U.S. patent application number 15/468807 was filed with the patent office on 2020-08-13 for simultaneous wavefield reconstruction and receiver deghosting of seismic streamer data using an l1 inversion.
This patent application is currently assigned to Saudi Arabian Oil Company. The applicant listed for this patent is Saudi Arabian Oil Company. Invention is credited to Yimin Sun, Dirk Jacob Verschuur.
Application Number | 20200257013 15/468807 |
Document ID | 20200257013 / US20200257013 |
Family ID | 1000004986775 |
Filed Date | 2020-08-13 |
Patent Application | download [pdf] |
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United States Patent
Application |
20200257013 |
Kind Code |
A2 |
Sun; Yimin ; et al. |
August 13, 2020 |
SIMULTANEOUS WAVEFIELD RECONSTRUCTION AND RECEIVER DEGHOSTING OF
SEISMIC STREAMER DATA USING AN L1 INVERSION
Abstract
Raw 3D seismic streamer wavefield data is received as a
receiver-ghosted shot gather. The received receiver-ghosted shot
gather shot gather is processed into a normalized form as
normalized data. The normalized data is partitioned into a
plurality of user-defined sub-gathers and processed to generate a
complete receiver-deghosted shot gather. Output of the complete
receiver-deghosted shot gather is initiated.
Inventors: |
Sun; Yimin; (Den Haag,
NL) ; Verschuur; Dirk Jacob; (Alphen aan den Rijn,
NL) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Saudi Arabian Oil Company |
Dhahran |
|
SA |
|
|
Assignee: |
Saudi Arabian Oil Company
Dhahran
SA
|
Prior
Publication: |
|
Document Identifier |
Publication Date |
|
US 20170276818 A1 |
September 28, 2017 |
|
|
Family ID: |
1000004986775 |
Appl. No.: |
15/468807 |
Filed: |
March 24, 2017 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62312934 |
Mar 24, 2016 |
|
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01V 1/368 20130101;
G01V 1/38 20130101; G01V 2210/56 20130101 |
International
Class: |
G01V 1/36 20060101
G01V001/36; G01V 1/38 20060101 G01V001/38 |
Claims
1. A computer-implemented method, comprising: receiving raw 3D
seismic streamer wavefield data as a receiver-ghosted shot gather;
processing the received receiver-ghosted shot gather into a
normalized form as normalized data; partitioning the normalized
data into a plurality of user-defined sub-gathers; processing, by a
computer, each of the plurality of user-defined sub-gathers to
generate a complete receiver-deghosted shot gather; and initiating
output of the complete receiver-deghosted shot gather.
2. The computer-implemented method of claim 1, further comprising
binning the normalized data into a user-defined, dense, regular
grid if the receiver-ghosted shot gather is in an irregular
grid.
3. The computer-implemented method of claim 1, further comprising
determining apex positions of Radon curves associated with a
particular user-defined sub-gather.
4. The computer-implemented method of claim 3, wherein the
determination of the apex positions uses a Redundant, Hybrid,
Apex-Shifted Radon Dictionary such that a function of variable .xi.
is expressed as:
f(.xi.)=.tau.+p.xi.+.SIGMA..sub.n=2.sup..infin..SIGMA..sub.i.sub.n.sub.=A-
.sub.n.sup.B.sup.nq.sub.i.sub.n(.xi.-.xi..sub.i.sub.n).sup.n.
5. The computer-implemented method of claim 4, wherein
.xi..sub.i.sub.n is manually introduced as an additional apex
shift, q.sub.i.sub.n is a corresponding representation, and A.sub.n
and B.sub.n are control parameters.
6. The computer-implemented method of claim 5, further comprising
performing a sparseness inversion using the determined apex
positions and solving for: min x Ax - b 2 s . t . x 1 < t .
##EQU00012##
7. The computer-implemented method of claim 6, further comprising
combining the processed partition data corresponding to each of the
plurality of user-defined, sub-gathers to generate the
receiver-deghosted shot gather.
8. A non-transitory, computer-readable medium storing one or more
instructions executable by a computer system to perform operations
comprising: receiving raw 3D seismic streamer wavefield data as a
receiver-ghosted shot gather; processing the received
receiver-ghosted shot gather into a normalized form as normalized
data; partitioning the normalized data into a plurality of
user-defined sub-gathers; processing each of the plurality of
user-defined sub-gathers to generate a complete receiver-deghosted
shot gather; and initiating output of the complete
receiver-deghosted shot gather.
9. The non-transitory, computer-readable medium of claim 8, further
comprising binning the normalized data into a user-defined, dense,
regular grid if the receiver-ghosted shot gather is in an irregular
grid.
10. The non-transitory, computer-readable medium of claim 8,
further comprising one or more instructions to determine apex
positions of Radon curves associated with a particular
user-defined, sub-gather.
11. The non-transitory, computer-readable medium of claim 10,
wherein the determination of the apex positions uses a Redundant,
Hybrid, Apex-Shifted Radon Dictionary such that a function of
variable .xi. is expressed as:
f(.xi.)=.tau.+p.xi.+.SIGMA..sub.n=2.sup..infin..SIGMA..sub.i.sub.n.sub.=A-
.sub.n.sup.B.sup.nq.sub.i.sub.n(.xi.-.xi..sub.i.sub.n).sup.n.
12. The non-transitory, computer-readable medium of claim 11,
wherein .xi..sub.i.sub.n is manually introduced as an additional
apex shift, q.sub.i.sub.n is a corresponding representation, and
A.sub.n and B.sub.n are control parameters.
13. The non-transitory, computer-readable medium of claim 12,
further comprising one or more instructions to perform a sparseness
inversion using the determined apex positions and solving for: min
x Ax - b 2 s . t . x 1 < t . ##EQU00013##
14. The non-transitory, computer-readable medium of claim 13,
further comprising one or more instructions to combine the
processed partition data corresponding to each of the plurality of
user-defined sub-gathers to generate the receiver-deghosted shot
gather.
15. A computer system, comprising: a computer memory; and a
hardware processor interoperably coupled with the computer memory
and configured to perform operations comprising: receiving raw 3D
seismic streamer wavefield data as a receiver-ghosted shot gather;
processing the received receiver-ghosted shot gather into a
normalized form as normalized data; partitioning the normalized
data into a plurality of user-defined sub-gathers; processing each
of the plurality of user-defined sub-gathers to generate a complete
receiver-deghosted shot gather; and initiating output of the
complete receiver-deghosted shot gather.
16. The computer system of claim 15, further comprising binning the
normalized data into a user-defined, dense, regular grid if the
receiver-ghosted shot gather is in an irregular grid.
17. The computer system of claim 15, further comprising one or more
instructions to determine apex positions of Radon curves associated
with a particular user-defined sub-gather, wherein the
determination of the apex positions uses a Redundant, Hybrid,
Apex-Shifted Radon Dictionary such that a function of variable .xi.
is expressed as:
f(.xi.)=.tau.+p.xi.+.SIGMA..sub.n=2.sup..infin..SIGMA..sub.i.sub.n.sub.=A-
.sub.n.sup.B.sup.nq.sub.i.sub.n(.xi.-.xi..sub.i.sub.n).sup.n.
18. The computer system of claim 17, wherein .xi..sub.i.sub.n
manually introduced as an additional apex shift, q.sub.i.sub.n is a
corresponding representation, and A.sub.n and B.sub.n are control
parameters.
19. The computer system of claim 18, further comprising one or more
instructions to perform a sparseness inversion using the determined
apex positions and solving for: min x Ax - b 2 s . t . x 1 < t .
##EQU00014##
20. The computer system of claim 19, further configured to combine
the processed partition data corresponding to each of the plurality
of user-defined sub-gathers to generate the receiver-deghosted shot
gather.
Description
CROSS REFERENCE TO RELATED APPLICATION(S)
[0001] This application claims the benefit of priority to U.S.
Provisional Application Ser. No. 62/312,934, filed on Mar. 24,
2016, the contents of which are hereby incorporated by
reference.
BACKGROUND
[0002] Receiver deghosting for seismic streamer data is a data
processing challenge in geophysical prospecting. As the air-water
interface is a strong reflector for pressure waves, upgoing seismic
waves are reflected downward at the air-water interface and then
further propagate back into the water where they interfere with an
existing seismic wavefield at the seismic streamer locations. This
effect is referred to as the "Receiver Ghost" effect in marine
streamer data acquisition, causes distortions of both phase and
amplitude, and normally a representative notch can be observed in
the frequency spectrum of the recorded signals.
SUMMARY
[0003] The present disclosure describes simultaneous wavefield
reconstruction and receiver deghosting of three-dimensional (3D)
seismic streamer data using an L1 inversion.
[0004] In an implementation, raw 3D seismic streamer wavefield data
is received as a receiver-ghosted shot gather. The received
receiver-ghosted shot gather shot gather is processed into a
normalized form as normalized data. The normalized data is
partitioned into a plurality of user-defined sub-gathers and
processed to generate a complete receiver-deghosted shot gather.
