Note: Descriptions are shown in the official language in which they were submitted.
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CALIBRATION OF A WELL ACOUSTIC SENSING SYSTEM
TECHNICAL FIELD
This disclosure relates generally to equipment utilized
and operations performed in conjunction with a subterranean
well and, in examples described below, more particularly
provides for calibration of a well acoustic sensing system.
BACKGROUND
An optical distributed acoustic sensor (DAS) system
uses an optical waveguide, such as an optical fiber, as a
distributed sensor to detect acoustic waves that vibrate the
waveguide. This sensing is performed by detecting
backscattered light transmitted through the waveguide.
Changes in the backscattered light can indicate not only the
presence of acoustic waves, but also certain characteristics
of the acoustic waves.
Unfortunately, when an optical waveguide is installed
in a well, various factors (such as, acoustic couplings and
wellbore construction) can influence measured acoustic power
as a function of frequency, as well as other characteristics
of the acoustic waves which impinge on the optical
waveguide. For example, if the waveguide is positioned
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outside of casing in a wellbore, the intensity of acoustic
waves originating in the casing and impinging on the
waveguide outside of the casing can vary significantly along
the waveguide, depending on changes in the casing thickness,
changes in cement outside the casing, etc. Additionally,
this variation in the characteristics of the acoustic waves
which impinge on the waveguide makes it difficult to
interpret measurements made by a DAS system.
Thus, it will be appreciated that improvements are
continually needed in the art of using distributed acoustic
sensing systems in conjunction with subterranean wells. Such
improvements could be useful for calibrating well acoustic
sensing systems other than DAS systems, for example, well
acoustic sensing systems which include arrays of multiplexed
point sensors, such as fiber Bragg gratings, or non-optical
distributed acoustic sensing systems.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a representative partially cross-sectional
view of a well system and associated method which can embody
principles of this disclosure.
FIG. 2 is a representative partially cross-sectional
view of another example of the well system and method.
FIG. 3 is a representative plot of measured acoustic
intensity data as a function of well depth and time, and
indicates abrupt changes in intensity where well features
change abruptly.
FIG. 4 is a representative schematic view of an
interrogator having a polarization controller used for
fading mitigation.
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FIG. 5 is a representative flowchart for a method of
mitigating fading using the polarization controller.
FIG. 6 is a representative partially cross-sectional
view of another example of the system and method, in which a
seismic source at a surface location and a three-axis
geophone are used for calibration.
FIG. 7 is a representative partially cross-sectional
view of another example of the system and method, in which
an acoustic source in an offset well and a three-axis
geophone are used for calibration.
DETAILED DESCRIPTION
Representatively illustrated in FIG. 1 is a system 10
for use with a well, and an associated method, which system
and method can embody principles of this disclosure.
However, it should be clearly understood that the system 10
and method are merely one example of an application of the
principles of this disclosure in practice, and a wide
variety of other examples are possible. Therefore, the scope
of this disclosure is not limited at all to the details of
the system 10 and method described herein and/or depicted in
the drawings.
In this example, an active sound source or sources are
housed within an object (a ball, a cylinder, etc.), which is
dropped, injected or lowered by cable into a wellbore for
the purpose of calibrating an optical distributed acoustic
sensor previously installed in a well. In the case of
dropping or injecting one or more objects with active sound
source(s), the object(s) may also be used to control
downhole devices (such as valves, etc.) and/or to plug
perforations.
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There are various vibration speakers, vibrating
actuators, and acoustic transducers, e.g., flextensional
SONAR transducers, etc., that are capable of actively
producing sounds within an object. Such acoustic sources are
well known to those skilled in the art and, thus, are not
described further here.
