US 2023/0367027 A1 · METHOD FOR COMBINED UP-DOWN WAVEFIELD SEPARATION AND REDUCING NOISE IN VERTICAL PARTICLE MOTION MEASUREMENTS USING JOINT SPARSITY RECOVERY

Abstract

A method for estimating noise in particle motion seismic recordings and upgoing (deghosted) and downgoing components of ecorded wavefields includes inputting pressure related and particle motion related seismic signals. A sparsity promoting transformation is applied to the input seismic signals. A matrix Ã and column vector {tilde over (b)} are constructed according to the expression: A ~ = ( I I 0 I - I λ ⁢ I ) x ~ = ( d u n ) b ~ = ( A - 1 ⁢ p A - 1 ⁢ z ) , wherein d represents a down-going seismic wavefield, u represents an up-going seismic wavefield, n represents the noise and λ represents a user-chosen scalar to adjust emphasis of the noise. A constrained minimization is solved according to the expression x ~ = arg ⁢ min ⁢ μ ⁢  x ~  1 + 1 2 ⁢  x ~  2 2 st A ~ ⁢ x ~ = b ~ for {tilde over (x)}; wherein μ represents a user-chosen scalar to adjust relative importance of minimization norms. The solved constrained minimization is inverse transformed and reordered back into a domain of the input seismic signals. An output is generated comprising an estimate of the noise contained in the particle motion recording, the downgoing wavefield and the upgoing (deghosted) wavefield.

Claims49

Dependent claims

A method for estimating noise in particle motion seismic sensor recordings resulting from at least one of unwanted vibrations, turbulence in a water column and/or interface waves back-scattered from shallow heterogeneities, the method comprising:

sending as input to a computer seismic signals comprising pressure related signals and particle motion related signals detected at spaced apart locations with reference to position of a seismic energy source in a body of water partly in response to actuation of the seismic energy source and partly in response to noise comprising vibrations and turbulence;
in the computer, applying a sparsity promoting transformation to the input seismic signals;
in the computer, constructing a matrix Ã and column vector {tilde over (b)} according to the expression:
A
~
=
(
I
I
0
I
-
I
λ
⁢
I
)
x
~
=
(
d
u
n
)
b
~
=
(
A
-
1
⁢
p
A
-
1
⁢
z
)
,
wherein d represents a down-going seismic wavefield, u represents an up-going seismic wavefield, n represents the noise and λ represents a user-chosen scalar to adjust emphasis of the noise;
in the computer, solving a constrained minimization according to the expression
x
~
=
arg
⁢
min
⁢
μ
⁢

x
~

1
+
1
2
⁢

x
~

2
2
s
.
t
.
A
~
⁢
x
~
=
b
~
for {tilde over (x)};
wherein μ represents a user-chosen scalar to adjust relative importance of minimization norms;
in the computer, inverse transforming and reordering the solved constrained minimization back into a domain of the input seismic signals;
and
in the computer, generating an output comprising an estimate of the noise in the particle motion related signals.

81 more elements

A method for seismic surveying, comprising:

at selected times, actuating a seismic energy source in a body of water;
detecting seismic signals at a plurality of spaced apart locations in the body of water, the signals comprising pressure related signals and particle motion related partly in response to actuation of the seismic energy source and partly in response to noise comprising at least one of interface waves back-scattered from shallow heterogeneities, vibrations and/or turbulence;
conducting the detected signals to a computer;
in the computer, applying a sparsity promoting transformation to the input seismic signals;
in the computer, constructing a matrix Ã and column vector {tilde over (b)} according to the expression:
A
~
=
(
I
I
0
I
-
I
λ
⁢
I
)
x
~
=
(
d
u
n
)
b
~
=
(
A
-
1
⁢
p
A
-
1
⁢
z
)
,
wherein d represents a down-going seismic wavefield, u represents an up-going seismic wavefield, n represents the noise and λ represents a user-chosen scalar to adjust emphasis of the noise;
in the computer, solving a constrained minimization according to the expression
x
~
=
arg
⁢
min
⁢
μ
⁢

x
~

1
+
1
2
⁢

x
~

2
2
s
.
t
.
A
~
⁢
x
~
=
b
~
for {tilde over (x)};
wherein μ represents a user-chosen scalar to adjust relative importance of minimization norms;
in the computer, inverse transforming and reordering the solved constrained minimization back into a domain of the input seismic signals;
and
in the computer, generating an output comprising an estimate of the noise in the particle motion related signals.

83 more elements

A method for estimating noise in particle motion seismic sensor recordings resulting from interface waves back-scattered from shallow heterogeneities, the method comprising:

sending as input to a computer seismic signals comprising pressure related signals and particle motion related signals detected on a bottom of a body of water in response to actuation of a seismic energy source;
in the computer, applying a sparsity promoting transformation to the input seismic signals;
in the computer, constructing a matrix Ã and column vector {tilde over (b)} according to the expression:
A
~
=
(
I
I
0
I
-
I
λ
⁢
I
)
x
~
=
(
d
u
n
)
b
~
=
(
A
-
1
⁢
p
A
-
1
⁢
z
)
,
wherein d represents a down-going seismic wavefield, u represents an up-going seismic wavefield, n represents the noise and λ represents a user-chosen scalar to adjust emphasis of the noise;
in the computer, solving a constrained minimization according to the expression
x
~
=
arg
⁢
min
⁢
μ
⁢

x
~

1
+
1
2
⁢

x
~

2
2
s
.
t
.
A
~
⁢
x
~
=
b
~
for
⁢
x
~
;
wherein μ represents a user-chosen scalar to adjust relative importance of minimization norms;
in the computer, inverse transforming and reordering the solved constrained minimization back into a domain of the input seismic signals;
and
in the computer, generating an output comprising an estimate of the noise in the particle motion related signals resulting from the interface waves.

85 more elements

A computer program stored in a non-transitory computer readable medium, the program comprising logic operable to cause a programmable computer to perform actions comprising:

accepting as input to the computer seismic signals comprising pressure related signals and particle motion related signals detected at spaced apart locations with reference to position of a seismic energy source in a body of water partly in response to actuation of the seismic energy source and partly in response to noise comprising vibrations and turbulence;
applying a sparsity promoting transformation to the input seismic signals;
constructing a matrix Ã and column vector {tilde over (b)} according to the expression,
A
~
=
(
I
I
0
I
-
I
λ
⁢
I
)
x
~
=
(
d
u
n
)
b
~
=
(
A
-
1
⁢
p
A
-
1
⁢
z
)
,
wherein d represents a down-going seismic wavefield, u represents an up-going seismic wavefield, n represents the noise and λ represents a user-chosen scalar to adjust emphasis of the noise;
solving a constrained minimization according to the expression
x
~
=
arg
⁢
min
⁢
μ
⁢

x
~

1
+
1
2
⁢

x
~

2
2
s
.
t
.
A
~
⁢
x
~
=
b
~
for {tilde over (x)};
wherein μ represents a user-chosen scalar to adjust relative importance of minimization norms;
inverse transforming and reordering the solved constrained minimization back into a domain of the input seismic signals;
and
generating an output comprising an estimate of the noise in the particle motion related signals.

81 more elements

Dependencies are inferred from the claim text.

Method for combined up-down wavefield separation and reducing noise in vertical particle motion measurements using joint sparsity recovery

Life of this patent

Method for combined up-down wavefield separation and reducing noise in vertical particle motion measurements using joint sparsity recovery

Life of this patent

Abstract

Claims49