Joint time-frequency processing for borehole acoustic arrays
Various embodiments include apparatus and methods to process acoustic signals according to joint time-frequency processing. The joint time-frequency processing can combine features of both time-based processing and frequency-based processing. This processing may be based on delay calculation from amplitude phases generated from the acoustic signals. The joint time-frequency processing may be applied to a variety of applications to evaluate properties associated with a borehole or surrounding formations. Additional apparatus, systems, and methods are disclosed.
1. A method comprising:
using a processor and data storage device coupled to an acoustic tool to process signals generated from operating the acoustic tool in a borehole such that the using includes
collecting signals from generation of acoustic waves using the acoustic tool;
generating delay values using frequency-based signals, the frequency-based signals correlated to the collected signals, wherein generating the delay values includes
processing the frequency-based signals into a representation that is a series sum of modes, each mode having an amplitude and a pole, and processing the amplitude of a mode such that a delay value is generated; or
processing the frequency-based signals into an amplitude proportional to a sum of products of the frequency-based signals and a corresponding phase factor, the phase factor based on a slowness from a phase coherence of the frequency-based signals, and processing the amplitude such that a delay value is generated; and
evaluating properties associated with the borehole, surrounding formations, or quality of a measurement using the delay values.
2. The method of claim 1 , wherein generating delay values includes
processing the frequency-based signals into a representation that is a series sum of modes, each mode having an amplitude and a pole; and
processing the amplitude of a mode such that a delay value is generated.
3. The method of claim 1 , wherein the method includes converting pressure at receivers of the acoustic tool to voltages expanded into a series sum of modes given by
V
i
(
f
)
=
∑
n
=
1
N
m
A
n
(
Z
n
)
i
-
i
ref
where f is frequency, N m is a total number of modes in the expansion, A n is a complex valued amplitude of mode n, Z n is a complex valued pole of mode n, and i ref is a reference index, and delay for mode n generated according to
d
n
=
-
ⅆ
ⅆ
f
(
angle
(
A
n
)
2
π
)
.
4. The method of claim 1 , wherein generating delay values includes
processing the frequency-based signals into an amplitude proportional to a sum of products of the frequency-based signals and a corresponding phase factor, the phase factor based on a slowness from a phase coherence of the frequency-based signals; and
processing the amplitude such that a delay value is generated.
5. The method of claim 1 , wherein the method includes collecting voltages from receivers of the acoustic tool and generating delay according to
delay
=
-
ⅆ
ⅆ
f
(
angle
(
A
)
2
π
)
from
A
=
1
N
r
∑
i
=
1
N
r
V
i
(
f
)
ⅇ
j2π
fs
PC
(
f
)
(
z
i
-
z
ref
)
with A being amplitude where j is the imaginary number, N r is a total number of receivers, z i is axial position of an i'th receiver, z ref is a reference position, and s pc (f) is slowness from a phase coherence as a function of frequency, f.
6. The method of claim 1 , wherein processing the amplitude includes determining a phase delay of the mode or determining a group delay of the mode.
7. The method of claim 6 , wherein determining the phase delay includes determining
-
angle
(
A
n
)
2
π
f
and determining the group delay includes determining
-
ⅆ
ⅆ
f
(
angle
(
A
n
)
2
π
)
,
A n being a complex-valued amplitude of a mode n, f being frequency.
8. The method of claim 1 , wherein evaluating properties associated with the borehole or surrounding formations includes pairing the delay values with frequency, pairing the delay values with slowness values, or pairing the delay values with frequency and pairing the delay values with slowness values.
9. The method of claim 1 , wherein the method includes using the calculated delay values to determine a window in time for further processing in time.
10. The method of claim 9 , wherein the method includes determining delay values multiple times with each determination having a different time window to evaluate separate wave packets with a same frequency and slowness arriving at different times.
11. The method of claim 1 , wherein collecting signals includes acquiring pressure at receivers of the acoustic tool, the pressure generated by a transmitter of the acoustic tool at different depths of the borehole.
