
~5~8~5
compressional and shear wave velocity determination, without the need
for utilizing information from the previously processed depth level,
to arrive at a decision concerning velocity at the depth level being
processed. In fact, the present invention has been found to operate
advantageously in situations where prior art techniques exhibited
inability to track shear or through casing signals arrivals when
continuity of these arrivals is absent. It will be mderstood that
alternate techniques for rendering a decision, using the provisional
velocity values obtained with the technique of the invention, can be
set forth. For example, FIG. 10 illustrates the provisional
compressional velocity values and provisional shear velocity values
obtained at a particular depth level. The resultant "clusters" of
values can be used to render a decision concerning an output
compressional and/or shear wave velocity graphically, or alternative
automotive techniques can be employed. In FIG. 3, there is shown a
plot of shear velocity versus depth which is similar to the one of
FIG. 1, but wherein the range of provisional values obtained at each
depth level also appear in the plot in the form of a vertical line, at
each depth level, which indicates the range of provisional values
obtained. For example, the dashed block 101 in FIG. 4 and the loop
102 associated therewith could be used to repeat the compressional
velocity-determining correlation of block 120 for different individual
cycles (which may or may not overlap) near the beginning of the Rl
waveform (instead of saving time by skipping through these cycles as
described in conjunction with the loop 199). In such case, a
plurality of provisional compressional wave velocities would be
-31-
~5~8~5
determined and an output compressional wave velocity may be obtained
from these provisional values as is the case for the output shear wave
velocity determination. Also, it will be understood that alternative
relatively short portions of the waveforms, such as two cycle
portions, could be used for the correlations. Alternate correlation
techniques can also be employed, consistent with the principles of the
invention.
