yaxun selective stacking - sep.stanford.edu

Selective stacking in the reflection-

angle and azimuth domain

Yaxun Tang

[email protected]

SEP-129, p157

[email protected] SEP-129 2

Sub-salt zero-offset image


Angle-domain selective stack


Why artifacts in ADCIGs?

reflection angle

depth

reflection

azimuth


• Wave-equation ADCIGs

• Artifacts in the angle gathers

• SEG/EAGE salt model

Outline


• ADCIGs before imaging condition Step 1: Decompose source and receiver wavefield into

local plane-waves

Step 2: Local plane-wave imaging for each opening angle

• ADCIGs after imaging condition Step 1: Compute subsurface-offset domain common-image

gathers (SODCIGs)

Step 2: Transform the SODCIGs into ADCIGs

ADCIGs for shot-profile migration


Downward continuation

Downward continue source wavefield Downward continue receiver wavefield


Multi-offset imaging


Multi-offset imaging condition


Extracting ADCIGs in 2-D

tanx

h

z x

k z

k h= =

: opening angle

: dip angleSava and Fomel (2003)


3-D Common-azimuth extension

tan cosx

h

z

k

k=

tanym

z

k

k=

: opening angle

: crossline dip angleTisserant and Biondi (2003)


3-D full prestack extension


3-D full prestack extension

: opening angle

: reflection azimuth

2

1tan

1 sin cosyx

zmm

z z

k kk

k k

=

+ +

hk

Tisserant and Biondi (2003)





Outline


A simple example


Migrated images


Migrated SODCIGs (CMP=0)

All receivers One receiver


A space and time domain perspective

Source wavefront

Receiver wavefront

Well sampled

receiver wavefield

Locally constant media

( ) [ ]

[ ] [ ] [ ]

22 2

2 2 2

( ) sin( )

cos( 2 ) sin( 2 ) ( ) sin( )

m

m

x h s z x s

x h s z s x s

+ = +

+ + = +



Source wavefront

Receiver wavefront

Well sampled

receiver wavefield


( ) [ ]

[ ] [ ] [ ]

22 2

2 2 2

( ) sin( )

cos( 2 ) sin( 2 ) ( ) sin( )

m

m

x h s z x s

x h s z s x s

+ = +

+ + = +

tan tanx

z x h=

Linear



Source wavefront

Receiver wavefront

Poorly sampled

receiver wavefield


[ ]

[ ]

22 2

22 2

( ) ( ) sin( )

( ) ( ) sin( )

m

m

x h s z x s

x h r z x r

+ = +

+ + =



Source wavefront

Receiver wavefront

Poorly sampled

receiver wavefield


[ ]

[ ]

22 2

22 2

( ) ( ) sin( )

( ) ( ) sin( )

m

m

x h s z x s

x h r z x r

+ = +

+ + =

[ ]22 2 2( ) ( ) tan( ) tan( )

x xz h r s h r s= + + + +

Non-linear


Migrated ADCIGs (CMP=0)

All receivers One receiver


Migrated ADCIGs (CMP=0)

One receiverAll receivers





Outline


Shot layout

45 shots in total

Shot spacing is

about 960 m


Receiver distribution

Offsets ranging

from -2000 m to

2000 m


Azimuth vs. offset


Migrated image


Locations for output gathers

x

z

y

x

z

y


SODCIGs

hx [m] hx [m]

hy [m] hy [m]

z [m] z [m]


ADCIGs

reflection angle

azimuth

z [m]

azimuth

z [m]

reflection angle


Angular images

Angle=0 Azimuth=0 Angle=25 Azimuth=30 Angle=55 Azimuth=60


Model-space weighting function

Half length of

moving window

Determines the shape

of window

Envelope of the ADCIG for a CMP location

The weighting function

1( , , ) ( ) ( , , )

2 1

L

j L

W z s j E z j z j jL =

= + + ++


Suppressing the artifacts


Sub-salt zero-offset image


Angle stacking without weighting function


Angle stacking with weighting function


• ADCIGs are prone to illumination and

sampling related artifacts

• Even with wide-azimuth data

• Artifacts are identifiable in the ADCIGs

• Model-space weighting function can

attenuate them effectively

• Selective stacking results in better image

with higher S/N

Conclusions


• Signal processing based

• If artifacts are strong, it may not work well

• Better model-space weighting function

needed

Problems with current method


• Hessian can be a measure of subsurface

illumination (Valenciano and Biondi, 2004)

• Angle-domain Hessian can give a range of

angle and azimuth that are well illuminated

• So is angle-domain Hessian the answer?

Future work


Thanks

yaxun selective stacking - sep.stanford.edu

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