Enhanced Algorithm for Internal Multiple Attenuation in Seismic Imaging
Xinglu Lin* and Arthur B. Weglein
May 29
th
, 2014
Austin, TX
ISS internal multiple attenuation
algorithm for a
3-D source
and a
one-dimensional subsurface
Outline
•
Motivation;
•
Reduced form of 3-D ISS internal multiple attenuator for a
1-D layered earth:
•
Circular symmetry;
•
3-D source ISS internal multiple attenuator for a 1-D earth;
•
Numerical test;
•
Conclusions.
2
Outline
•
Motivation;
•
Reduced form of 3-D ISS internal multiple attenuator for a
1-D layered earth:
•
Circular symmetry;
•
3-D source ISS internal multiple attenuator for a 1-D earth;
•
Numerical test;
•
Conclusions.
3
Motivation
•
There are on-shore and off-shore regions, which are
close
to 1-D earth
and have serious
internal multiple problems
.
For example, Central North sea (B. Duquet, 2013),
Canada, offshore Brazil and Middle East.
•
When the earth is close to 1-D,
we
do not have to pay for
a “complete” data set and high computation as in 3-D
earth by using the reduced 3-D source-1-D earth
algorithm;
•
3-D source
－
1-D earth ISS internal multiple attenuator is
needed for the ISS eliminator of internal multiple.
4
Motivation
- Current state of ISS internal multiple attenuator
•
2-D Line Source:
•
2-D algorithm assume that whole world is 2-D. A point
source in the 2-D world is a line
in
a 3-D world.
•
2-D source-1-D earth: The algorithm is derived from 2-D
source, which is a reduced form for a 1-D earth. It
requires one source and receivers on one single line.
•
(Araujo, et al,1994; Weglein, et al,1997)
•
code released by P. Terenghi; S. Kaplan;
•
Application: Qiang Fu, Encana data, 2014 M-OSRP
annual report
5
•
3-D Point Source:
•
In 3-D theory the world is considered as 3-D. Source is a
point in a 3-D world.
•
3-D Source-3-D Earth
•
3-D Source-2-D Earth
•
3-D Source-1-D Earth (in Cartesian Coordinates)
•
3-D Source-1-D Earth (in Cylindrical Coordinates)
6
Motivation
- Current state of ISS internal multiple attenuator
•
3-D Source-3-D Earth
•
3-D Source-2-D Earth
•
3-D Source-1-D Earth (in Cartesian Coordinates)
•
3-D Source-1-D Earth (in Cylindrical Coordinates)
7
Requirements of 3-D ISS internal multiple attenuator
3-D Source-3-D Earth
8
Source
Receiver
Requirements: Areal coverage of sources; Areal coverage of receivers.
X-direction
3-D Source-3-D Earth
9
Source
Receiver
X-direction
Requirements: Areal coverage of sources; Areal coverage of receivers.
Z
Y
X
3-D Source-3-D Earth
10
10
Source
Receiver
X-direction
Requirements: Areal coverage of sources; Areal coverage of receivers.
Z
Y
X
3-D Source-3-D Earth
11
11
Source
Receiver
X-direction
Requirements: Areal coverage of sources; Areal coverage of receivers.
Z
Y
X
3-D Source-3-D Earth
12
12
Source
Receiver
X-direction
Requirements: Areal coverage of sources; Areal coverage of receivers.
Z
Y
X
3-D Source-3-D Earth
13
13
Source
Receiver
X-direction
Requirements: Areal coverage of sources; Areal coverage of receivers.
Z
Y
X
3-D Source-3-D Earth
14
14
Source
Receiver
Y-direction
Requirements: Areal coverage of sources; Areal coverage of receivers.
Z
Y
X
3-D Source-3-D Earth
15
15
Source
Receiver
Y-direction
Requirements: Areal coverage of sources; Areal coverage of receivers.
Z
Y
X
3-D Source-3-D Earth
16
16
Source
Receiver
Y-direction
Requirements: Areal coverage of sources; Areal coverage of receivers.
Z
Y
X
3-D Source-3-D Earth
17
17
Source
Receiver
Y-direction
Requirements: Areal coverage of sources; Areal coverage of receivers.
Z
Y
X
3-D Source-3-D Earth
18
18
Source
Receiver
Y-direction
Requirements: Areal coverage of sources; Areal coverage of receivers.
