Transcript Jian Mao and Ru-Shan Wu, 3D True Reflection Imaging

3D True Reflection Imaging:
Beamlet Migration with
Acquisition Aperture Correction
in Local Angle Domain
Jian Mao and Rushan Wu
WTOPI, Modeling & Imaging Lab., UCSC
Outline
Motivations
3D beamlet migration
Acquisition aperture correction
Numerical results
Conclusions
Outline
Motivations
3D beamlet migration
Acquisition aperture correction
Numerical results
Conclusions
Motivations
 Traditional wave equation based migration method can
provide a reflector map consistent with the real subsurface
structure, but the reflection/scattering strength (or image
amplitude) of subsurface structures is unreliable.
 True-reflection imaging tries to give not only correct location
but also correct image amplitude of the reflectors.
 The factors influencing the image amplitude include
propagator errors (e.g. geometrical spreading, focusing and
defocusing by heterogeneity, path absorption and path
scattering loss, numerical dispersion and numerical anisotropy),
and acquisition aperture effect, etc.
Motivations
 Wu et al. (2004) proposed an amplitude correction method
with acquisition aperture correction in local angle domain.
The numerical examples demonstrated the significance of
aperture correction in true-reflection imaging.
Before aperture correction
After aperture correction
Motivations
 With new advances in beamlet decomposition (e.g. GaborDaubechies frame, local cosine basis, local exponential frame)
(Chen et al., 2006, Wu et al., 2008, Mao and Wu, 2007, 2009,
2010), the wavefield can be decomposed and propagated in
beamlet domain. Beamlet propagator has high accuracy when
dealing with high contrast medium.
 Here we present the true reflection imaging method in the 3D
case. We combined 3D beamlet migration method with
acquisition aperture correction method in local angle domain.
This method is developed for target oriented purpose. The
expensive local angle domain decomposition and storage need
only to be performed in some target areas we are interested.
Outline
Motivations
3D beamlet migration
Acquisition aperture correction
Numerical results
Conclusions
3D beamlet migration
Wave field decomposition using beamlet
wave equation based
Beamlets:
local perturbation theory
wavelet decomposition
The space domain wavefield can be decomposed by beamlets:
u (x, z,  )    u, bmn (x)  bmn ( x)
n
m
n
m
  uˆ z ( xn ,  m ,  )bmn (x)
3D beamlet migration
Beamlet decomposition and propagation
3D beamlet migration
FFD
Beamlet
Reference velocity
3D beamlet migration
3D SEG model: Velocity map
3D beamlet migration
Prestack migration image using FFD propagator
3D beamlet migration
Prestack migration image using LCB propagator
Outline
Motivations
3D beamlet migration
Acquisition aperture correction
Numerical results
Conclusions
Theory of local angle decomposition
Wave field decomposition
The space domain wavefield can be decomposed in local angle domain or local
wavenumber domian.
f-x domain
Wavefiled
Local slant stack
Beamlet decomposition
Local angle domain
Wavefiled
Theory of local angle decomposition
Local slant stack
u(x, z,)
u (x, z; θs , θg )
Gabor-Daubechies frame
u (x, z; k s , k g )
u(x, z, )
Local exponential frame
Theory of local angle decomposition
Local angles
s
g
n
r
: incident angle
: receiving angle
: dip angle
: reflection angle
 n   s   g  / 2
 r   s   g  / 2
Theory of aperture correction
Acquisition aperture effect
For complex medium, the limited acquisition aperture often results in stronglynonuniform dip-dependent illumination and distorted image amplitude of
subsurface structures. Wave-equation based aperture correction in local angle
domain (Wu et al., 2004) can compensate the acquisition aperture effect.
Source
Receiver
Ur
Us
s
g
Theory of aperture correction
• Imaging condition in local angle domain:
L(, x, θs , θ g )  2 G (, x, θs ; θs )  
*
I
A( x g , x s )
xs
dx g
GI* (, x, θ g ; θ g )
z
us (, x g ; xs )
• Amplitude correction factor matrix :
Fa (x, θs , θ g )  2 GI* (x, θs ; xs )GF (x, θs ; xs ) 
xs

A( x g , x s )
dx g GF (x, θ g ; x g )
• Final image in local dip angle domain:
| I ( x ) |2 

1  n  2
[ | L( x , θn , θr ) |2 ] /[| Da ( x , θn ) |2  ]
r
| Da ( x , θn ) |2   | Fa ( x , θn , θr ) |2
r
2

1/ 2
Workflow of aperture correction
Prestack data
Depth migration
Local angle
decomposition
Green’s function calculation
Imaging
condition
Partial image in local angle
domain in target area
Local angle
decomposition
Aperture correction factors in
local angle domain
Image with aperture correction
Outline
Motivations
Theory of local angle decomposition
Theory of aperture correction
Numerical results
Conclusions
Numerical results
3D SEG salt model
( Velocity model: nx=ny=676,nz=210, dx=dy=dz=20m )
(a)location of the 45 shots
(b)location of the slices
Numerical results
Velocity model on slice A
Numerical results
Migration image on slice A (one-way beamlet migration)
Partial image and correction factors
Partial image after correction
Summation of the partial images after correction
00    50
00    400
00    200
00    600
Numerical results
Image after aperture correction
Velocity model on slice A
Numerical results
Migration image on slice A (one-way beamlet migration)
Numerical results
Migration image with AGC (plus z) on slice A
Numerical results
Image after 3D aperture correction on slice A
Numerical results
Velocity model on slice C
Numerical results
Migration image on slice C (one-way beamlet migration)
Numerical results
Image after 3D aperture correction on slice C
Outline
Motivations
Theory of local angle decomposition
Theory of aperture correction
Numerical results
Conclusions
Conclusions
1
We present the 3D true reflection imaging method, which is
based on beamelt migration and the acquisition aperture
correction in the local-angle domain.
2
Beamlet migration method provide us better migration
images with high accuracy. The aperture correction results
show great improvement of the image quality, for both
shallow part and some subsalt structures.
3
The computational efficiency of the method still needs to be
improved for practical use. It still have potential to improve
the image quality.
Acknowledgements
The author would like to acknowledge:
The support from WTOPI consortium at UC Santa
Cruz and Institute of wave propagation and
information at Xi’an Jiaotong University.
TOTAL E&P USA research group, Biaolong Hua and
Paul Williamson.
Xiao-Bi Xie, Jinghuai Gao, Chuck Mosher, Jun Cao,
Yaofeng He and Hui Yang for helpful discussions.