In one example, the distributed acoustic sensor
calibration uses a measurement of a power of acoustic
signals at several acoustic frequencies, as well as an
extent of the acoustic signals. The calibration will ideally
be done over the entirety of the acoustic sensor, or at
least in a specific wellbore area of interest. A measurement
of the intensity of the sound energy provides the acoustic
sensitivity as a function of position along the distributed
acoustic sensor. A measurement of the extent of the acoustic
signal along the acoustic sensor provides a well location
dependent point spread function (e.g., blurring function,
blurring kernel, etc.) of acoustic waves as detected by the
sensor.
Spatial blurring can result from an acoustic sensor at
a particular location picking up acoustic waves which
originate at multiple locations. That is, a measurement of
acoustic power at a specific point in a well is comprised of
sounds far away from this specific location. A calibration
method to account for this effect is proposed here. A
calibration measurement of the acoustic point spread
function (spatial blurring function, impulse response, etc.)
would allow the acoustic signals to be spatially
deconvolved, inverted, deblurred, etc., to enhance the
sounds heard at only one location in the well. Yet another
calibration factor for distributed acoustic sensing can be
determined from measuring an echo-response (i.e., an
acoustic impulse response) of the well, so that echoes in
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the well can be removed or reduced as desired. This is
typically done using a frequency domain adaptive filter that
maximizes a term referred to as the Echo Return Loss
Enhancement factor, which is a measure of the amount the
echo has been reduced or attenuated.
The sounds can be emitted as continuous single-
frequency tones, continuous dual tone multiple frequency
(DTMF, similar to what is used for pushbutton telephones),
continuous multiple-frequency tones, continuous wide
spectrum tones, continuous white noise, continuous colored
noise, continuously repeating swept-frequency waveforms,
continuous pseudorandom waveforms, or other continuously
repeating complex waveforms. The sounds can also be emitted
as pulsed single-frequency tones, pulsed dual tone multiple
frequency (DTMF, similar to what is used for pushbutton
telephones), pulsed multiple-frequency tones, pulsed wide
spectrum tones pulsed white noise, pulsed colored noise,
pulsed swept-frequency waveforms, pulsed pseudorandom
waveforms, or other pulsed complex waveforms.
The sounds can be transmitted in synchrony. The sounds
can be transmitted at different volumes at each location.
The scope of this disclosure is not limited to any
particular predetermined acoustic signals transmitted by an
acoustic source.
If the sounds are transmitted at different volumes at
various locations, nonlinearities in the gain response as a
function of location in the well can be determined.
The FIG. 1 example provides for in-situ calibration of
an optical acoustic sensor used to measure acoustic energy.
The sensor comprises a distributed acoustic sensing (DAS)
system, which is capable of detecting acoustic energy as
distributed along an optical waveguide. The sensor comprises
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surface electronics and software, commonly known to those
skilled in the art as an interrogator, and the optical
waveguide. The optical waveguide may be installed in a
wellbore, inside or outside of casing or other tubulars,
optionally in cement surrounding a casing, etc.
The interrogator launches light into the optical
waveguide (e.g., from an infrared laser), and the DAS system
uses measurement of backscattered light (e.g., coherent
Rayleigh backscattering) to detect the acoustic energy along
the waveguide. Signal processing is used to segregate the
waveguide into an array of individual "microphones" or
acoustic sensors, typically corresponding to 1-10 meter
segments of the waveguide.
The waveguide may be housed in a metal tubing or
control line and positioned in a wellbore. In some examples,
the waveguide may be in cement surrounding a casing, in a
wall of the casing or other tubular, suspended in the
wellbore, in or attached to a tubular, etc. The scope of
this disclosure is not limited to any particular placement
of the waveguide.
A sensitivity of the waveguide to acoustic energy can
depend significantly on how the waveguide is installed in
the well, and on local variations (such as, cement
variations, casing variations, presence of other equipment
such as packers or cable clamps, temperature variations,
presence of gas or liquids in the wellbore, type of fluid in
the wellbore or cement, etc.). For example, significant
temperature variations along a wellbore can affect the
amount of Rayleigh backscattering in the waveguide.
