Method for attenuating particle motion sensor noise in dual sensor towed marine seismic streamers
Signals detected by particle motion sensors in a towed dual sensor marine seismic streamer are scaled to match signals detected by pressure sensors in the streamer. The pressure sensor signals and the scaled particle motion sensor signals are combined to generate up-going and down-going pressure wavefield components. The up-going and down-going pressure wavefield components are extrapolated to a position just below a water surface. A first matching filter is applied to the extrapolated down-going pressure wavefield component. The filtered down-going pressure wavefield component is subtracted from the extrapolated up-going pressure wavefield component, generating an up-going pressure wavefield component with attenuated particle motion sensor noise. A second matching filter is applied to the extrapolated up-going pressure wavefield component. The filtered up-going pressure wavefield component is subtracted from the extrapolated down-going pressure wavefield component, generating a down-going pressure wavefield component with attenuated particle motion sensor noise.
1. A method for processing seismic data from a towed marine seismic streamer having particle motion sensors and pressure sensors, comprising:
scaling signals detected by the particle motion sensors to match signals detected by the pressure sensors;
combining the pressure sensor signals and the scaled particle motion sensor signals to generate up-going and down-going pressure wavefield components;
extrapolating the up-going and down-going pressure wavefield components to a position just below a water surface;
applying a first matching filter to the extrapolated down-going pressure wavefield component; and
subtracting the matching filtered extrapolated down-going pressure wavefield component from the extrapolated up-going pressure wavefield component, generating an up-going pressure wavefield component with particle motion sensor noise attenuated with a cosine filter.
2. The method of claim 1 , further comprising:
applying a second matching filter to the extrapolated up-going pressure wavefield component to math the extrapolated up-going and down-going pressure wavefield components; and
subtracting the matching filtered extrapolated up-going pressure wavefield component from the extrapolated down-going pressure wavefield component, generating a down-going pressure wavefield component with particle motion sensor noise attenuated with a cosine filter.
3. The method of claim 1 , wherein the scaling a particle motion sensor signal comprises applying an amplitude scaling function to the particle motion sensor signal to correct for amplitude differences between the pressure sensor signal and particle motion sensor signal.
4. The method of claim 2 , wherein the pressure sensor signal is a hydrophone signal and the particle motion sensor signal is a geophone signal.
5. The method of claim 4 , wherein the extrapolating the up-going and down-going pressure wavefield components further comprises:
backward extrapolating the extrapolated up-going and down-going pressure wavefield components to a virtual observation surface.
6. The method of claim 5 , wherein the extrapolating the up-going and down-going pressure wavefield components further comprises:
forward extrapolating the extrapolated up-going and down-going pressure wavefield components to a virtual observation surface.
7. The method of claim 4 , wherein the subtracting the filtered down-going pressure wavefield component from the extrapolated up-going pressure wavefield component is obtained by calculating the following expression in the frequency-wavenumber domain:
1
2
(
H
~
-
w
~
G
~
2
)
exp
[
-
ⅈ
k
z
(
z
r
-
z
)
]
|
z
->
+
0
-
F
~
1
1
2
(
H
~
+
w
~
G
~
2
)
exp
[
ⅈ
k
z
(
z
r
-
z
)
]
|
z
->
+
0
,
where {tilde over (H)} is the hydrophone signal, {tilde over (G)} is the geophone signal, {tilde over (w)} is the amplitude scaling function, k z is a vertical wavenumber, z r is depth of the streamer below the water surface, z is vertical direction measured downward from the water surface, and {tilde over (F)} 1 is the first matching filter.
8. The method of claim 7 , wherein the subtracting the filtered up-going pressure wavefield component from the extrapolated down-going pressure wavefield component is obtained by calculating the following expression in the frequency-wavenumber domain:
1
2
(
H
~
+
w
~
G
~
2
)
exp
[
ⅈ
k
z
(
z
r
-
z
)
]
|
z
->
+
0
-
F
~
2
1
2
(
H
~
-
w
~
G
~
2
)
exp
[
-
ⅈ
k
z
(
z
r
-
z
)
]
|
z
->
+
0
,
where {tilde over (F)} 2 is the second matching filter.
9. The method of claim 8 , wherein the matching filters {tilde over (F)} 1 and {tilde over (F)} 2 compensate for inconsistencies between the up-going and down-going pressure wavefield components.
10. The method of claim 9 , wherein the matching filters {tilde over (F)} 1 and {tilde over (F)} 2 compensate for amplitude inconsistencies between the up-going and down-going pressure wavefield components.
11. The method of claim 9 , wherein the matching filters {tilde over (F)} 1 and {tilde over (F)} 2 compensate for phase inconsistencies between the up-going and down-going pressure wavefield components.
12. The method of claim 8 , wherein the matching filters {tilde over (F)} 1 and {tilde over (F)} 2 are adaptive Wiener filters.
13. The method of claim 8 , wherein the matching filters {tilde over (F)} 1 and {tilde over (F)} 2 equal zero.
14. The method of claim 8 , wherein the matching filters {tilde over (F)} 1 and {tilde over (F)} 2 equal one.
15. The method of claim 5 wherein the subtracting the filtered down-going component from the extrapolated up-going component attenuates the particle motion sensor noise in the up-going pressure wavefield component with a cosine filter.
16. The method of claim 6 , wherein the subtracting the filtered up-going pressure wavefield component from the extrapolated down-going pressure wavefield component attenuates the particle motion sensor noise in the down-going pressure wavefield component with a cosine filter.
17. The method of claim 5 , wherein the subtracting the filtered down-going pressure wavefield component from the extrapolated up-going pressure wavefield component is obtained by calculating the following expression in the frequency-wavenumber domain:
1
2
(
H
~
-
w
~
G
~
2
)
exp
[
-
ⅈ
k
z
(
z
r
-
z
obs
)
]
-
F
~
1
1
2
(
H
~
+
w
~
G
~
2
)
exp
[
ⅈ
k
z
(
z
r
+
z
obs
)
]
,
where {tilde over (H)} is the hydrophone signal, {tilde over (G)} is the geophone signal, {tilde over (w)} is the amplitude scaling function, k z is a vertical wavenumber, z r is depth of the streamer below the water surface, z obs is depth of the virtual observation surface below the water surface, and {tilde over (F)} 1 is the first matching filter.
18. The method of claim 6 , wherein the subtracting the filtered up-going pressure wavefield component from the extrapolated down-going pressure wavefield component is obtained by calculating the following expression in the frequency-wavenumber domain:
1
2
(
H
~
+
w
~
G
~
2
)
exp
[
ⅈ
k
z
(
z
r
-
z
obs
)
]
-
F
~
2
1
2
(
H
~
-
w
~
G
~
2
)
exp
[
-
ⅈ
k
z
(
z
r
+
z
obs
)
]
,
where {tilde over (H)} is the hydrophone signal, {tilde over (G)} is the geophone signal, {tilde over (w)} is the amplitude scaling function, k z is a vertical wavenumber, z r is depth of the streamer below the water surface, z obs is depth of the virtual observation surface below the water surface, and {tilde over (F)} 2 is the first matching filter.