Z
Y
X
3-D Source-3-D Earth
19
19
Source
Receiver
Y-direction
Requirements: Areal coverage of sources; Areal coverage of receivers.
Z
Y
X
3-D Source-3-D Earth
20
20
Source
Receiver
Requirements: Areal coverage of sources; Areal coverage of receivers.
Z
Y
X
•
3-D Source-3-D Earth
•
3-D Source-2-D Earth
•
3-D Source-1-D Earth (in Cartesian Coordinates)
•
3-D Source-1-D Earth (in Cylindrical Coordinates)
21
21
Requirements of 3-D ISS internal multiple attenuator
3-D Source-2-D Earth
22
22
Source
Receiver
Requirements: Sources on a single line (x-direction); Areal coverage of receivers.
Z
Y
X
3-D Source-2-D Earth
23
23
Source
Receiver
Requirements: Sources on a single line (x-direction); Areal coverage of receivers.
Z
Y
X
3-D Source-2-D Earth
24
24
Source
Receiver
Requirements: Sources on a single line (x-direction); Areal coverage of receivers.
Z
Y
X
3-D Source-2-D Earth
25
25
Source
Receiver
Requirements: Sources on a single line (x-direction); Areal coverage of receivers.
Z
Y
X
3-D Source-2-D Earth
26
26
Source
Receiver
Requirements: Sources on a single line (x-direction); Areal coverage of receivers.
Z
Y
X
3-D Source-2-D Earth
27
27
Source
Receiver
Requirements: Sources on a single line (x-direction); Areal coverage of receivers.
Z
Y
X
3-D Source-2-D Earth
28
28
Source
Receiver
Requirements: Sources on a single line (x-direction); Areal coverage of receivers.
Z
Y
X
3-D Source-2-D Earth
29
29
Source
Receiver
Requirements: Sources on a single line (x-direction); Areal coverage of receivers.
Z
Y
X
•
3-D Source-3-D Earth
•
3-D Source-2-D Earth
•
3-D Source-1-D Earth (in Cartesian Coordinates)
•
3-D Source-1-D Earth (in Cylindrical Coordinates)
30
30
Requirements of 3-D ISS internal multiple attenuator
3-D Source-1-D Earth
(Cartesian Coordinates)
31
31
Source
Receiver
Requirements: One single source; Areal coverage of receivers.
Z
Y
X
•
3-D Source-3-D Earth
•
3-D Source-2-D Earth
•
3-D Source-1-D Earth (in Cartesian Coordinates)
•
3-D Source-1-D Earth (in Cylindrical Coordinates)
32
32
Requirements of 3-D ISS internal multiple attenuator
3-D Source-1-D Earth
(Cylindrical Coordinates)
33
33
Source
Receiver
Requirements: One single source; Receivers on one single line.
Z
Y
X
3-D Source-1-D Earth
(Cylindrical Coordinates)
34
34
Source
Receiver
Requirements: One single source; Receivers on one single line.
Z
Y
X
Motivation
- Current state of ISS internal multiple attenuator
•
3-D Point Source:
•
1-D earth-3-D source: Current algorithm requires a shot
record with areal coverage of receivers (all the x
g
and y
g
)
for a fixed source (x
s
, y
s
).
•
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35
35
Motivation
36
36
I.
Preprocessing for on-shore applications.
II.
Beyond the ISS internal multiple attenuator.
1.
elimination:
Start the ISS internal multiple attenuator for a 3D source - 1D earth at
first.
2.
spurious events removal.
III.
New adaptive subtraction criteria.
37
37
Outline
•
Motivation;
•
Reduced form of 3-D ISS internal multiple attenuator for a
1-D layered earth:
•
Circular symmetry
;
•
3-D source ISS internal multiple attenuator for a 1-D earth;
•
Numerical test;
•
Conclusions.
38
38
Cylindrical Coordinate
39
39
3-D source-1-D earth data only depends on offset and frequency,
which has a circular symmetry under cylindrical coordinate
(independent of angle).
Circular Symmetry
•
3D-1DE-----3D source, 1-D earth;
•
Circular symmetry after a two-dimensional Fourier
transform or a Fourier-Bessel transform.
•
Applying the symmetry to b
1
gives a product of and
a symmetry factor.