In a calibration procedure described below, these
variations can be compensated for by detecting predetermined
acoustic signals transmitted along the waveguide by an
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acoustic source. The acoustic source may comprise an object
which is released, injected or lowered into the wellbore
using an electric wireline, a slickline, a wellbore tractor,
etc.
By emitting sound in a controlled manner from the
acoustic source, and receiving the resulting acoustic energy
along the waveguide, the DAS sensor can measure the acoustic
sensitivity (e.g., the acoustic coupling factor or gain
factor) as a function of acoustic frequency, and as a
function of position along the waveguide. Another embodiment
is to measure the cumulative power only as a function of
position along the waveguide.
The measurement of the gain per DAS channel allows for
a gain normalization scale factor to be applied at each
location. This gain scale factor can be either frequency
dependent or not.
Another embodiment is to synchronize the sound
emissions with a clock so a phase of the signals can be
measured as a function of position along the waveguide. The
calibrating technique can include measuring the phase of the
acoustic signal along the optical waveguide. Measured phase
or phase inversion is related to either stretching or
compression of the optical waveguide.
To measure the phase, the acoustic source is
synchronized with the clock of the interrogator. The
acoustic source preferably has an accurate clock to make
this measurement.
The sound emitted from the acoustic source can also
travel along the wellbore and acoustically illuminate other
sections of the waveguide, thus allowing determination of
the point spread function as a function of acoustic
frequency and as a function of position along the wellbore.
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These parameters (acoustic sensitivity and point spread
function) are used to calibrate the DAS system.
The measurement of the acoustic point spread function
allows the acoustic field to be deblurred using any of a
number of deblurring methodologies, such as, the Wiener
deblurring filter, regularized deblurring filter, Lucy-
Richardson deblurring algorithm, blind deconvolution
deblurring algorithm, or Vardi-Lee expectation maximization
deblurring algorithm, for example.
Generally, there are a percentage (usually small) of
channels of some DAS systems that experience an issue known
as "fading," where the signal-to-noise ratio (SNR) of the
channel will be reduced temporarily. This reduction in SNR,
may reduce the accuracy of the calibration. Fading can be
caused by several different effects, with polarization
effects being a predominant cause.
The calibration can be done by averaging out the
occasional fading effects by collecting sufficient data over
a longer time. Additionally, by oversampling spatially, the
calibration data for faded channels may be ignored and the
calibration of adjacent non-faded channels used instead for
those that are faded.
In an additional method representatively illustrated in
FIGS. 4 & 5, a polarization controller 48 is placed in
series with an optical source 50 of the device 26 to adjust
the polarization of the light being launched into the
optical waveguide 22. Backscattered light is detected by an
optical receiver 52.
By adjusting the polarization of the outgoing light,
the relative backscattered optical power from each channel
will change. Using an iterative optimization process of
adjusting the launch polarization (see FIG. 5), the optical
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signal power from the channel being currently calibrated is
optimized until an acceptable signal to noise ratio for the
channel being calibrated is obtained. Use of polarization
maintaining fiber optic cables can also be employed to
mitigate polarization fading, etc.
In one example, the object which emits the acoustic
signals can be injected into the wellbore during a
fracturing or other stimulation operation. The object could,
for example, be a ball, dart or plug used to actuate one or
more valves for selectively communicating between the
wellbore and an earth formation penetrated by the wellbore.
In this manner, the calibration procedure can be part of the
stimulation operation, instead of separate therefrom.
In another example, the object can be lowered into the
wellbore using a wireline, slickline or wellbore tractor.
This procedure could be performed separately as needed, or
as part of another operation (such as, a wireline logging
operation).
FIG. 1 depicts an example in which an acoustic source
12 is conveyed into a wellbore 14 by means of a cable 16
(e.g., wireline, slickline, other type of cable, etc.). The
wellbore 14 in this example is lined with casing 18 and
cement 20, but in other examples the wellbore could be
uncased or open hole.