Output of the complete receiver-deghosted shot gather is
initiated.
[0005] The previously described implementation is implementable
using a computer-implemented method; a non-transitory,
computer-readable medium storing computer-readable instructions to
perform the computer-implemented method; and a computer-implemented
system comprising a computer memory interoperably coupled with a
hardware processor configured to perform the computer-implemented
method/the instructions stored on the non-transitory,
computer-readable medium.
[0006] The subject matter described in this specification can be
implemented in particular implementations so as to realize one or
more of the following advantages. First, the described receiver
deghosting method has no limitations on seismic streamer data
acquisition schemes (for example, horizontal, slanted or curved),
and can be applied on any type of measurements (for example,
pressure or components of particle velocity). Second, a new
redundant, hybrid, apex-shifted Radon dictionary (RHARD) is used as
a basis dictionary for reconstructing a dense up-going wavefield at
the surface of the water. The RHARD makes it possible to ideally
build a complex wavefield (that is, with a mix of linear and curved
events) with a few basic functions; making the use of sparsity
inversion a suitable scheme in the described receiver deghosting
method. Third, the use of the RHARD permits intelligent selection
of equation terms to tradeoff between deghosting functionality and
consumption of computing resources. Fourth, the described receiver
deghosting method provides robust to realistic sparse data
acquisition, and final output is a completely reconstructed and
deghosted wavefield which can be located at arbitrary positions.
Other advantages will be apparent to those of ordinary skill in the
art.
[0007] The details of one or more implementations of the subject
matter of this specification are set forth in the accompanying
drawings and the description. Other features, aspects, and
advantages of the subject matter will become apparent from the
description, the drawings, and the claims.
DESCRIPTION OF DRAWINGS
[0008] FIG. 1 is a diagram illustrating seismic streamer data
acquisition, according to an implementation.
[0009] FIG. 2 is a diagram illustrating a proposed solution to the
reflection illustrated in FIG. 1, according to an
implementation.
[0010] FIG. 3 is an illustration of a tailored three-dimensional
(3D) EAGE/SEG overthrust model, according to an implementation.
[0011] FIG. 4A is a plot illustrating a horizontal streamer
configuration, according to an implementation.
[0012] FIG. 4B is a plot illustrating a denser grid which the
deghosted wavefield is output onto in the horizontal streamer
configuration of FIG. 4A, according to an implementation.
[0013] FIG. 5A is a plot illustrating a quasi-slanted streamer
configuration, according to an implementation.
[0014] FIG. 5B is a plot illustrating a deghosted wavefield output
to a denser grid for the quasi-slanted streamer configuration of
FIG. 5A, according to an implementation.
[0015] FIGS. 6A/6B and 10A/10B are plots illustrating different
crossline sections before and after deghosting and reconstruction
manipulation in the horizontal streamer situation and in the
quasi-slanted streamer situation, respectively, according to an
implementation.
[0016] FIGS. 7A/7B, 8A/8B, 11A/11B, and 12A/12B are plots
illustrating different inline sections before and after receiver
deghosting in both acquisition scenarios, according to an
implementation.
[0017] FIGS. 9A-9C and 13A-13C are plots illustrating trace
comparisons, both before and after execution, of the described
receiver deghosting method, according to an implementation.
[0018] FIG. 14 illustrates a flowchart of an example method for
simultaneous wavefield reconstruction and receiver deghosting of
seismic streamer data using an L1 inversion, according to an
implementation.
[0019] FIG. 15 is a block diagram of an example computer system
1500 used to provide computational functionalities associated with
described algorithms, methods, functions, processes, flows, and
procedures, as described in the instant disclosure, according to an
implementation.
[0020] Like reference numbers and designations in the various
drawings indicate like elements.
DETAILED DESCRIPTION
[0021] The following detailed description describes simultaneous
wavefield reconstruction and receiver deghosting of seismic
streamer data using an L1 inversion and is presented to enable any
person skilled in the art to make and use the disclosed subject
matter in the context of one or more particular implementations.
Various modifications to the disclosed implementations will be
readily apparent to those skilled in the art, and the defined
general principles may be applied to other implementations and
applications without departing from the scope of the disclosure.
The present disclosure is not intended to be limited to the
described or illustrated implementations, but to be accorded the
widest scope consistent with the described principles and
features.
[0022] Receiver deghosting for seismic streamer data is a data
processing challenge in geophysical prospecting. As the air-water
interface is a strong reflector for pressure waves, upgoing seismic
waves are reflected downward at the air-water interface and then
further propagate back into the water where they interfere with an
existing seismic wavefield at the seismic streamer locations. This
effect is referred to as the "Receiver Ghost" effect in marine
streamer data acquisition, causes distortions of both phase and
amplitude, and normally a representative notch can be observed in
the frequency spectrum of the recorded signals. Receiver deghosting
aims at removal of the receiver ghost reflection from the marine
seismic streamer data. With the advancement of marine broadband
data acquisition and processing, it is becoming more crucial to
apply proper three-dimensional (3D) receiver deghosting
technologies to better preserve both bandwidth and resolution in
the final receiver ghost-free signals.
[0023] To date, various receiver deghosting methods have been
proposed, including or variants of: 1) use of Green's theorem as a
general theoretical framework in deghosting; 2) use of a filter in
the F-K domain; 3) use of a twin seismic streamer configuration; 4)
use of both a hydrophone and geophone as a robust deghosting tool
for ocean bottom cable (OBC) data (generally referred to as
PZ-summation, which exploits the unique physical characteristics of
the air-water interface reflected pressure and particle velocity
signals); 5) consideration of multi-component seismic streamer data
as an input for deghosting; 6) .tau.-p inversion; 7) use of an
approximated pressure gradient to remove ghost signals; 8)
application of a deconvolution method to suppress ghost signals; 9)
deghosting based on building mirror data first using ray tracing;
10) consideration of similarity between deghosting and de-blending
to handle deghosting as de-blending; 11) deghosting with over/under
source acquisition; 12) developing an optimal stacking procedure
that can help minimize ghost effects in a final image; 13) use of
joint interpolation-deghosting to achieve genuine 3D deghosting;
and 14) a method to exploit the causality property of the ghost
effect by honoring, as much as possible, wave propagation.
[0024] Regardless of the listed and other receiver ghosting
methods, a robust and physical 3D receiver deghosting utility is
still lacking. Almost all of the proposed methods require dense
wavefield sampling, but in real data acquisition a crossline
interval is normally much larger than an inline interval (for
example, typically, the ratio of the inline interval to the
crossline interval varies between 1:4 and 1:8), which violates this
fundamental assumption. As a trade-off solution, some methods are
configured to work only on densely sampled two-dimensional (2D)
inline data or even to make a bold one-dimensional (1D) propagation
assumption. Other proposed methods involve interpolation explicitly
as an independent operation. However, for real data situations,
interpolation by itself is not a trivial problem, making optimal
application of both steps difficult without propagation of errors.
As a result, for 3D real data, the receiver deghosting challenge
includes: 1) receiver ghost signal removal and 2) data
sparsity.
[0025] Described is a receiver deghosting method capable of
simultaneously deghosting receiver ghost signals and reconstructing
a deghosted wavefield for seismic streamer data. The described
method rigorously honors wave propagation phenomena during the
receiver ghost process in a real 3D sense, and a new redundant,
hybrid, apex-shifted Radon dictionary (RHARD) is used as a basis
dictionary for reconstructing a dense up-going wavefield at the
surface of water. The described receiver deghosting method frames
the receiver deghosting problem as a Lasso problem, with a goal to
minimize a mismatch between actual measurements and a simulated
wavefield with an L1 constraint in the extended Radon space
exploited in order to handle an under-determination challenge in an
inversion. The receiver deghosting algorithm can be demonstrated,
for example, on a realistic tailored 3D EAGE/SEG Overthrust
model.
[0026] Theory and Method
[0027] In marine data acquisition, watercraft towed seismic
streamers, which can be in any form (for example, horizontal,
slanted, or curved), are normally situated from a few meters to
several tens of meters below the surface of the water. As a result,
an incident wavefield will pass the seismic streamers twice--once
upward and once downward after being reflected by the surface of
the water. Certain wavefield frequency components are suppressed or
even cancelled due to the interference of the upgoing and downgoing
seismic wavefields.
[0028] FIG. 1 is a diagram 100 illustrating seismic streamer data
acquisition, according to an implementation. As illustrated seismic
streamer 102 is situated below the surface of the water 104.
Seismic streamer 104 can be in any form (for example, curved,
horizontal, or slanted). Upgoing incident wavefield 106 passes
seismic streamer 102 and reflects of the surface of the water 104
to generate downgoing incident wavefield 108.