12. The method of claim 11 , wherein acquiring pressure at receivers of the acoustic tool includes acquiring pressure at a plurality of stations of the tool, each station having a plurality of receivers around the acoustic tool.
13. The method of claim 1 , wherein collecting signals from generation of acoustic waves using the acoustic tool includes generating acoustic waves at a plurality of frequencies from the acoustic tool.
14. A method comprising:
using a processor and data storage device coupled to an acoustic tool to process signals generated from operating the acoustic tool in a borehole such that the using includes
collecting signals from generation of acoustic waves using the acoustic tool;
generating delay values using frequency-based signals, the frequency-based signals correlated to the collected signals;
evaluating properties associated with the borehole, surrounding formations, or quality of measurement using the delay values; and
generating a fan from slowness values, the delay values, and associated frequency values to generate filtered points.
15. The method of claim 14 , wherein generating filtered points includes applying a fan on a point, the point given by frequency and mode (f, n), according to a three-dimension coordinate system of frequency, slowness, delay of a mode, (f, s n , delay n ), by discarding the solutions that lie out of the fan as follows
action
on
point
(
f
,
n
)
=
{
keep
,
if
fan
(
f
,
s
n
,
delay
n
)
=
1
discard
,
otherwise
.
.
16. The method of claim 14 , wherein generating filtered points includes applying a fan based on the frequency values and the delay values, applying a fan based on the delay values and the slowness values, and applying a fan based on the frequency values and the slowness values.
17. A method comprising:
using a processor and data storage device coupled to an acoustic tool to process signals generated from operating the acoustic tool in a borehole such that the using includes
collecting signals from generation of acoustic waves using the acoustic tool;
generating delay values using frequency-based signals, the frequency-based signals correlated to the collected signals;
evaluating properties associated with the borehole, surrounding formations, or quality of a measurement using the delay values;
discretizing a range of frequency, mud, borehole, and formation parameters to form a grid of points;
performing a modeling on each point to generate modeled received acoustic signals;
processing the received acoustic signals forming points (f i , s i , d i ) corresponding to frequency, slowness, and delay of each point, respectively; and
interpolating the formed points to yield a multi-dimensional volume as a fan.
18. The method of claim 17 , wherein the method includes forming a frequency-slowness-delay fan (fan FSD ) with respect to the grid of points and data according to
fan
FSD
=
{
1
,
∃
i
,
f
i
l
-
f
i
d
<
Δ
f
,
s
i
l
-
s
i
d
<
Δ
s
and
d
i
l
-
d
i
d
<
Δ
d
,
0
,
otherwise
,
where
Δf: frequency threshold for comparison
Δs: slowness threshold for comparison
Δd: delay threshold for comparison
f i l :frequency of i'th point in the gird
s i l :slowness of i'th point in the gird
d l l :delay of i'th point in the gird
f i d :frequency of i'th point in the data
s i d :slowness of i'th point in the data
d i d : delay of i'th point in the data.
19. A machine-readable storage device having instructions stored thereon, which, when performed by a machine, cause the machine to perform operations, the operations comprising:
using a processor and data storage device coupled to an acoustic tool to process signals generated from operating the acoustic tool in a borehole such that the using includes
collecting signals from generation of acoustic waves using the acoustic tool;
generating delay values using frequency-based signals, the frequency-based signals correlated to the collected signals, wherein generating delay values includes
processing the frequency-based signals into a representation that is a series sum of modes, each mode having an amplitude and a pole, and processing the amplitude of a mode such that a delay value is generated; or
processing the frequency-based signals into an amplitude proportional to a sum of products of the frequency-based signals and a corresponding phase factor, the phase factor based on a slowness from a phase coherence of the frequency-based signals, and processing the amplitude such that a delay value is generated; and
evaluating properties associated with the borehole, surrounding formations, or quality of a measurement using the delay values.