As used herein, the term "casing" is used to indicate a
protective wellbore lining. Casing may be made up of
tubulars known to those skilled in the art as casing, liner
or tubing. Casing may be segmented or continuous. Casing may
be made of metals, composites or other materials.
In the FIG. 1 example, an optical waveguide 22 is
positioned external to the casing 18, and in the cement 20.
The waveguide 22 may be attached externally to the casing
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18. In other examples, the waveguide 22 could be positioned
in a wall of the casing 18, in an interior of the casing, or
in any other location.
Note that one section of the casing 18 has a greater
thickness than adjacent sections. This can cause acoustic
signals transmitted through the casing 18 to be more
attenuated at the thicker section, so that the waveguide 22
detects a lower intensity of the acoustic signals at that
location.
It would be desirable to calibrate an output of a DAS
system 24 (including the waveguide 22 and an interrogator or
backscattered light detection and analysis device 26), so
that the output is compensated for such variations. Of
course, other types of variations (e.g., variations in fluid
types in the wellbore 14, casing 18 and cement 20,
variations in temperature, etc.) can also be compensated for
in the calibration procedure. The scope of this disclosure
is not limited to compensation for any particular type of
variation.
In the calibration procedure, the acoustic source 12 is
displaced to various different locations along the waveguide
22, and the acoustic source transmits a predetermined
acoustic signal 28 at the different locations. The acoustic
source 12 may transmit the acoustic signal continuously
while the source is being displaced along the waveguide 22,
or the acoustic signal could be separately transmitted at
the respective separate locations.
As mentioned above, the acoustic signal 28 may comprise
a single or multiple acoustic frequencies, certain
combinations of frequencies, white noise, colored noise, or
pseudorandom waveforms. The acoustic signal 28 may be
transmitted at a single or multiple power levels. The scope
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of this disclosure is not limited to any particular type of
acoustic signal(s) 28 transmitted by the acoustic source 12.
Referring additionally now to FIG. 2, another example
of the system 10 is representatively illustrated. In this
example, the acoustic source 12 is dropped or injected into
the well, such as, during a fracturing or other stimulation
operation.
The acoustic source 12 emits the acoustic signal 28 as
it displaces through a tubular string 30 in the wellbore 14.
A valve 32 is included in the tubular string 30 for
providing selective communication between an interior of the
tubular string 30 and an earth formation 34 penetrated by
the wellbore 14. The acoustic source 12 may comprise a ball,
plug or dart which, when received in the valve 32, allows
the valve to be operated to permit or prevent such
communication.
Thus, in the FIG. 2 example, the acoustic source 12
serves at least two purposes: enabling calibration of the
DAS system 24, and enabling operation of the valve 32. In
this manner, the DAS system 24 can be calibrated while the
stimulation operation proceeds. In other examples, the
acoustic source 12 could be used to plug perforations 36, or
to perform any other function.
Although only one acoustic source 12 is depicted in
each of the FIGS. 1 & 2 examples, it will be appreciated
that any number of acoustic sources may be used. Multiple
acoustic sources 12 could be displaced along the waveguide
22 simultaneously or separately. The acoustic sources 12
could each transmit the same predetermined acoustic signal
28, or different acoustic signals could be transmitted by
respective different acoustic sources.
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Referring additionally now to FIG. 3, an example plot
of measured acoustic intensity data as a function of well
depth and time is representatively illustrated. Note that,
in the plot abrupt changes in intensity are indicated, for
example, where well features change abruptly.
The presence of the thicker casing 18, a packer, or
other discontinuities can be causes of the abrupt changes in
intensity. Use of the calibration techniques described above
in conjunction with the acoustic source 12 can eliminate or
at least significantly reduce the abrupt changes in acoustic
intensity as depicted in the FIG. 3 plot.