[0029] FIG. 2 is a diagram 200 illustrating a proposed solution to
the reflection illustrated in FIG. 1, according to an
implementation. In the described implementation, the desired
upgoing incident wavefield 106 is parameterized at the surface of
the water 104 using dense sampling (dense wavefield) 202 and both
forward propagated with water surface reflection considered (108)
and backwardly propagated incident wavefield 204 to form measured
data. Performing incident wavefield parameterization at the surface
of the water 104 better meets the plane integral surface
requirement in a Rayleigh integral, and realistic seismic streamer
movements due to water currents in field data acquisition become a
reduced challenge.
[0030] Data sparsity must also be considered in seismic streamer
data processing. Normally, the inline direction of the seismic
streamer is a dense data acquisition direction, while the crossline
direction has a much larger interval (for example, the ratio of
inline interval to crossline interval is typically between 1:4 and
1:8--a ratio of 1:4 is used in FIGS. 4A and 5A). As a result, a
final acquired seismic wavefield data is usually aliased in the
crossline direction, which complicates receiver deghosting.
[0031] In order to optimally handle both the receiver deghosting
problem and data sparsity, both challenges should be simultaneously
addressed while rigorously honoring actual physics principles.
Therefore, the aim is finding a densely sampled upgoing wavefield
that, after including the correct physics of a free water surface,
matches measured data at receiver locations. The previously
described receiver ghosting process happens in water, which here is
treated as an isotropic and homogeneous medium. Therefore, acoustic
wave propagation theory is already sufficient, and the Rayleigh
integral is chosen to physically describe the receiver ghosting
effect.
[0032] In order for the Rayleigh integral to function correctly,
two conditions must be fulfilled: 1) the integral surface must be a
plane and 2) wavefield sampling on the plane must be dense. The
dense wavefield sampling requirement is automatically met in the
described method, as a dense wavefield being targeted as the final
solution, but the integral plane condition must be handled with
care in order for the method to be versatile and robust for any
possible streamer shapes, even including feathering effects in real
data acquisition scenarios.
[0033] The surface of the water 104, which, in reality, is roughly
planar, is used as an integral plane, and the dense upgoing
incident wavefield 106 at the surface of the water is treated as a
final solution target. The receiver ghost process can be described
as a summation of the backwardly propagated incident wavefield 204
(from the water surface to the receiver locations) and the water
surface reflected and forwardly propagated (downgoing) incident
wavefield 108 (also from the surface of the water 104 to seismic
receiver locations--not illustrated).
[0034] Mathematically, the receiver ghosting process can be
described as:
b=SP.sup.-y+SP.sup.+Ry=S(P.sup.-+P.sup.+R)y, (1)
where:
[0035] b is a vector containing measured data, y is a dense
wavefield vector at the surface of the water, S is a sub-sampling
matrix corresponding to a real, sparse data acquisition scheme in
both the inline and the crossline directions, P.sup.- and P.sup.+
are one-way wavefield propagation matrices (backward and forward,
respectively) from the surface of the water to pre-defined dense
target locations, and R is a water surface reflectivity matrix.
[0036] The dense wavefield 202 at the surface of the water 104 can
be considered a 3D seismic data cube f(g.sub.x, g.sub.y, t), where
g.sub.x and g.sub.y are x position and y position of the receiver
at the surface, and t is time. This dense wavefield 202 is packed
into the vector y of Equation (1).
[0037] With S (indicating that the measured data is sparse (that
is, dim(b)<dim(y)) in Equation (1)), S(P.sup.-+P.sup.+R) is
generally not mathematically invertible. In order to overcome this
mathematical problem, the receiver deghosting problem is framed
as:
min x Ax - b 2 s . t . x 1 < t , ( 2 ) ##EQU00001##
where:
A=S(P.sup.-+P.sup.+R)D. (3)
[0038] Equation (2) is the Lasso problem in mathematics. In
Equations (2) and (3), x is a vector containing an encoded dense
wavefield at the surface of the water and D is a corresponding
transformation matrix, which ensures that y=Dx. The key to the
success of Equation (2) is to find a suitable dictionary so that
the encoded wavefield x in this dictionary is indeed a sparse
representation of the dense wavefield y at the surface of the
water.
[0039] In the described method, this dense wavefield is encoded per
crossline slice, and every crossline slice has its own particular
representation. Together with the transformation matrix D, this
encoding step can be expressed mathematically as:
y = [ y slice 1 y slice 2 y slice n - 1 y slice n ] = Dx = [ D 2 d
0 0 0 0 D 2 d 0 0 0 0 D 2 d 0 0 0 0 D 2 d ] [ x slice 1 x slice 2 x
slice n - 1 x slice n ] , ( 4 ) ##EQU00002##
where:
[0040] x.sub.slice i is a vector containing wavefield
representations of the crossline slice i of the dense wavefield and
D.sub.2d is the corresponding matrix that transforms the encoded
wavefield x.sub.slice i to wavefield y.sub.slice i. As previously
discussed, in order for x.sub.slice i to be sparse, a redundant
dictionary should be used. An explanation of building an
appropriate redundant dictionary follows.
[0041] The method starts with the known Taylor Series for function
f of variable .xi.:
f ( .xi. ) = n = 0 .infin. f ( n ) ( .xi. 0 ) n ! ( .xi. - .xi. 0 )
n , ( 5 ) ##EQU00003##
where:
[0042] f.sup.(n) is the n.sup.th order derivative function and
.xi..sub.0 is a constant apex value. Equation (5) indicates that
any smooth 2D curve can be described by representations
( f ( 0 ) ( .xi. 0 ) 0 ! , f ( 1 ) ( .xi. 0 ) 1 ! , f ( 2 ) ( .xi.
0 ) 2 ! , , f ( n ) ( .xi. 0 ) n ! , ) ##EQU00004##
with the corresponding dictionary ((.xi.-.xi..sub.0).sup.0,
(.xi.-.xi..sub.0).sup.1, (.xi.-.xi..sub.0).sup.2, . . . ,
(.xi.-.xi..sub.0).sup.n, . . . ) used. However, if Equation (5) is
scrutinized, the dictionary is actually sparse--for every term
containing .xi..sup.n, there is only one building block available,
(.xi.-.xi..sub.0).sup.n, meaning that for any curve with the apex
far away from .xi..sub.0, many terms will be required for an
accurate approximation of f(.xi.).
[0043] Therefore, this kind of sparse dictionary cannot meet the
fundamental requirement for sparse representation, so modifications
to Equation (5) are necessary. As a result, manual introduction of
more apex shifts are made into Equation (5). The modified equation
becomes:
f(.xi.)=.tau.+p.xi.+.SIGMA..sub.n=2.sup..infin..SIGMA..sub.i.sub.n.sub.=-
A.sub.n.sup.B.sup.nq.sub.i.sub.n(.xi.-.xi..sub.i.sub.n).sup.n,
(6)
where:
[0044] the 0.sup.th order and 1.sup.st order term are untouched
compared to Equation (5), but for the n.sup.th order term (n>1),
there are multiple building blocks available,
(.xi.-.xi..sub.i.sub.n).sup.n, where .xi..sub.i.sub.n is a manually
introduced apex and q.sub.i.sub.n is the corresponding
representation. This extra redundancy is controllable in Equation
(6) using control parameters A.sub.n and B.sub.n. Equation (6)
reflects thinking regarding redundancy building, implemented in the
Radon domain as a dictionary and, as previously described, is
referred to as a Redundant, Hybrid, Apex-Shifted Radon Dictionary
(RHARD).
[0045] Using the RHARD, D.sub.2d in Equation (4) can be expressed
as:
D.sub.2d=F.sup.-1O.sup.-1[L.sub.1L.sub.2,1L.sub.2,2 . . .
L.sub.2,n.sub.2L.sub.3,1 . . . L.sub.3,n.sub.3 . . .