40
40
Outline
•
Motivation;
•
Reduced form of 3-D ISS internal multiple attenuator for a
1-D layered earth:
•
Circular symmetry;
•
3-D source ISS internal multiple attenuator for 1-D earth;
•
Numerical test;
•
Conclusions.
41
41
3-D ISS internal multiple attenuation algorithm in
cylindrical coordinate
(1-D earth, k-
ω
domain)
42
42
•
The circular symmetry produces the simple form, which is
reduced from original 3-D ISS attenuation algorithm:
k-
ω
domain:
3-D ISS internal multiple attenuation algorithm in
cylindrical coordinate
(1-D earth, Hankel Transform, r-
ω
(x-
ω
) domain )
•
Fourier-Bessel transform over the b
3
.
•
The reduced 3-D algorithm is,
43
43
Hankel Transform
r-
ω
(x-
ω
) domain:
3-D ISS internal multiple attenuation algorithm for 1-D
earth
44
44
For example, to deal with a shot record generated by 3-D source-1-D
earth, we need to do
3-D source -1-D earth data
Comparison between 3-D source and 2-D source ISS
internal multiple algorithm
45
45
Comments
•
From the above chart, we can conclude that the 3-D
source ISS internal multiple attenuation algorithm remains
all its merits for a 1-D earth, since the prediction kernel
does not change.
46
46
Outline
•
Motivation;
•
Reduced form of 3-D ISS internal multiple attenuator for a
1-D layered earth:
•
Circular symmetry;
•
3-D source ISS internal multiple attenuator for a 1-D earth;
•
Numerical test;
•
Conclusions.
47
47
Numerical Test
48
48
Assumptions and 3-D source-1-D earth data
49
49
Assumptions:
1.
1-D earth;
2.
3-D source (on streamer, no lateral offset, );
3.
Transform data from spatial-frequency domain to
wavenumber-frequency by using Fourier-Bessel
transform before multiple prediction.
Data
is generated in (k
rh
,q) domain.
( Aki and Richard, Chapter 6)
50
50
3-D earth-1-D earth data set (one
streamer)
2-D ISS internal multiple
prediction
3-D ISS internal multiple prediction
(Asymptotic Bessel)
3-D ISS internal multiple prediction
( Hankel transformation)
(courtesy of Yanglei Zou)
3-D source-1-D earth data, 2-D Prediction, 3-D Prediction with full bandwidth
primary
I
primary II
Internal multiple
51
51
Primaries
First-order internal multiple
Trace #2:
3-D source-1-D earth data, 3-D prediction and 2-D prediction
Primaries
First-order internal multiple
Trace #2:
3-D and 2-D prediction detail with enlarged scale
52
52
Trace #2:
3-D prediction detail with enlarged scale
53
53
54
54
Primaries
First-order internal multiple
Trace #80:
3-D source-1-D earth data, 3-D prediction and 2-D prediction
Primaries
First-order internal multiple
55
55
Trace #80:
3-D and 2-D prediction detail with enlarged scale
56
56
Trace #80:
3-D prediction detail with enlarged scale
Outline
•
Motivation;
•
Reduced form of 3-D ISS internal multiple attenuation a
algorithm for 1-D layered earth:
•
Circular symmetry;
•
3-D source ISS internal multiple attenuator for a 1-D earth;
•
Numerical test;
•
Conclusions.
57
57
Conclusions
•
The 3-D ISS Internal multiple attenuation algorithm can be
reduced to a simpler form in order to process data that is
generated by a
3-D
point source and a one-dimensional
subsurface. The simple form requires
one single source
and receivers on one single line
, instead of an areal
coverage.
58
58
Conclusions
•
This initial test
demonstrates that for data from a 3-D
source and a 1-D earth, using an ISS internal multiple
attenuation algorithm designed for a 2-D source and a 1-
D earth could make the multiple problem worse –
producing a larger multiple than the original.
•
The 3-D source, 1-D earth ISS internal multiple attenuator
always reduce (attenuates) the internal multiple in data
from a 3-D source and a 1-D earth.
•
This is important to understand/recognize in developing/
applying an ISS internal multiple attenuator on field data
where the earth is close to 1-D.
59
59
Conclusions
•
Dr. Terenghi produced several ISS internal multiple codes
at M-OSRP. One code reduced a 2-D ISS internal multiple
attenuator (a 2-D source, 2-D earth) to a 2-D source and
a 1-D earth. The work starts with a 3-D ISS internal
multiple attenuator (a 3-D source, 3-D earth) and reduces
it to a 3-D source and 1-D earth.