Although the examples described herein use the
waveguide 22 as a distributed acoustic sensor, multiple
individual acoustic sensors may alternatively (or
additionally) be used. For example, multiple multiplexed
fiber Bragg gratings could be used as discreet acoustic
sensors 40 (see FIG. 1) distributed along the waveguide 22.
The calibration techniques described herein may be used
to calibrate the measurements made using the distributed
acoustic sensors 40. The calibration techniques described
herein may also be used to calibrate measurements made using
the distributed acoustic sensors 40, even if the sensors are
not optical sensors.
One of the issues with conventional DAS systems is that
a fiber channel is a sensor that produces a single "value,"
but the sensor actually responds to energy propagating in
different orientations or directions simultaneously. In some
examples described below, a three-component (x, y, z)
geophone can be used as a reference in a calibration
technique, so that vibration energy in the x, y, and z
directions can be separated out to determine what the
fiber's response is to vibrations that are oriented in the
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x, y, and z axis directions separately. The x, y, and z
directions can be any three orthogonal directions as long as
the orientation is known during calibration.
For example, in many seismic applications, it would be
desirable to know how the fiber responds to p-waves coming
from the side (cross-well) versus longitudinal (along the
wellbore). For microseismic detection, it would be desirable
to know the response of the fiber to shear or s-waves,
including s-waves of different polarizations, because shear
waves are a major energy component of microseismic events
(typically fractures). If the response of the fiber to
horizontally polarized s-waves and vertically polarized s-
waves could be separately determined, it would be possible
to infer the response to other polarizations. If the
calibration could help in determining the polarization of
the shear wave components generated by a microseismic event,
the orientation (azimuth) of the fracture (which is a very
important piece of information) could be determined.
Due to the distance and weakness of most microseismic
events, it would be desirable to combine the response of
many DAS channels using techniques like beamforming in order
to see these events. To do beamforming effectively, each
channel is preferably corrected or normalized based on a
calibration.
Stoneley waves (or tube waves) travel along the walls
of the borehole and are a noise source in vertical seismic
profiling. Preferably, the effect of Stoneley waves is
subtracted out of a recorded signal before stacking when
doing a vertical seismic profiling application. If Stoneley
waves could be generated at a wellhead or using a downhole
source designed to generate that kind of wave, we could see
how each channel responds and this will enable us able to
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compensate for them in vertical seismic profiling or other
applications.
As representatively illustrated in FIG. 6, another
calibration method can include the use of a remote vibratory
or impulse seismic source 12, and preferably, a calibrated
reference receiver 42 (such as a three-axis geophone) placed
adjacent to the distributed acoustic sensor (such as the
optical waveguide 22 or sensors 40). The calibrated
reference receiver 42 is not required for the methods
described herein, but will improve the accuracy of the
calibration by accounting for the signal attenuation and
distortion effects caused by the formation 34 between the
source 12 and the DAS sensor. In this method, the seismic
source can be located either on the surface (as depicted in
FIG. 6), or in a nearby well (as depicted in FIG. 7). A
calibrated seismic receiver 42 (accelerometer, geophone,
hydrophone, etc.), for example a three-axis geophone, is
optionally lowered into the well containing the distributed
acoustic sensor to the depth of the channel being
calibrated. The seismic source, located at the surface or a
nearby well is energized to emit seismic energy ( P-wave, S-
wave, etc.) to be received by the DAS sensor. Both the DAS
sensor and geophone receive substantially the same energy.
Using the receiver 42 as a reference, the DAS sensor
response to a variety of different signals produced by the
seismic source 12, including various amplitude, frequency,
and directional variations, can be compared to the receiver
response to derive a calibration for the DAS sensor.
For example, in one method the seismic source 12 is
placed near a wellhead 44, such that a seismic wave is sent
vertically down the length of the well and longitudinally
along the length of the DAS sensor. In another method, the
seismic source is located a significant distance away from
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the wellhead 44 so that the seismic energy is oriented
mostly horizontally. In a deviated or horizontal well, the
direction of travel of the seismic energy relative to the
wellbore 14 would be altered or reversed based on the layout
of the wellbore.