L.sub.p,n.sub.p]OF, (7)
where:
L 1 = [ L 1 , .omega. 1 0 0 0 0 L 1 , .omega. 2 0 0 0 0 L 1 ,
.omega. N max - 1 0 0 0 0 L 1 , .omega. N max ] , ( 8 )
##EQU00005##
with:
L 1 , .omega. i = [ e - i .omega. i x 1 p 1 e - i .omega. i x 1 p 2
e - i .omega. i x 1 p M 1 - 1 e - i .omega. i x 1 p M 1 e - i
.omega. i x 2 p 1 e - i .omega. i x 2 p 2 e - i .omega. i x 2 p M 1
- 1 e - i .omega. i x 2 p M 1 e - i .omega. i x N - 1 p 1 e - i
.omega. i x N - 1 p 2 e - i .omega. i x N - 1 p M 1 - 1 e - i
.omega. i x N - 1 p M 1 e - i .omega. i x N p 1 e - i .omega. i x N
p 2 e - i .omega. i x N p M 1 - 1 e - i .omega. i x N p M 1 ] , 1
.ltoreq. i .ltoreq. N max , ( 9 ) ##EQU00006##
and where:
L s , n s = [ L s , n s , .omega. 1 0 0 0 0 L s , n s , .omega. 2 0
0 0 0 L s , n s , N max - 1 0 0 0 0 L s , n s , .omega. N max ] , 2
.ltoreq. s .ltoreq. n p , ( 10 ) ##EQU00007##
with:
L s , n s , .omega. i = [ e - i .omega. i ( x 1 - a n s ) s q 1 e -
i .omega. i ( x 1 - a n s ) s q 2 e - i .omega. i ( x 1 - a n s ) s
q M s - 1 e - i .omega. i ( x 1 - a n s ) s q M s e - i .omega. i (
x 2 - a n s ) s q 1 e - i .omega. i ( x 2 - a n s ) s q 2 e - i
.omega. i ( x 2 - a n s ) s q M s - 1 e - i .omega. i ( x 2 - a n s
) s q M s e - i .omega. i ( x N - 1 - a n s ) s q 1 e - i .omega. i
( x N - 1 - a n s ) s q 2 e - i .omega. i ( x N - 1 - a n s ) s q M
S - 1 e - i .omega. i ( x N - 1 - a n s ) s q M s e - i .omega. i (
x N - a n s ) s q 1 e - i .omega. i ( x N - a n s ) s q 2 e - i
.omega. i ( x N - a n s ) s q M s - 1 e - i .omega. i ( x N - a n s
) s q M s ] , 1 .ltoreq. i .ltoreq. N max , ( 11 ) ##EQU00008##
where:
[0046] .omega..sub.i is the angular frequency.
[0047] In Equation (7), F is a Fourier transformation matrix;
F.sup.-1 is an inverse Fourier transformation matrix; [L.sub.1
L.sub.2,1 L.sub.2,2 . . . L.sub.2,n.sub.2 L.sub.3,1 . . .
L.sub.3,n.sub.3 . . . L.sub.p,n.sub.p] is a RHARD matrix which
reflects the idea of Equation (6), where L.sub.1 is the linear
Radon transformation matrix as detailed in Equations (8) and (9),
and L.sub.p,n.sub.p is the p.sup.th order Radon transformation
matrix with the curve apex at a.sub.n.sub.p, as detailed in
Equations (10) and (11); O is a matrix that reorders the vector so
that the RHARD matrix can be used; O.sup.-1 is an inverse
manipulation corresponding to O which reorders the vector back to
the original order so that the F.sup.-1 matrix can be used.
[0048] Equations (2)-(11) form the backbone of the described
deghosting method, and once x is solved, then either in-situ
deghosted wavefield, SP.sup.-Dx, or deghosted and reconstructed
wavefield, P.sup.-Dx, can be calculated in a straightforward
manner. Further, since the upgoing dense wavefield at the surface
of the water, y=Dx, is available, the wavefield at any position in
the water can be calculated provided that a corresponding
propagation matrix is available.
[0049] Equation (2) is the Lasso problem in Mathematics, for which
various solvers can be used. In one implementation, a spectral
projected gradient (SPGL1) solver can be is used. In other
implementations, other solvers (for example, public, proprietary,
or commercial) can be used.
[0050] In order to achieve satisfactory results, it is crucial to
build P.sup.- and P.sup.+ in Equation (3) suitably. Theoretically
speaking, in the Rayleigh theory, the integral aperture should be
infinite, but in reality this requirement is not practical. As a
result, P.sup.- and P.sup.+ must take this limited aperture effect
into consideration, and different choices with respect to these two
matrices bring slightly different results. Experimental evidence
suggests optimally to use smooth, weighted, least-squares
optimized, one-way wavefield propagation operators to build P.sup.-
and P.sup.3+. An advantage of using limited aperture is that the
wavefield calculation can be decoupled: for a wavefield within a
certain area, only limited integral area in the integral plane
needs to be considered. Therefore, in the described calculations,
the complete solution area is divided into overlapping smaller
spatial-time windows which are separately processed. All the
results of the separate processing are averaged and spliced
together to form a final result. Two benefits can be obtained from
this approach: 1) although the complete solution area may be large,
a sub-area can be configured to be of a size to be handled with
limited computational resources and 2) due to edge effects of the
integral aperture, computational artifacts exist but can be largely
suppressed using averaging since the sub-areas overlap.
[0051] R in Equation (3) should also be handled with care. Although
in most reported methods R is always assumed to be -I, in reality
its behavior is much more complex since the surface of the water
cannot be perfectly planar. Fluctuations of the surface of the
water mainly influence reflection behavior of high-frequency
components. Tuning the value of R can provide better results in
realistic field data situations, especially for high frequency
signals. Note that R is set to -I in the following example.
[0052] FIG. 3 is an illustration of a tailored 3D EAGE/SEG
overthrust model 300, according to an implementation. An example
using a tailored 3D European Association of Geoscientists
(EAGE)/Society of exploration Geophysicists (SEG) overthrust model
is now described. To generate the tailored overthrust model, a 500m
thick water layer 302 is placed on top of a base EAGE/SEG
overthrust model. A subset of this modified base model (crossline
direction 304 (X direction) between 10 km and 11.5 km, inline
direction 306 (Y direction) between 7.5 km and 14.5 km, and depth
308 (Z direction) between 0 and 5 km) is selected as the tailored
SEG overthrust model 300. The velocity (m/s) 310 indicates the
medium velocity of this tailored model. In this implementation, a
3D acoustic finite-difference time-domain (FDTD) simulation package
is used as a forward modelling engine.
[0053] A corresponding density model is also built based upon this
tailored velocity model, and density values are connected with the
velocity values using the Gardner Equation relating P-wave velocity
to bulk density (except for the water layer, where the density
value is 1000 kg/m.sup.3):
.rho.=.alpha.V.sub.P.sup..beta., (12)
where:
[0054] .rho. is bulk density given in kg/m.sup.3, V.sub.P is P-wave
velocity given in m/s, and .alpha. and .beta. are empirically
derived constants that depend on geology.
[0055] Regarding the data acquisition schemes, two situations are
considered: 1) a horizontal streamer situation and 2) a slanted
streamer situation (as illustrated in FIG. 2). In both situations,
the source wavelet is a Ricker wavelet with the dominant frequency
set at 20 Hz, and the source position 402 is located at (crossline
(X) position (m) 404 at 750m, inline (Y) position (m) 406 at 750m,
and depth (m) 408 at 5m). The maximum frequency for the inversion
is set at 75 Hz, so the inversion is band limited. The streamer
data acquisition covers an area of 500m (X direction, between 500m
and 1000m) by 6 km (Y direction, between 500m and 6500m). The
inline (Y direction) interval is set at 12.5m, and the crossline (X
direction) interval is set at 50m.
[0056] FIG. 4A is a plot 400a illustrating a horizontal streamer
configuration, according to an implementation. The red star
designates the source position, (crossline (X) position (m) 402 at
750m, inline (Y) position (m) 404 at 750m, and depth (m) 406 at
5m). Inline (Y direction) interval is 12.5m, and crossline (X
direction) interval is 50m. Graphed points represent receiver
locations and illustrate where a wavefield was sampled. For the
horizontal streamer situation, the streamer depth is set at
30m.
[0057] FIG. 4B is a plot 400b illustrating a denser grid which the
deghosted wavefield is output onto in the horizontal streamer
configuration of FIG. 4A, according to an implementation. After
reconstruction of the deghosted wavefield, both inline interval and
crossline interval are 12.5m, and the receiver depth remains at
30m. Graphed points represent receiver locations and illustrate
where a wavefield was sampled.
[0058] FIG. 5A is a plot 500a illustrating a quasi-slanted streamer
configuration, according to an implementation. Graphed points
represent receiver locations and illustrate where a wavefield was
sampled. Inline (Y direction) interval is 12.5m, and crossline (X
direction) interval is 50m. For the slanted streamer situation, due
to the fact that FDTD is the simulation method, continuously
varying depth is not possible, so as a trade-off solution a
quasi-slanted data-acquisition scheme is used as shown in FIG. 5A.
In this quasi-slanted data-acquisition scheme, the crossline
direction receivers are all at the same depth, while in the inline
direction the receiver depth within the initial 500m is set at 25m,
and after every 1 km the receiver depth is further increased by
2.5m, until the receiver depth reaches 40m at the boundary of the
data acquisition area. After reconstruction of the deghosted
wavefield, both inline interval and crossline interval are 12.5m,
and the receiver depth geometry remains the same as before the
reconstruction as shown in FIG. 5B. Before and after
reconstruction, the receiver depth geometry follows the same design
rules.
[0059] In order to suppress computation artifacts, in one
particular implementation, thirty-four overlapped spatial windows
are used to carry out the described deghosting procedure on data:
in the time direction the whole window being taken; x [500m,
1000m], y [500+200*im, 500+200*i+500m], 0.ltoreq.i.ltoreq.27, and y
[500*im, 500*(i+1)m], i=1, 3, 5, 7, 9, 11. The final deghosted
result is the arithmetic average of all the spatial windows. A
square Rayleigh integral aperture with side length of 250m is
used.