•
This paper shows that this work represents more than an
increase in effectiveness when the data is generated by a
3-D source and a 1-D earth. It changes from “can make
matter worse” to “making things better”.
60
60
This research discusses the development of an improved algorithm for internal multiple attenuation in seismic imaging. The focus is on addressing the challenges in onshore and offshore regions close to a 1-D earth model. The algorithm aims to enhance the efficiency and accuracy of data processing in such scenarios, offering a cost-effective solution. Various perspectives on the current state of internal multiple attenuators and the requirements for a 3-D approach are explored. The study presents insights on reduced forms of 3-D source-1-D earth algorithms, motivation, numerical testing, and conclusions.
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Presentation Transcript
ISS internal multiple attenuation algorithm for a 3-D source and a one-dimensional subsurface Xinglu Lin* and Arthur B. Weglein May 29th, 2014 Austin, TX
2 Outline Motivation; Reduced form of 3-D ISS internal multiple attenuator for a 1-D layered earth: Circular symmetry; 3-D source ISS internal multiple attenuator for a 1-D earth; Numerical test; Conclusions.
3 Outline Motivation; Reduced form of 3-D ISS internal multiple attenuator for a 1-D layered earth: Circular symmetry; 3-D source ISS internal multiple attenuator for a 1-D earth; Numerical test; Conclusions.
4 Motivation There are on-shore and off-shore regions, which are close to 1-D earth and have serious internal multiple problems. For example, Central North sea (B. Duquet, 2013), Canada, offshore Brazil and Middle East. When the earth is close to 1-D, we do not have to pay for a complete data set and high computation as in 3-D earth by using the reduced 3-D source-1-D earth algorithm; 3-D source 1-D earth ISS internal multiple attenuator is needed for the ISS eliminator of internal multiple.
5 Motivation - Current state of ISS internal multiple attenuator 2-D Line Source: 2-D algorithm assume that whole world is 2-D. A point source in the 2-D world is a line in a 3-D world. 2-D source-1-D earth: The algorithm is derived from 2-D source, which is a reduced form for a 1-D earth. It requires one source and receivers on one single line. (Araujo, et al,1994; Weglein, et al,1997) code released by P. Terenghi; S. Kaplan; Application: Qiang Fu, Encana data, 2014 M-OSRP annual report
6 Motivation - Current state of ISS internal multiple attenuator 3-D Point Source: In 3-D theory the world is considered as 3-D. Source is a point in a 3-D world. 3-D Source-3-D Earth 3-D Source-2-D Earth 3-D Source-1-D Earth (in Cartesian Coordinates) 3-D Source-1-D Earth (in Cylindrical Coordinates)
7 Requirements of 3-D ISS internal multiple attenuator 3-D Source-3-D Earth 3-D Source-2-D Earth 3-D Source-1-D Earth (in Cartesian Coordinates) 3-D Source-1-D Earth (in Cylindrical Coordinates)
8 3-D Source-3-D Earth X-direction Source Receiver Z Y X Requirements: Areal coverage of sources; Areal coverage of receivers.
9 3-D Source-3-D Earth X-direction Source Receiver Z Y X Requirements: Areal coverage of sources; Areal coverage of receivers.
10 3-D Source-3-D Earth X-direction Source Receiver Z Y X Requirements: Areal coverage of sources; Areal coverage of receivers.
11 3-D Source-3-D Earth X-direction Source Receiver Z Y X Requirements: Areal coverage of sources; Areal coverage of receivers.
12 3-D Source-3-D Earth X-direction Source Receiver Z Y X Requirements: Areal coverage of sources; Areal coverage of receivers.
13 3-D Source-3-D Earth X-direction Source Receiver Z Y X Requirements: Areal coverage of sources; Areal coverage of receivers.
14 3-D Source-3-D Earth Y-direction Source Receiver Z Y X Requirements: Areal coverage of sources; Areal coverage of receivers.
15 3-D Source-3-D Earth Y-direction Source Receiver Z Y X Requirements: Areal coverage of sources; Areal coverage of receivers.
16 3-D Source-3-D Earth Y-direction Source Receiver Z Y X Requirements: Areal coverage of sources; Areal coverage of receivers.
17 3-D Source-3-D Earth Y-direction Source Receiver Z Y X Requirements: Areal coverage of sources; Areal coverage of receivers.