In the case of a cross-well calibration (as depicted in
FIG. 7), the seismic source 12 is lowered into a neighboring
well 46. The seismic source may generate S-waves or P-waves
to provide a multicomponent calibration of the DAS cable
(e.g., optical waveguide 22) based on the type of wave. The
cross-well calibration case may be particularly important
for micro-seismic detection during hydraulic fracturing
operations where the DAS cable may be located in an
observation well nearby the well to receive the fracturing
treatment. In this scenario, the seismic source is lowered
into the well to be fractured to emit seismic energy (P-
wave, S-wave, etc.) into the formation. The DAS cable
receives the seismic energy in the observation well, along
with a calibration geophone to provide the calibration data.
It may now be fully appreciated that the above
disclosure provides significant advancements to the art of
optical distributed acoustic sensing. In examples described
above, variations in acoustic sensitivity of the DAS system
24 can be compensated for by displacing the acoustic source
12 along the optical waveguide 22 or other distributed
acoustic sensors 40, with the acoustic source transmitting
the predetermined acoustic signal 28 at different locations
along the sensors. In this manner, the output of the DAS
system 24 is calibrated.
A method of calibrating an optical distributed acoustic
sensing system 24 is described above. In one example, the
method comprises receiving predetermined acoustic signals 28
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along an optical waveguide 22 or other distributed acoustic
sensors 40 positioned proximate a well, and calibrating the
optical distributed acoustic sensing system 24 based on the
received predetermined acoustic signals 28.
The method can include displacing at least one acoustic
source 12 adjacent the optical waveguide 22. The displacing
can include displacing the acoustic source 12 through a
wellbore 14.
The acoustic source 12 preferably transmits the
predetermined acoustic signals 28 at multiple locations
along the optical waveguide 22.
The receiving step can include determining a power,
power spectral density, phase, and/or extent of the acoustic
signals 28 as received along the optical waveguide 22.
The calibrating step can include measuring an acoustic
sensitivity along the optical waveguide 22.
In one example, a method of calibrating an optical
distributed acoustic sensing system 24 can include
displacing at least one acoustic source 12 along an optical
waveguide 22 positioned proximate a well, transmitting
predetermined acoustic signals 28 from the acoustic source
12, receiving the predetermined acoustic signals 28 with the
optical waveguide 22, and calibrating the optical
distributed acoustic sensing system 24 based on the received
predetermined acoustic signals 28.
A well system 10 is also described above. In one
example, the well system 10 can comprise an optical
distributed acoustic sensing system 24 including an optical
waveguide 22 installed in a well and a backscattered light
detection and analysis device 26, and at least one acoustic
source 12 which transmits predetermined acoustic signals 28
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at multiple spaced apart locations along the optical
waveguide 22.
In this example, the backscattered light detection and
analysis device 26 compensates an output of the optical
distributed acoustic sensing system 24 based on the
predetermined acoustic signals 28 as received at the spaced
apart locations along the optical waveguide 22. The
backscattered light detection and analysis device 26 may
determine an acoustic sensitivity along the optical
waveguide, measure a phase of the acoustic signals along the
optical waveguide 22, determine a power spectral density of
the acoustic signals as received along the optical waveguide
22, and/or determine an extent of the acoustic signals as
received along the optical waveguide 22.
In a broad aspect, it is not necessary for the
distributed acoustic sensing system to be "optical," or for
the distributed acoustic sensors to be "optical." A method
of calibrating a distributed acoustic sensing system 10 can
include receiving predetermined acoustic signals 28 along
multiple acoustic sensors 40 (whether or not the sensors are
optical sensors, and whether or not the sensors comprise
channels of an optical waveguide, such as an optical fiber)
distributed proximate a well; and calibrating the optical
distributed acoustic sensing system 10 based on the received
predetermined acoustic signals 28.