[0060] In Equation (7), the linear Radon term plus three parabolic
Radon terms are used, and, in an implementation, apex value
selection can be as follows: for each spatial window, a sparse
central crossline image is selected; the parabolic Radon
contribution is calculated with the apex scanned through the whole
crossline range, x [500m, 1000m], and an apex value is selected
that leads to the smallest residual on this crossline image. After
the apex value is singled out, the residual image is used as a new
crossline image and the process repeated until all needed apex
values have been selected. The apex value selection process
reflects the known concept of Matching Pursuits.
[0061] FIG. 5B is a plot 500b illustrating a denser grid which the
deghosted wavefield is output onto in the quasi-slanted streamer
configuration of FIG. 5A, according to an implementation. Graphed
points represent receiver locations and illustrate where a
wavefield was sampled.
[0062] FIGS. 6A/6B and 10A/10B are plots (600a/600b and
1000a/1000b, respectively) illustrating different crossline
sections before and after deghosting and reconstruction
manipulation in the horizontal streamer situation and in the
quasi-slanted streamer situation, respectively, according to an
implementation.
[0063] As illustrated, FIG. 6A illustrates 500m crossline sections
602a-602f (at 1 km inline increments and 4 s time duration) of a
ghosted wavefield in the horizontal streamer situation with the
previously described, tailored 3D EAGE/SEG overthrust model. FIG.
6B illustrates corresponding crossline sections of FIG. 6A of the
deghosted and reconstructed wavefield in the horizontal streamer
situation using the described receiver deghosting method.
[0064] Similar to FIG. 6A, FIG. 10A illustrates 500m crossline
sections 1002a-1002f (at 1 km inline increments and 4 s time
duration) of a ghosted wavefield in the quasi-slanted streamer
situation with the previously described, tailored 3D EAGE/SEG
overthrust model. Likewise, FIG. 6B, FIG. 10B illustrates
corresponding crossline sections of FIG. 10A of the deghosted and
reconstructed wavefield in the quasi-slanted streamer situation
using the described receiver deghosting method. Wavefield
reconstruction effects can be observed in both FIG. 6B and FIG. 10B
as events are continuous in the X direction.
[0065] FIGS. 7A/7B, 8A/8B, 11A/11B, and 12A/12B are plots
(700a/700b, 800a/800b, 1100a/1100b, and 1200a/1200b, respectively)
illustrating different inline sections before and after deghosting
in both acquisition scenarios, according to an implementation. FIG.
7A illustrates a single inline section 702a (x=750m and of 4s time
duration) of the ghosted wavefield in the horizontal streamer
situation with the previously described, tailored 3D EAGE/SEG
overthrust model. FIG. 7B illustrates a corresponding deghosted
inline section 702b using the described receiver deghosting method,
and it can be observed at 704b that receiver ghosting has been
removed when compared to the corresponding portion of FIG. 7A.
[0066] FIG. 8A illustrates a single inline section 802a (x=650m and
of 4 s time duration) of the ghosted wavefield in the horizontal
streamer situation with the previously described, tailored 3D
EAGE/SEG overthrust model. FIG. 8B illustrates a corresponding
deghosted inline section 802b using the described receiver
deghosting method, and it can be observed at 804b that receiver
ghosting has been removed when compared to the corresponding
portion of FIG. 8A.
[0067] FIG. 11A illustrates a single inline section 1102a (x=750m
and of 4 s time duration) of the ghosted wavefield in the
quasi-slanted streamer situation with the previously described,
tailored 3D EAGE/SEG overthrust model. FIG. 11B illustrates a
corresponding deghosted inline section 1102b using the described
receiver deghosting method, and it can be observed at 1104b that
receiver ghosting has been removed when compared to the
corresponding portion of FIG. 11A.
[0068] FIG. 12B illustrates a graph 1200b of a corresponding
in-situ deghosted inline section, according to an implementation.
FIG. 12A illustrates a single inline section 1202a (x=650m and of 4
s time duration) of the ghosted wavefield in the quasi-slanted
streamer situation with the previously described, tailored 3D
EAGE/SEG overthrust model. FIG. 12B illustrates a corresponding
deghosted inline section 1202b using the described receiver
deghosting method, and it can be observed at 1204b that receiver
ghosting has been removed when compared to the corresponding
portion of FIG. 12A.
[0069] FIGS. 9A-9C and 13A-13C are plots (900a-900c and
1300a-1300c, respectively) illustrating comparison of seismic
traces (amplitude vs. time (s)), both before and after execution,
of the described receiver deghosting method, according to an
implementation. FIGS. 9A-9C represent the described horizontal
streamer case. FIGS. 13A-13C represent the described quasi-slanted
streamer case. Amplitude is in Arbitrary Unit (AU) as the data has
been normalized. The illustrated results demonstrate the
effectiveness of the described receiver deghosting method. While
crossline wavefield reconstruction capability is demonstrated in
FIGS. 6A-6B and 10A-10B, FIGS. 9A-9C and 13A-13C demonstrate the
deghosting effect (indicated by arrows) and that better event
recognition is possible (indicated by circles).
[0070] FIG. 9A illustrates comparison of seismic traces 902a
(ghosted) and 904a (deghosted) in the horizontal streamer situation
with the previously described, tailored 3D EAGE/SEG overthrust
model and the trace located at x=1050m and y=750m. It can be
observed that receiver ghosting has been removed in corresponding
portions of the deghosted wavefield 904a when compared to the
ghosted wavefield 902a.
[0071] FIG. 9B illustrates comparison of seismic traces 902b
(ghosted) and 904b (deghosted) in the horizontal streamer situation
with the previously described, tailored 3D EAGE/SEG overthrust
model and the trace located at x=3000m and y=650m. It can be
observed that receiver ghosting has been removed in corresponding
portions of the deghosted wavefield 904b when compared to the
ghosted wavefield 902b.
[0072] FIG. 9C illustrates comparison of seismic traces 902c
(ghosted) and 904c (deghosted) in the horizontal streamer situation
with the previously described, tailored 3D EAGE/SEG overthrust
model and the trace located at x=5000m and y=950m. It can be
observed that receiver ghosting has been removed in corresponding
portions of the deghosted wavefield 904c when compared to the
ghosted wavefield 902c. Also, it can be observed that events 908c
and 912c are better defined in the deghosted wavefield 904c when
compared to the corresponding events 906c and 910c, respectively,
of the ghosted wavefield 902c.
[0073] FIG. 13A illustrates comparison of seismic traces 1302a
(ghosted) and 1304a (deghosted) in the quasi-slanted streamer
situation with the previously described, tailored 3D EAGE/SEG
overthrust model and the trace located at x=1050m and y=750m. It
can be observed that receiver ghosting has been removed in
corresponding portions of the deghosted wavefield 1304a when
compared to the ghosted wavefield 1302a.
[0074] FIG. 13B illustrates comparison of seismic traces 1302b
(ghosted) and 1304b (deghosted) in the quasi-slanted streamer
situation with the previously described, tailored 3D EAGE/SEG
overthrust model and the trace located at x=3000m and y=650m. It
can be observed that receiver ghosting has been removed in
corresponding portions of the deghosted wavefield 1304b when
compared to the ghosted wavefield 1302b.
[0075] FIG. 13C illustrates comparison of seismic traces 1302c
(ghosted) and 1304c (deghosted) in the quasi-slanted streamer
situation with the previously described, tailored 3D EAGE/SEG
overthrust model and the trace located at x=5000m and y=950m. It
can be observed that receiver ghosting has been removed in
corresponding portions of the deghosted wavefield 1304c when
compared to the ghosted wavefield 1302c. Also, it can be observed
that events 1308c and 1312c are better defined in the deghosted
wavefield 1304c when compared to the corresponding events 1306c and
1310c, respectively, of the ghosted wavefield 1302c.
[0076] FIG. 14 is a flowchart of an example method 1400 for
simultaneous wavefield reconstruction and receiver deghosting of
seismic streamer data using an L1 inversion, according to an
implementation. For clarity of presentation, the description that
follows generally describes methods 1400 in the context of the
other FIGS. in this description. However, it will be understood
that method 1400 may be performed, for example, by any suitable
system, environment, software, and hardware, or a combination of
systems, environments, software, and hardware as appropriate. In
some implementations, various steps of method 1400 can be run in
parallel, in combination, in loops, or in any order.
[0077] At 1402, 3D ghosted raw seismic streamer wavefield data is
received (for example, using push, pull, or both push and pull
operations). In typical implementations, the raw seismic streamer
wavefield data is a receiver-ghosted shot gather. From 1402, method
1400 proceeds to 1404.