18 3-D Source-3-D Earth Y-direction Source Receiver Z Y X Requirements: Areal coverage of sources; Areal coverage of receivers.
19 3-D Source-3-D Earth Y-direction Source Receiver Z Y X Requirements: Areal coverage of sources; Areal coverage of receivers.
20 3-D Source-3-D Earth Source Receiver Z Y X Requirements: Areal coverage of sources; Areal coverage of receivers.
21 Requirements of 3-D ISS internal multiple attenuator 3-D Source-3-D Earth 3-D Source-2-D Earth 3-D Source-1-D Earth (in Cartesian Coordinates) 3-D Source-1-D Earth (in Cylindrical Coordinates)
22 3-D Source-2-D Earth Source Receiver Z Y X Requirements: Sources on a single line (x-direction); Areal coverage of receivers.
23 3-D Source-2-D Earth Source Receiver Z Y X Requirements: Sources on a single line (x-direction); Areal coverage of receivers.
24 3-D Source-2-D Earth Source Receiver Z Y X Requirements: Sources on a single line (x-direction); Areal coverage of receivers.
25 3-D Source-2-D Earth Source Receiver Z Y X Requirements: Sources on a single line (x-direction); Areal coverage of receivers.
26 3-D Source-2-D Earth Source Receiver Z Y X Requirements: Sources on a single line (x-direction); Areal coverage of receivers.
27 3-D Source-2-D Earth Source Receiver Z Y X Requirements: Sources on a single line (x-direction); Areal coverage of receivers.
28 3-D Source-2-D Earth Source Receiver Z Y X Requirements: Sources on a single line (x-direction); Areal coverage of receivers.
29 3-D Source-2-D Earth Source Receiver Z Y X Requirements: Sources on a single line (x-direction); Areal coverage of receivers.
30 Requirements of 3-D ISS internal multiple attenuator 3-D Source-3-D Earth 3-D Source-2-D Earth 3-D Source-1-D Earth (in Cartesian Coordinates) 3-D Source-1-D Earth (in Cylindrical Coordinates)
31 3-D Source-1-D Earth (Cartesian Coordinates) Source Receiver Z Y X Requirements: One single source; Areal coverage of receivers.
32 Requirements of 3-D ISS internal multiple attenuator 3-D Source-3-D Earth 3-D Source-2-D Earth 3-D Source-1-D Earth (in Cartesian Coordinates) 3-D Source-1-D Earth (in Cylindrical Coordinates)
33 3-D Source-1-D Earth (Cylindrical Coordinates) Source Receiver r q Z Y X Requirements: One single source; Receivers on one single line.
34 3-D Source-1-D Earth (Cylindrical Coordinates) Source Receiver Z Y X Requirements: One single source; Receivers on one single line.
35 Motivation - Current state of ISS internal multiple attenuator 3-D Point Source: 1-D earth-3-D source: Current algorithm requires a shot record with areal coverage of receivers (all the xg and yg) for a fixed source (xs, ys). In this presentation, the ISS internal multiple attenuator will be changed into cylindrical coordinates for a 3-D source and a 1-D earth, which allows a single source and receivers on a single line, rather than a full surface of receivers.
36 Motivation This presentation will examine what difference the 3-D source attenuation algorithm makes versus current 2-D line source algorithm for a data generated by a 3-D source and a 1-D earth. The difference will be amplified when the attenuator b3 enters the elimination algorithm, e.g., that Yanglei Zou and Dr. Weglein are developing. The ISS internal multiple eliminator is an important step in the three-pronged strategy.
37 M-OSRP The three-pronged strategy Preprocessing for on-shore applications. Beyond the ISS internal multiple attenuator. 1. elimination: Start the ISS internal multiple attenuator for a 3D source - 1D earth at first. 2. spurious events removal. New adaptive subtraction criteria. I. II. III.
38 Outline Motivation; Reduced form of 3-D ISS internal multiple attenuator for a 1-D layered earth: Circular symmetry; 3-D source ISS internal multiple attenuator for a 1-D earth; Numerical test; Conclusions.