The method can include displacing at least one acoustic
source 12 adjacent the acoustic sensors 40. The displacing
may include displacing the acoustic source 12 through a
wellbore 14.
The acoustic source 12 may transmit the predetermined
acoustic signals 28 at multiple locations along the acoustic
sensors. The acoustic source 12 may transmit the
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predetermined acoustic signals 28 at different amplitudes at
each of the multiple locations.
The acoustic source 12 may transmit the predetermined
acoustic signals 28 in synchrony with an interrogator (such
as the device 26). The calibrating step can include
measuring a phase of the acoustic signals 28 along the
acoustic sensors 40.
The receiving step may include determining a power, a
power spectral density, and/or an extent of the acoustic
signals 28 as received along the acoustic sensors 40.
The calibrating step can include measuring an acoustic
sensitivity along the acoustic sensors 40.
The method can include transmitting the acoustic
signals 28 from another well 46, or from at or near the
earth's surface.
The method can include transmitting Stoneley waves from
at or near a wellhead 44, or from a downhole location.
The receiving step can include receiving the acoustic
signals 28 by a three-axis reference sensor (such as
receiver 42) positioned proximate the distributed acoustic
sensors 40 or optical waveguide 22.
The calibrating step can include calibrating the
distributed acoustic sensing system 24 based on the
predetermined acoustic signals 28 as detected by the three-
axis reference sensor 42. The three-axis reference sensor
may comprise a geophone.
The calibrating step can include computing an acoustic
point spread function along the sensors 40 for each of
multiple source 12 locations. The calibrating can further
comprise using the point spread function determined by the
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computing to deblur acoustic emissions along a wellbore 14
as received by the distributed acoustic sensors 40.
Although various examples have been described above,
with each example having certain features, it should be
understood that it is not necessary for a particular feature
of one example to be used exclusively with that example.
Instead, any of the features described above and/or depicted
in the drawings can be combined with any of the examples, in
addition to or in substitution for any of the other features
of those examples. One example's features are not mutually
exclusive to another example's features. Instead, the scope
of this disclosure encompasses any combination of any of the
features.
Although each example described above includes a
certain combination of features, it should be understood
that it is not necessary for all features of an example to
be used. Instead, any of the features described above can be
used, without any other particular feature or features also
being used.
It should be understood that the various embodiments
described herein may be utilized in various orientations,
such as inclined, inverted, horizontal, vertical, etc., and
in various configurations, without departing from the
principles of this disclosure. The embodiments are described
merely as examples of useful applications of the principles
of the disclosure, which is not limited to any specific
details of these embodiments.
In the above description of the representative
examples, directional terms (such as "above," "below,"
"upper," "lower," etc.) are used for convenience in
referring to the accompanying drawings. However, it should
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be clearly understood that the scope of this disclosure is
not limited to any particular directions described herein.
The terms "including," "includes," "comprising,"
"comprises," and similar terms are used in a non-limiting
sense in this specification. For example, if a system,
method, apparatus, device, etc., is described as "including"
a certain feature or element, the system, method, apparatus,
device, etc., can include that feature or element, and can
also include other features or elements. Similarly, the term
"comprises" is considered to mean "comprises, but is not
limited to."
Of course, a person skilled in the art would, upon a
careful consideration of the above description of
representative embodiments of the disclosure, readily
appreciate that many modifications, additions,
substitutions, deletions, and other changes may be made to
the specific embodiments, and such changes are contemplated
by the principles of this disclosure. For example,
structures disclosed as being separately formed can, in
other examples, be integrally formed and vice versa.
Accordingly, the foregoing detailed description is to be
clearly understood as being given by way of illustration and
example only, the spirit and scope of the invention being
limited solely by the appended claims and their equivalents.