[0078] At 1404, the received 3D receiver-ghosted shot gather is
normalized and regularized. For example, if the raw data is
structured in an irregular grid, each trace can be binned to a
user-defined dense regular grid for further processing.
Normalization operations can be based on any criteria consistent
with this disclosure (for example, amplitude normalization by the
total energy of the shot gather). From 1404, method 1400 proceeds
to 1406.
[0079] At 1406, the regularized data is partitioned for processing.
For example, the normalized data can be partitioned into a
plurality of user-defined, overlapping sub-gathers based on time,
geographic location, or other criteria. The partition method can be
influenced by signal-to-noise ratio in the regularized data, but
typically, the complete crossline range as a whole is used in the
user-defined partition scheme. From 1406, method 1400 proceeds to
1408.
[0080] At 1408, a determination is made whether there are remaining
partitions to process. If there are no remaining partitions to
process, method 1400 proceeds back to 1416. If there are remaining
partitions to process, method 1400 proceeds to process a remaining
partition using the described simultaneous wavefield reconstruction
and receiver deghosting method. From 1408, method 1400 proceeds to
1410.
[0081] At 1410, apex positions are determined for the current
partition to decide where the apexes, .xi..sub.i.sub.n, of
different Radon curves should be using Equation (6). From 1410,
method 1400 proceeds to 1412.
[0082] At 1412, a sparseness inversion is performed on the current
partition using Equation (2). From 1412, method 1400 proceeds to
1414.
[0083] At 1414, the processed partition is stored for output. For
example, the processed partition can be stored in RAM memory or a
database. From 1414, method 1400 proceeds back to 1408 to determine
whether there are remaining partitions to process.
[0084] At 1416, the processed partition data is recovered from
storage and combined to form a receiver-deghosted shot gather. For
example, in an implementation, the processed partition data can be
mathematically averaged with a user-defined weight function (for
example, a trapezoidal weight function) and combined to form the
complete receiver-deghosted shot gather. From 1416, method 1400
proceeds to 1418.
[0085] At 1418, output of the receiver-deghosted shot gather is
initiated. For example, the receiver-deghosted shot gather can be
output as a data set for storage in a computer data store or
displayed on a graphical user interface. After 1418, method 1400
stops.
[0086] FIG. 15 is a block diagram of an example computer system
1500 used to provide computational functionalities associated with
described algorithms, methods, functions, processes, flows, and
procedures, as described in the instant disclosure, according to an
implementation. The illustrated computer 1502 is intended to
encompass any computing device such as a server, desktop computer,
laptop/notebook computer, wireless data port, smart phone, personal
data assistant (PDA), tablet computing device, one or more
processors within these devices, or any other suitable processing
device, including physical or virtual instances (or both) of the
computing device. Additionally, the computer 1502 may comprise a
computer that includes an input device, such as a keypad, keyboard,
touch screen, or other device that can accept user information, and
an output device that conveys information associated with the
operation of the computer 1502, including digital data, visual, or
audio information (or a combination of information), or a graphical
user interface (GUI).
[0087] The computer 1502 can serve in a role as a client, network
component, a server, a database or other persistency, or any other
component (or a combination of roles) of a computer system for
performing the subject matter described in the instant disclosure.
The illustrated computer 1502 is communicably coupled with a
network 1530. In some implementations, one or more components of
the computer 1502 may be configured to operate within environments,
including cloud-computing-based, local, global, or other
environment (or a combination of environments).
[0088] At a high level, the computer 1502 is an electronic
computing device operable to receive, transmit, process, store, or
manage data and information associated with the described subject
matter. According to some implementations, the computer 1502 may
also include or be communicably coupled with an application server,
e-mail server, web server, caching server, streaming data server,
or other server (or a combination of servers).
[0089] The computer 1502 can receive requests over network 1530
from a client application (for example, executing on another
computer 1502) and respond to the received requests by processing
the received requests using an appropriate software application(s).
In addition, requests may also be sent to the computer 1502 from
internal users (for example, from a command console or by other
appropriate access method), external or third-parties, other
automated applications, as well as any other appropriate entities,
individuals, systems, or computers.
[0090] Each of the components of the computer 1502 can communicate
using a system bus 1503. In some implementations, any or all of the
components of the computer 1502, hardware or software (or a
combination of both hardware and software), may interface with each
other or the interface 1504 (or a combination of both), over the
system bus 1503 using an application programming interface (API)
1512 or a service layer 1513 (or a combination of the API 1512 and
service layer 1513). The API 1512 may include specifications for
routines, data structures, and object classes. The API 1512 may be
either computer-language independent or dependent and refer to a
complete interface, a single function, or even a set of APIs. The
service layer 1513 provides software services to the computer 1502
or other components (whether or not illustrated) that are
communicably coupled to the computer 1502. The functionality of the
computer 1502 may be accessible for all service consumers using
this service layer. Software services, such as those provided by
the service layer 1513, provide reusable, defined functionalities
through a defined interface. For example, the interface may be
software written in JAVA, C++, or other suitable language providing
data in extensible markup language (XML) format or other suitable
format. While illustrated as an integrated component of the
computer 1502, alternative implementations may illustrate the API
1512 or the service layer 1513 as stand-alone components in
relation to other components of the computer 1502 or other
components (whether or not illustrated) that are communicably
coupled to the computer 1502. Moreover, any or all parts of the API
1512 or the service layer 1513 may be implemented as child or
sub-modules of another software module, enterprise application, or
hardware module without departing from the scope of this
disclosure.
[0091] The computer 1502 includes an interface 1504. Although
illustrated as a single interface 1504 in FIG. 15, two or more
interfaces 1504 may be used according to particular needs, desires,
or particular implementations of the computer 1502. The interface
1504 is used by the computer 1502 for communicating with other
systems that are connected to the network 1530 (whether illustrated
or not) in a distributed environment. Generally, the interface 1504
comprises logic encoded in software or hardware (or a combination
of software and hardware) and is operable to communicate with the
network 1530. More specifically, the interface 1504 may comprise
software supporting one or more communication protocols associated
with communications such that the network 1530 or interface's
hardware is operable to communicate physical signals within and
outside of the illustrated computer 1502.
[0092] The computer 1502 includes a processor 1505. Although
illustrated as a single processor 1505 in FIG. 15, two or more
processors may be used according to particular needs, desires, or
particular implementations of the computer 1502. Generally, the
processor 1505 executes instructions and manipulates data to
perform the operations of the computer 1502 and any algorithms,
methods, functions, processes, flows, and procedures as described
in the instant disclosure.
[0093] The computer 1502 also includes a database 1506 that can
hold data for the computer 1502 or other components (or a
combination of both) that can be connected to the network 1530
(whether illustrated or not). For example, database 1506 can be an
in-memory, conventional, or other type of database storing data
consistent with this disclosure. In some implementations, database
1506 can be a combination of two or more different database types
(for example, a hybrid in-memory and conventional database)
according to particular needs, desires, or particular
implementations of the computer 1502 and the described
functionality. Although illustrated as a single database 1506 in
FIG. 15, two or more databases (of the same or combination of
types) can be used according to particular needs, desires, or
particular implementations of the computer 1502 and the described
functionality. While database 1506 is illustrated as an integral
component of the computer 1502, in alternative implementations,
database 1506 can be external to the computer 1502. As illustrated,
the database 1506 holds the previously described received
receiver-ghosted shot gather 1516, partition data 1518, and
receiver-deghosted shot gather 1520.
[0094] The computer 1502 also includes a memory 1507 that can hold
data for the computer 1502 or other components (or a combination of
both) that can be connected to the network 1530 (whether
illustrated or not). For example, memory 1507 can be random access
memory (RAM), read-only memory (ROM), optical, magnetic, and the
like, storing data consistent with this disclosure. In some
implementations, memory 1507 can be a combination of two or more
different types of memory (for example, a combination of RAM and
magnetic storage) according to particular needs, desires, or
particular implementations of the computer 1502 and the described
functionality. Although illustrated as a single memory 1507 in FIG.
15, two or more memories 1507 (of the same or combination of types)
can be used according to particular needs, desires, or particular
implementations of the computer 1502 and the described
functionality. While memory 1507 is illustrated as an integral
component of the computer 1502, in alternative implementations,
memory 1507 can be external to the computer 1502.
[0095] The application 1508 is an algorithmic software engine
providing functionality according to particular needs, desires, or
particular implementations of the computer 1502, particularly with
respect to functionality described in this disclosure. For example,
application 1508 can serve as one or more components, modules, or
applications. Further, although illustrated as a single application
1508, the application 1508 may be implemented as multiple
applications 1508 on the computer 1502. In addition, although
illustrated as integral to the computer 1502, in alternative
implementations, the application 1508 can be external to the
computer 1502.