20. A system comprising:
an acoustic tool having a transmitter and an array of receivers;
a control unit operable to manage generation of acoustic signals from the transmitter and to manage collection of received signals at the receivers; and
a processing unit, wherein the acoustic tool, the control unit, and the processing unit are configured to process signals generated from operation of the acoustic tool in a borehole, collect signals from the generation of acoustic waves from use of the acoustic tool, generate delay values using frequency-based signals, the frequency-based signals correlated to the collected signals, and evaluate properties associated with the borehole, surrounding formations, or quality of a measurement from use of the delay values, wherein generation of the delay values includes
processing the frequency-based signals into a representation that is a series sum of modes, each mode having an amplitude and a pole, and processing the amplitude of a mode such that a delay value is generated; or
processing the frequency-based signals into an amplitude proportional to a sum of products of the frequency-based signals and a corresponding phase factor, the phase factor based on a slowness from a phase coherence of the frequency-based signals and processing the amplitude such that a delay a value is generated.
21. The system of claim 20 , wherein the acoustic tool, the control unit, and the processing unit are configured to convert pressure at the receivers of the acoustic tool to voltages expanded into a series sum of modes given by
V
i
(
f
)
=
∑
n
=
1
N
m
A
n
(
Z
n
)
i
-
i
ref
where f is frequency, N, m is a total number of modes in the expansion, A n is a complex valued amplitude of mode n, Z n is a complex valued pole of mode n, and i ref is a reference index, and delay for mode n generated according to
d
n
=
-
ⅆ
ⅆ
f
(
angle
(
A
n
)
2
π
)
.
22. The system of claim 20 , wherein the acoustic tool, the control unit, and the processing unit are configured to collect voltages from the receivers of the acoustic tool and to generate the delay values according to delay
=
-
ⅆ
ⅆ
f
(
angle
(
A
)
2
π
)
from
A
=
1
N
r
∑
i
=
1
N
r
V
i
(
f
)
ⅇ
j2π
fs
PC
(
f
)
(
z
i
-
z
ref
)
with A being amplitude where j is the imaginary number, N r is a total number of receivers, z i is axial position of an i'th receiver, z ref is a reference position, and s pc (f) is slowness from a phase coherence as a function of frequency, f.
23. The system of claim 20 , wherein the acoustic tool, the control unit, and the processing unit are configured to determine a phase delay by determination of
-
angle
(
A
n
)
2
π
f
and to determine a group delay by determination of
-
ⅆ
ⅆ
f
(
angle
(
A
n
)
2
π
)
,
A n being a complex-valued amplitude of a mode n, f being frequency and a mode being one of a series sum of modes of a representation of the frequency-based signals.
24. A system comprising:
an acoustic tool having a transmitter and an array of receivers;
a control unit operable to manage generation of acoustic signals from the transmitter and to manage collection of received signals at the receivers; and
processing unit, wherein the acoustic tool, the control unit, and the processing unit are configured to process signals generated from operation of the acoustic tool in a borehole, collect signals from the generation of acoustic waves from use of the acoustic tool, generate delay values using frequency-based signals, the frequency-based signals correlated to the collected signals, and evaluate properties associated with the borehole, surrounding formations, or quality of a measurement from use of the delay values, wherein the acoustic tool, the control unit, and the processing unit are configured to generate a fan from slowness values, the delay values, and associated frequency values to generate filtered points.
25. A system comprising:
an acoustic tool having a transmitter and an array of receivers;
a control unit operable to manage generation of acoustic signals from the transmitter and to manage collection of received signals at the receivers; and
a processing unit, wherein the acoustic tool, the control unit, and the processing unit are configured to process signals generated from operation of the acoustic tool in a borehole, collect signals from the generation of acoustic waves from use of the acoustic tool, generate delay values using frequency-based signals, the frequency-based signals correlated to the collected signals, and evaluate properties associated with the borehole, surrounding formations, or quality of a measurement from use of the delay values, wherein the acoustic tool, the control unit, and the processing unit are configured to:
discretize a range of frequency, mud, borehole, and formation parameters to form a grid of points;
perform a modeling on each point to generate modeled received acoustic signals;
process the received acoustic signals forming points (f i , s i , d i ) corresponding to frequency, slowness, and delay of each point, respectively; and
interpolate the formed points to yield a multi-dimensional volume as a fan.