Method and device for wave fields separation in seismic data
View Patent ↗Apparatus, computer instructions and method for processing seismic data related to a subsurface of a body of water. The method includes receiving input data for a vertical direction and radial direction and/or from a hydrophone, applying a radon transform to the input data, separating primary signals from ghosts signals based on the vertical and radial components, applying an inverse radon transform to determine up-going and down-going wave fields in a time-distance domain, and separating interfering up-going and down-going wave fields that are recorded by the same receivers.
1. A method for ZX separating up-going and down-going wave fields in seismic data related to a subsurface of a body of water, the method comprising:
receiving as input vertical and radial components, wherein the vertical component is related to a particle velocity measured along a depth direction relative to a surface of the water and the radial component is related to the particle velocity measured along a radial direction parallel to the surface of the water and substantially perpendicular to the depth direction and the radial direction and the vertical direction define a plane in which the wave fields propagate;
applying a radon transform to the vertical and radial components to transform the vertical and radial components from a time-distance domain to a tau-apparent slowness domain, wherein the apparent slowness is the sine of an incidence angle divided by a speed of the wave fields in water;
calculating the up-going wave fields as a first combination of the radon transformed vertical and radial components multiplied by a scaling factor;
calculating the down-going wave fields as a second combination of the radon transformed vertical and radial components multiplied by the scaling factor; and
applying an inverse radon transform to the up-going wave fields and the down-going wave fields to obtain up-going wave fields and down-going wave fields in the time-distance domain.
2. The method of claim 1 , wherein the input vertical and radial components are determined from geophone or accelerometer sensors.
3. The method of claim 2 , wherein the geophone or accelerometer sensors are provided under water at a given depth.
4. The method of claim 1 , wherein the up-going wave fields U are given by:
U =s ( V sin(θ)+ R cos(θ)),
where V is the vertical component, R is the radial component, θ is an angle between a line substantially perpendicular to the surface of the water and a direction of propagation of the up-going wave fields U, and s is the scaling factor and it is equal to
1
sin
2
θ
.
5. The method of claim 1 , wherein the up-going wave fields U are given by:
U
=
1
μ
cos
α
(
2
θ
)
+
sin
(
2
θ
)
(
V
sin
θ
+
R
cos
θ
)
,
where μ and α are predetermined parameters.
6. The method of claim 5 , wherein μ and α are parameters selected to avoid singularities at angles θ around 0° and 90° for a predetermined water velocity.
7. The method of claim 1 , wherein the down-going wave fields D are given by:
D=s ( V sin(θ)− R cos(θ)),
where V is the vertical component, R is the radial component, θ is an angle between a line substantially perpendicular to the surface of the water and a direction of propagation of the down-going wave fields D, and s is the scaling factor and it is equal to
1
sin
2
θ
.
8. The method of claim 1 , wherein the down-going wave fields D are given by:
D
=
1
μ
cos
α
(
2
θ
)
+
sin
(
2
θ
)
(
V
sin
θ
-
R
cos
θ
)
,
where μ and α are predetermined parameters.
9. The method of claim 8 , wherein μ and α are parameters selected to avoid singularities at angles θ around 0° and 90° for a given water velocity.
10. The method of claim 1 , further comprising:
calculating a time shift
Δ
t
θ
=
2
z
cos
θ
V
P
for each of the down-going wave fields, where z is a depth of a receiver that records the input data, θ is an angle between a line substantially perpendicular to the surface of the water and a direction of propagation of the down-going wave fields, and V p is a speed in water of the down-going wave fields;
time shifting the down-going wave fields with a corresponding calculated time shift;
adding together the up-going wave fields and the time shifted down-going wave fields; and
generating a final image of the subsurface based on the added wave fields.
11. A method for PZX separating up-going and down-going wave fields in seismic data related to a subsurface of a body of water, the method comprising:
receiving as input vertical and radial components and a hydrophone component, wherein the vertical component is related to a particle velocity measured along a depth direction relative to the surface of the water, the radial component is related to the particle velocity measured along a direction parallel to the surface of the water and substantially perpendicular to the depth direction, the radial direction and the vertical direction define a plane in which the wave fields propagate, and the hydrophone component is related to a pressure measured in the body of water by the hydrophone at a predetermined depth;
applying a radon transform to the vertical and radial components and to the hydrophone component to transform the vertical and radial components and the hydrophone component from a time-distance domain to a tau-apparent slowness domain, wherein the apparent slowness is the sine of an incidence angle divided by a speed of the wave fields in water;
calculating the up-going wave fields as a first combination of the radon transformed vertical and radial components and the radon transformed hydrophone component, the first combination being multiplied by a scaling factor;
calculating the down-going wave fields as a second combination of the radon transformed vertical and radial components and the radon transformed hydrophone component, the second combination being multiplied by the scaling factor; and
applying an inverse radon transform to the up-going wave fields and the down-going wave fields to obtain up-going wave fields and down-going wave fields in the time-distance domain.