[0096] The computer 1502 can also include a power supply 1514. The
power supply 1514 can include a rechargeable or non-rechargeable
battery that can be configured to be either user- or
non-user-replaceable. In some implementations, the power supply
1514 can include power-conversion or management circuits (including
recharging, standby, or other power management functionality). In
some implementations, the power-supply 1514 can include a power
plug to allow the computer 1502 to be plugged into a wall socket or
other power source to, for example, power the computer 1502 or
recharge a rechargeable battery.
[0097] There may be any number of computers 1502 associated with,
or external to, a computer system containing computer 1502, each
computer 1502 communicating over network 1530. Further, the term
"client," "user," and other appropriate terminology may be used
interchangeably, as appropriate, without departing from the scope
of this disclosure. Moreover, this disclosure contemplates that
many users may use one computer 1502, or that one user may use
multiple computers 1502.
[0098] Described implementations of the subject matter can include
one or more features, alone or in combination.
[0099] For example, in a first implementation, a
computer-implemented method, comprising: receiving raw 3D seismic
streamer wavefield data as a receiver-ghosted shot gather;
processing the received receiver-ghosted shot gather into a
normalized form as normalized data; partitioning the normalized
data into a plurality of user-defined sub-gathers; processing, by a
computer, each of the plurality of user-defined sub-gathers to
generate a complete receiver-deghosted shot gather; and initiating
output of the complete receiver-deghosted shot gather.
[0100] The foregoing and other described implementations can each,
optionally, include one or more of the following features:
[0101] A first feature, combinable with any of the following
features, further comprising binning the normalized data into a
user-defined, dense, regular grid if the receiver-ghosted shot
gather is in an irregular grid.
[0102] A second feature, combinable with any of the previous or
following features, further comprising determining apex positions
of Radon curves associated with a particular user-defined
sub-gather.
[0103] A third feature, combinable with any of the previous or
following features, wherein the determination of the apex positions
uses a Redundant, Hybrid, Apex-Shifted Radon Dictionary such that a
function of variable .xi. is expressed as:
f(.xi.)=.tau.+p.xi.+.SIGMA..sub.n=2.sup..infin..SIGMA..sub.i.sub.n.sub.=-
A.sub.n.sup.B.sup.nq.sub.i.sub.n(.xi.-.xi..sub.i.sub.n).sup.n.
[0104] A fourth feature, combinable with any of the previous or
following features, wherein .xi..sub.i.sub.n is manually introduced
as an additional apex shift, q.sub.i.sub.n is a corresponding
representation, and A.sub.n and B.sub.n are control parameters.
[0105] A fifth feature, combinable with any of the previous or
following features, further comprising performing a sparseness
inversion using the determined apex positions and solving for:
min x Ax - b 2 s . t . x 1 < t . ##EQU00009##
[0106] A sixth feature, combinable with any of the previous or
following features, further comprising combining the processed
partition data corresponding to each of the plurality of
user-defined, sub-gathers to generate the receiver-deghosted shot
gather.
[0107] In a second implementation, a non-transitory,
computer-readable medium storing one or more instructions
executable by a computer system to perform operations comprising:
receiving raw 3D seismic streamer wavefield data as a
receiver-ghosted shot gather; processing the received
receiver-ghosted shot gather into a normalized form as normalized
data; partitioning the normalized data into a plurality of
user-defined sub-gathers; processing each of the plurality of
user-defined sub-gathers to generate a complete receiver-deghosted
shot gather; and initiating output of the complete
receiver-deghosted shot gather.
[0108] The foregoing and other described implementations can each,
optionally, include one or more of the following features:
[0109] A first feature, combinable with any of the following
features, further comprising binning the normalized data into a
user-defined, dense, regular grid if the receiver-ghosted shot
gather is in an irregular grid.
[0110] A second feature, combinable with any of the previous or
following features, further comprising one or more instructions to
determine apex positions of Radon curves associated with a
particular user-defined, sub-gather.
[0111] A third feature, combinable with any of the previous or
following features, wherein the determination of the apex positions
uses a Redundant, Hybrid, Apex-Shifted Radon Dictionary such that a
function of variable .xi. is expressed as:
f(.xi.)=.tau.+p.xi.+.SIGMA..sub.n=2.sup..infin..SIGMA..sub.i.sub.n.sub.=-
A.sub.n.sup.B.sup.nq.sub.i.sub.n(.xi.-.xi..sub.i.sub.n).sup.n.
[0112] A fourth feature, combinable with any of the previous or
following features, wherein .xi..sub.i.sub.n is manually introduced
as an additional apex shift, q.sub.i.sub.n is a corresponding
representation, and A.sub.n and B.sub.n are control parameters.
[0113] A fifth feature, combinable with any of the previous or
following features, further comprising one or more instructions to
perform a sparseness inversion using the determined apex positions
and solving for:
min x Ax - b 2 s . t . x 1 < t . ##EQU00010##
[0114] A sixth feature, combinable with any of the previous or
following features, further comprising one or more instructions to
combine the processed partition data corresponding to each of the
plurality of user-defined sub-gathers to generate the
receiver-deghosted shot gather.
[0115] In a third implementation, a computer system, comprising: a
computer memory; and a hardware processor interoperably coupled
with the computer memory and configured to perform operations
comprising: receiving raw 3D seismic streamer wavefield data as a
receiver-ghosted shot gather; processing the received
receiver-ghosted shot gather into a normalized form as normalized
data; partitioning the normalized data into a plurality of
user-defined sub-gathers; processing each of the plurality of
user-defined sub-gathers to generate a complete receiver-deghosted
shot gather; and initiating output of the complete
receiver-deghosted shot gather.
[0116] The foregoing and other described implementations can each,
optionally, include one or more of the following features:
[0117] A first feature, combinable with any of the following
features, further comprising binning the normalized data into a
user-defined, dense, regular grid if the receiver-ghosted shot
gather is in an irregular grid.
[0118] A second feature, combinable with any of the previous or
following features, further comprising one or more instructions to
determine apex positions of Radon curves associated with a
particular user-defined sub-gather.
[0119] A third feature, combinable with any of the previous or
following features, wherein the determination of the apex positions
uses a Redundant, Hybrid, Apex-Shifted Radon Dictionary such that a
function of variable .xi. is expressed as:
f(.xi.)=.SIGMA.+p.xi.+.SIGMA..sub.n=2.sup..infin..SIGMA..sub.i.sub.n.sub-
.=A.sub.n.sup.B.sup.nq.sub.i.sub.n(.xi.-.xi..sub.i.sub.n).sup.n.
[0120] A fourth feature, combinable with any of the previous or
following features, wherein .xi..sub.i.sub.n is manually introduced
as an additional apex shift, q.sub.i.sub.n is a corresponding
representation, and A.sub.n and B.sub.n are control parameters.
[0121] A fifth feature, combinable with any of the previous or
following features, further comprising one or more instructions to
perform a sparseness inversion using the determined apex positions
and solving for:
min x Ax - b 2 s . t . x 1 < t . ##EQU00011##
[0122] A sixth feature, combinable with any of the previous or
following features, further configured to combine the processed
partition data corresponding to each of the plurality of
user-defined sub-gathers to generate the receiver-deghosted shot
gather.
[0123] Implementations of the subject matter and the functional
operations described in this specification can be implemented in
digital electronic circuitry, in tangibly embodied computer
software or firmware, in computer hardware, including the
structures disclosed in this specification and their structural
equivalents, or in combinations of one or more of them.
Implementations of the subject matter described in this
specification can be implemented as one or more computer programs,
that is, one or more modules of computer program instructions
encoded on a tangible, non-transitory, computer-readable
computer-storage medium for execution by, or to control the
operation of, data processing apparatus. Alternatively, or
additionally, the program instructions can be encoded in/on an
artificially generated propagated signal, for example, a
machine-generated electrical, optical, or electromagnetic signal
that is generated to encode information for transmission to
suitable receiver apparatus for execution by a data processing
apparatus. The computer-storage medium can be a machine-readable
storage device, a machine-readable storage substrate, a random or
serial access memory device, or a combination of computer-storage
mediums.
[0124] The term "real-time," "real time," "realtime," "real (fast)
time (RFT)," "near(ly) real-time (NRT)," "quasi real-time," or
similar terms (as understood by one of ordinary skill in the art),
means that an action and a response are temporally proximate such
that an individual perceives the action and the response occurring
substantially simultaneously. For example, the time difference for
a response to display (or for an initiation of a display) of data
following the individual's action to access the data may be less
than 1 ms, less than 1 sec., or less than 5 secs. While the
requested data need not be displayed (or initiated for display)
instantaneously, it is displayed (or initiated for display) without
any intentional delay, taking into account processing limitations
of a described computing system and time required to, for example,
gather, accurately measure, analyze, process, store, or transmit
the data.