39 Cylindrical Coordinate 3-D source-1-D earth data only depends on offset and frequency, which has a circular symmetry under cylindrical coordinate (independent of angle). y y r x x
40 Circular Symmetry 3D-1DE-----3D source, 1-D earth; Circular symmetry after a two-dimensional Fourier transform or a Fourier-Bessel transform. 3D-1DE Applying the symmetry to b1 gives a product of and a symmetry factor. b1
41 Outline Motivation; Reduced form of 3-D ISS internal multiple attenuator for a 1-D layered earth: Circular symmetry; 3-D source ISS internal multiple attenuator for 1-D earth; Numerical test; Conclusions.
42 3-D ISS internal multiple attenuation algorithm in cylindrical coordinate (1-D earth, k- domain) The circular symmetry produces the simple form, which is reduced from original 3-D ISS attenuation algorithm: k- domain: 3D-1DE(krh,w) + b3 + z1 3D-1DE(krh,z2)e-i2qz2 3D-1DE(krh,z1)ei2qz1 3D-1DE(krh,z3)ei2qz3 = dz1 b1 dz2 b1 dz3 b1 - - z2 = = = ( /c ) 2 2 rh , wherek k k q k 0 rh rg rs
43 3-D ISS internal multiple attenuation algorithm in cylindrical coordinate (1-D earth, Hankel Transform, r- (x- ) domain ) Fourier-Bessel transform over the b3. The reduced 3-D algorithm is, r- (x- ) domain: Hankel Transform
44 3-D ISS internal multiple attenuation algorithm for 1-D earth For example, to deal with a shot record generated by 3-D source-1-D earth, we need to do 3-D source -1-D earth data 3D-1DE(krh,w) b1 3D-1DE(krh,w) b3 3D-1DE(rh,w)Inverse Hankel transform b3 Or using asymptotic Bessel function krh 3D-1DE(rh,w)=1 3D-1DE(krh,w) eikrhrhdkrh b3 b3 2p 2iprh -
45 Comparison between 3-D source and 2-D source ISS internal multiple algorithm Assumption: 1-D earth krh= kxh (k- ); (x- )---2-D; (r- )---3-D; rh= xh 2D-1DE(kxh,w) = + b1 b3 Fourier Transform b3 =1 2p 2D-1DE(xh,w) 2D-1DE(kxh,z1)ei2qz1 2-D dz1 - z1 line source ISS attenuator 2D-1DE(kxh,w) eikxhxhdkxh b3 2D-1DE(kxh,z2)e-i2qz2 dz2 b1 - - + 2D-1DE(kxh,z3)ei2qz3 dz3 b1 z2 3D-1DE(rh,w) b3 =1 Hankel Transform 3D-1DE(krh,w) = + b1 b3 3D-1DE(krh,w)krhdkrh 0(khrh) b3 J 3-D 3D-1DE(krh,z1)ei2qz1 2p dz1 0 - z1 point source ISS attenuator 3D-1DE(rh,w) 3D-1DE(krh,z2)e-i2qz2 Asymptotic Bessel b3 dz2 b1 - + krh 1 3D-1DE(krh,w) eikrhrhdkrh = b3 3D-1DE(krh,z3)ei2qz3 dz3 b1 2p 2iprh - z2
46 Comments From the above chart, we can conclude that the 3-D source ISS internal multiple attenuation algorithm remains all its merits for a 1-D earth, since the prediction kernel does not change.
47 Outline Motivation; Reduced form of 3-D ISS internal multiple attenuator for a 1-D layered earth: Circular symmetry; 3-D source ISS internal multiple attenuator for a 1-D earth; Numerical test; Conclusions.
48 Numerical Test 3-D source C0=1000m/s, 0=1g/cm3 30m C1=2000m/s, 1=2g/cm3 50m C2=8000m/s, 2=4g/cm3
49 Assumptions and 3-D source-1-D earth data Assumptions: 1. 1-D earth; = k k 2. 3-D source (on streamer, no lateral offset, ); rh rx 3. Transform data from spatial-frequency domain to wavenumber-frequency transform before multiple prediction. by using Fourier-Bessel Data is generated in (krh,q) domain. ( Aki and Richard, Chapter 6)
3-D source-1-D earth data, 2-D Prediction, 3-D Prediction with full bandwidth 50 primary I primary II Internal multiple 3-D earth-1-D earth data set (one streamer) (courtesy of Yanglei Zou) 3-D ISS internal multiple prediction ( Hankel transformation) 2-D ISS internal multiple prediction 3-D ISS internal multiple prediction (Asymptotic Bessel)