12. The method of claim 11 , wherein the input vertical and radial components are determined from geophone or accelerometer sensors.
13. The method of claim 11 , wherein the up-going wave fields U are given by
U
=
0.5
(
V
1
cos
θ
∓
R
sin
θ
1
+
sin
2
θ
+
H
1
1
+
sin
2
θ
)
,
where V is the radon transformed vertical component, R is the radon transformed radial component, H is the radon transformed hydrophone component, and θ is an angle between a line substantially perpendicular to the surface of the water and a direction of propagation of the up-going wave fields U.
14. The method of claim 11 , wherein the down-going wave fields D are given by:
D
=
0.5
(
V
1
cos
θ
-
R
sin
θ
1
+
sin
2
θ
-
H
1
1
+
sin
2
θ
)
,
where V is the radon transformed vertical component, R is the radon transformed radial component, H is the radon transformed hydrophone component, and θ is an angle between a line substantially perpendicular to the surface of the water and a direction of propagation of the down-going wave fields D.
15. The method of claim 11 , where the vertical component, the radial component, and the hydrophone component are measured and the up-going and down-going wave fields are calculated.
16. The method of claim 11 , further comprising:
calculating a time shift
Δ
t
θ
=
2
z
cos
θ
V
P
for each of the down-going wave fields, where z is a depth of a receiver that records the input data, θ is an angle between a line substantially perpendicular to the surface of the water and a direction of propagation of the down-going wave fields, and V p is a speed in water of the down-going wave fields;
time shifting the down-going wave fields with a corresponding calculated time shift;
adding together the up-going wave fields and the time shifted down-going wave fields; and
generating a final image of the subsurface based on the added wave fields.
17. A method for weighted PZX separation of up-going and down-going wave fields in seismic data related to a subsurface of a body of water, the method comprising:
receiving as input vertical and radial components and a hydrophone component, wherein the vertical component is related to a particle velocity measured along a depth direction relative to the surface of the water, the radial component is related to the particle velocity measured along a direction parallel to the surface of the water and substantially perpendicular to the depth direction, the radial direction and the vertical direction define a plane in which the wave fields propagate, and the hydrophone component is related to a pressure measured in the body of water by the hydrophone at a predetermined depth;
applying a radon transform to the vertical and radial components and to the hydrophone component to transform the vertical and radial components and the hydrophone component from a time-distance domain to a tau-apparent slowness domain, wherein the apparent slowness is the sine of an incidence angle divided by a speed of the wave fields in water;
applying a weighting matrix to the radon transformed vertical and radial components and to the radon transformed hydrophone component, the weighting matrix having a parameter β that has a value between 0 and 1;
calculating the up-going wave fields as a first combination of the radon transformed vertical and radial components and the radon transformed hydrophone component, the first combination being multiplied by a scaling factor;
calculating the down-going wave fields as a second combination of the radon transformed vertical and radial components and the radon transformed hydrophone component, the second combination being multiplied by the scaling factor; and
applying an inverse radon transform to the up-going wave fields and the down-going wave fields to obtain up-going wave fields and down-going wave fields in the time-distance domain.
18. The method of claim 17 , wherein the up-going wave fields U are given by
U
=
0.5
(
V
1
cos
θ
+
R
sin
θ
+
H
cos
2
θ
)
,
where V is the radon transformed vertical component, R is the radon transformed radial component, H is the radon transformed hydrophone component, θ is an angle between a line substantially perpendicular to the surface of the water and a direction of propagation of the up-going wave fields U, and β is equal to cos 2 (θ).
19. The method of claim 17 , wherein the down-going wave fields D are given by:
D
=
0.5
(
V
1
cos
θ
-
R
sin
θ
-
H
cos
2
θ
)
,
where V is the radon transformed vertical component, R is the radon transformed radial component, H is the radon transformed hydrophone component, θ is an angle between a line substantially perpendicular to the surface of the water and a direction of propagation of the down-going wave fields D, and β is equal to cos 2 (θ).
20. The method of claim 17 , wherein the weighting matrix is diagonal, and a sum of the squares of the diagonal elements is one.
21. The method of claim 17 , wherein if β=0, the hydrophone weight is zero and the up-going and down-going wave fields take into account only the vertical and radial components and if β=1, the weighting matrix is one and the method is similar to an unweighted PZX method.
22. The method of claim 17 , further comprising:
calculating a time shift
Δ
t
θ
=
2
z
cos
θ
V
P
for each of the down-going wave fields, where z is a depth of a receiver that records the input data, θ is an angle between a line substantially perpendicular to the surface of the water and a direction of propagation of the down-going wave fields, and V p is a speed in water of the down-going wave fields;
time shifting the down-going wave fields with a corresponding calculated time shift;
adding together the up-going wave fields and the time shifted down-going wave fields; and
generating a final image of the subsurface based on the added wave fields.