[0125] The terms "data processing apparatus," "computer," or
"electronic computer device" (or equivalent as understood by one of
ordinary skill in the art) refer to data processing hardware and
encompass all kinds of apparatus, devices, and machines for
processing data, including by way of example, a programmable
processor, a computer, or multiple processors or computers. The
apparatus can also be or further include special purpose logic
circuitry, for example, a central processing unit (CPU), an FPGA
(field programmable gate array), or an ASIC (application-specific
integrated circuit). In some implementations, the data processing
apparatus or special purpose logic circuitry (or a combination of
the data processing apparatus or special purpose logic circuitry)
may be hardware- or software-based (or a combination of both
hardware- and software-based). The apparatus can optionally include
code that creates an execution environment for computer programs,
for example, code that constitutes processor firmware, a protocol
stack, a database management system, an operating system, or a
combination of execution environments. The present disclosure
contemplates the use of data processing apparatuses with or without
conventional operating systems, for example LINUX, UNIX, WINDOWS,
MAC OS, ANDROID, IOS, or any other suitable conventional operating
system.
[0126] A computer program, which may also be referred to or
described as a program, software, a software application, a module,
a software module, a script, or code can be written in any form of
programming language, including compiled or interpreted languages,
or declarative or procedural languages, and it can be deployed in
any form, including as a stand-alone program or as a module,
component, subroutine, or other unit suitable for use in a
computing environment. A computer program may, but need not,
correspond to a file in a file system. A program can be stored in a
portion of a file that holds other programs or data, for example,
one or more scripts stored in a markup language document, in a
single file dedicated to the program in question, or in multiple
coordinated files, for example, files that store one or more
modules, sub-programs, or portions of code. A computer program can
be deployed to be executed on one computer or on multiple computers
that are located at one site or distributed across multiple sites
and interconnected by a communication network. While portions of
the programs illustrated in the various figures are shown as
individual modules that implement the various features and
functionality through various objects, methods, or other processes,
the programs may instead include a number of sub-modules,
third-party services, components, libraries, and such, as
appropriate. Conversely, the features and functionality of various
components can be combined into single components, as appropriate.
Thresholds used to make computational determinations can be
statically, dynamically, or both statically and dynamically
determined.
[0127] The methods, processes, or logic flows described in this
specification can be performed by one or more programmable
computers executing one or more computer programs to perform
functions by operating on input data and generating output. The
methods, processes, or logic flows can also be performed by, and
apparatus can also be implemented as, special purpose logic
circuitry, for example, a CPU, an FPGA, or an ASIC.
[0128] Computers suitable for the execution of a computer program
can be based on general or special purpose microprocessors, both,
or any other kind of CPU. Generally, a CPU will receive
instructions and data from a read-only memory (ROM) or a random
access memory (RAM), or both. The essential elements of a computer
are a CPU, for performing or executing instructions, and one or
more memory devices for storing instructions and data. Generally, a
computer will also include, or be operatively coupled to, receive
data from or transfer data to, or both, one or more mass storage
devices for storing data, for example, magnetic, magneto-optical
disks, or optical disks. However, a computer need not have such
devices. Moreover, a computer can be embedded in another device,
for example, a mobile telephone, a personal digital assistant
(PDA), a mobile audio or video player, a game console, a global
positioning system (GPS) receiver, or a portable storage device,
for example, a universal serial bus (USB) flash drive, to name just
a few.
[0129] Computer-readable media (transitory or non-transitory, as
appropriate) suitable for storing computer program instructions and
data includes all forms of non-volatile memory, media and memory
devices, including by way of example semiconductor memory devices,
for example, erasable programmable read-only memory (EPROM),
electrically erasable programmable read-only memory (EEPROM), and
flash memory devices; magnetic disks, for example, internal hard
disks or removable disks; magneto-optical disks; and CD-ROM,
DVD+/-R, DVD-RAM, and DVD-ROM disks. The memory may store various
objects or data, including caches, classes, frameworks,
applications, backup data, jobs, web pages, web page templates,
database tables, repositories storing dynamic information, and any
other appropriate information including any parameters, variables,
algorithms, instructions, rules, constraints, or references
thereto. Additionally, the memory may include any other appropriate
data, such as logs, policies, security or access data, reporting
files, as well as others. The processor and the memory can be
supplemented by, or incorporated in, special purpose logic
circuitry.
[0130] To provide for interaction with a user, implementations of
the subject matter described in this specification can be
implemented on a computer having a display device, for example, a
CRT (cathode ray tube), LCD (liquid crystal display), LED (Light
Emitting Diode), or plasma monitor, for displaying information to
the user and a keyboard and a pointing device, for example, a
mouse, trackball, or trackpad by which the user can provide input
to the computer. Input may also be provided to the computer using a
touchscreen, such as a tablet computer surface with pressure
sensitivity, a multi-touch screen using capacitive or electric
sensing, or other type of touchscreen. Other kinds of devices can
be used to provide for interaction with a user as well; for
example, feedback provided to the user can be any form of sensory
feedback, for example, visual feedback, auditory feedback, or
tactile feedback; and input from the user can be received in any
form, including acoustic, speech, or tactile input. In addition, a
computer can interact with a user by sending documents to and
receiving documents from a device that is used by the user; for
example, by sending web pages to a web browser on a user's client
device in response to requests received from the web browser.
[0131] The term "graphical user interface," or "GUI," may be used
in the singular or the plural to describe one or more graphical
user interfaces and each of the displays of a particular graphical
user interface. Therefore, a GUI may represent any graphical user
interface, including but not limited to, a web browser, a touch
screen, or a command line interface (CLI) that processes
information and efficiently presents the information results to the
user. In general, a GUI may include a plurality of user interface
(UI) elements, some or all associated with a web browser, such as
interactive fields, pull-down lists, and buttons. These and other
UI elements may be related to or represent the functions of the web
browser.
[0132] Implementations of the subject matter described in this
specification can be implemented in a computing system that
includes a back-end component, for example, as a data server, or
that includes a middleware component, for example, an application
server, or that includes a front-end component, for example, a
client computer having a graphical user interface or a Web browser
through which a user can interact with an implementation of the
subject matter described in this specification, or any combination
of one or more such back-end, middleware, or front-end components.
The components of the system can be interconnected by any form or
medium of wireline or wireless digital data communication (or a
combination of data communication), for example, a communication
network. Examples of communication networks include a local area
network (LAN), a radio access network (RAN), a metropolitan area
network (MAN), a wide area network (WAN), Worldwide
Interoperability for Microwave Access (WIMAX), a wireless local
area network (WLAN) using, for example, 802.11 a/b/g/n or 802.20
(or a combination of 802.11x and 802.20 or other protocols
consistent with this disclosure), all or a portion of the Internet,
or any other communication system or systems at one or more
locations (or a combination of communication networks). The network
may communicate with, for example, Internet Protocol (IP) packets,
Frame Relay frames, Asynchronous Transfer Mode (ATM) cells, voice,
video, data, or other suitable information (or a combination of
communication types) between network addresses.
[0133] The computing system can include clients and servers. A
client and server are generally remote from each other and
typically interact through a communication network. The
relationship of client and server arises by virtue of computer
programs running on the respective computers and having a
client-server relationship to each other.
[0134] While this specification contains many specific
implementation details, these should not be construed as
limitations on the scope of any invention or on the scope of what
may be claimed, but rather as descriptions of features that may be
specific to particular implementations of particular inventions.
Certain features that are described in this specification in the
context of separate implementations can also be implemented, in
combination, in a single implementation. Conversely, various
features that are described in the context of a single
implementation can also be implemented in multiple implementations,
separately, or in any suitable sub-combination. Moreover, although
previously described features may be described as acting in certain
combinations and even initially claimed as such, one or more
features from a claimed combination can, in some cases, be excised
from the combination, and the claimed combination may be directed
to a sub-combination or variation of a sub-combination.
[0135] Particular implementations of the subject matter have been
described. Other implementations, alterations, and permutations of
the described implementations are within the scope of the following
claims as will be apparent to those skilled in the art. While
operations are depicted in the drawings or claims in a particular
order, this should not be understood as requiring that such
operations be performed in the particular order shown or in
sequential order, or that all illustrated operations be performed
(some operations may be considered optional), to achieve desirable
results. In certain circumstances, multitasking or parallel
processing (or a combination of multitasking and parallel
processing) may be advantageous and performed as deemed
appropriate.
[0136] Moreover, the separation or integration of various system
modules and components in the previously described implementations
should not be understood as requiring such separation or
integration in all implementations, and it should be understood
that the described program components and systems can generally be
integrated together in a single software product or packaged into
multiple software products.
[0137] Accordingly, the previously described example
implementations do not define or constrain this disclosure. Other
changes, substitutions, and alterations are also possible without
departing from the spirit and scope of this disclosure.
[0138] Furthermore, any claimed implementation is considered to be
applicable to at least a computer-implemented method; a
non-transitory, computer-readable medium storing computer-readable
instructions to perform the computer-implemented method; and a
computer system comprising a computer memory interoperably coupled
with a hardware processor configured to perform the
computer-implemented method or the instructions stored on the
non-transitory, computer-readable medium.
* * * * *