Wellbore telemetry and noise cancellation systems and methods for the same
A method of signal processing includes providing at least a first pressure sensor and a second pressure sensor spaced in a drilling system and using an algorithm to separate the downwardly propagating waves from the upwardly propagating waves. In one or more examples, an algorithm may include determining a velocity of pressure signals in a wellbore, time-shifting and stacking pressure signals from at least the first pressure sensor and the second pressure sensor to determine a downwardly propagating noise signal, and subtracting the downwardly propagating noise signal from at least the signal from the first pressure sensor.
1. A method for wellbore communications, comprising:
obtaining a first corrected pressure signal and a downwardly propagating noise signal from at least a first pressure sensor;
computing a cross-correlation function between the first corrected pressure signal and the downwardly propagating noise signal for at least the first pressure sensor;
computing the standard deviation of the downwardly propagating noise signal;
computing a reflection coefficient for the downwardly propagating noise signal; from the standard deviation of the downwardly propagating noise signal;
computing the reflected, upwardly propagating noise signal from the reflection coefficient for the downwardly propagating noise signal; and
subtracting the reflected, upwardly propagating noise signal from the first corrected pressure signal.
2. The method of claim 1 , wherein:
the cross-correlation function comprises:
C
3
D
(
d
)
=
∑
k
=
0
m
-
1
{
[
R
3
(
t
k
)
-
R
3
_
]
·
[
N
D
(
t
j
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-
N
D
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]
}
;
computing the reflection coefficient for the downwardly propagating noise signal comprises averaging the following equation over a plurality of measurements;
A
·
ⅇ
ⅈϕ
=
〈
C
3
D
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d
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〉
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σ
N
2
〉
;
subtracting the reflected, upwardly propagating noise signal is performed using the following equation:
{tilde over (R)} 3 ( t )= R 3 ( t )− Ae iφ ·N D ( t·Tc−Ta ); and
wherein C 3D (d) represents the cross-correlation function, R 3 (t k ) represents the first corrected pressure signal at time t k , R 3 represents an average corrected pressure signal, N D (t j ) represents the downwardly propagating noise signal at time t j , N D represents an average downwardly propagating noise signal, Ae iφ represents the reflection coefficient for the downwardly noise signal, σ N represents the standard deviation of the downwardly propagating noise signal, (•) represents an average over many measurements, Ae iφ ·N D (t+T c −T a ) represents the reflected, upwardly propagating noise signal; R 3 (t) represents the first corrected pressure signal, and {tilde over (R)} 3 (t) represents a twice corrected pressure signal.
3. The method of claim 1 , wherein computing the standard deviation of the downwardly propagating noise signal is performed in a time window corresponding to a maximum value for the cross-correlation function.
4. The method of claim 1 , wherein subtracting the reflected, upwardly propagating noise signal from the first corrected pressure signal yields a first twice corrected pressure signal, and further comprising:
obtaining a second corrected pressure signal and a downwardly propagating noise signal from a second pressure sensor;
computing a cross-correlation function between the second corrected pressure signal and the downwardly propagating noise signal for the second pressure sensor;
computing the standard deviation of the downwardly propagating noise signal from the second pressure sensor;
computing a reflection coefficient for a mud pump noise at the second pressure sensor;
subtracting an upwardly propagating noise signal at the second pressure sensor from the second corrected pressure signal to obtain a second twice corrected pressure signal; and
time-shifting and stacking the first twice corrected pressure signal and the second twice corrected pressure signal.