with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology Outline Summary Theory Use ghost extrapolation to reduce stairstep diffractions from ID: 287390
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Slide1
Multi-source Least-squares Migration with Topography
Dongliang
Zhang and Gerard Schuster
King Abdullah University of Science and Technology
Slide2
Outline
Summary
Theory
Use
ghost
extrapolation
to reduce stair-step diffractions from
irregular
surfaces
Numerical Example
Tests on
Marmousi model and Foothills model
Motivation
Irregular surface problemsSlide3
Outline
Summary
Theory
Use
ghost extrapolation
to reduce stair-step diffractions from
irregular
surfaces
Numerical Example
Tests on
M
armousi model and Foothills model
Motivation
Irregular surface problemsSlide4
Irregular Surface ProblemsDatuming
the data from irregular surface to flat surface
MotivationSlide5
Problem: Irregular Surface
Using Ghost extrapolation
Motivation
RTM migrates directly from the
irregular
surface
Air
Surface
Stair
step
Subsurface
Solution: Ghost RTMSlide6
Outline
Summary
Theory
Use
ghost
extrapolation
to reduce stair-step diffractions from
irregular
surfaces
Numerical Example
Tests on
Marmousi model and Foothills model
Motivation
Irregular surface problemsSlide7
Least-squares Migration
f
(m)
+regularization term
g
)
Slide8
Workflow of Multisource LSM
with Topography
Forward modeling with topography to calculate
the data residual
3. Update the
reflectivity
using the conjugate gradient method
2. Calculate gradient (RTM image) of data residual with topographyBlended encoded shot gathersSlide9
Forward Modeling with TopographyDifficulty
:
I
mplement free surface boundary
condition Calculate the pressure on the points near by the free surface
Acoustic equation:
Ghost pointSlide10
Ghost Extrapolation
Z
i,j
Z
i-1,j
Z
i-2,j
Z
i+1,j
Z
i+2,j
Surface
Z
b
0
Taylor Series Slide11
Extrapolation in z direction
Extrapolation in x direction
Ghost ExtrapolationSlide12
Example of Dipping Surface
Surface
Air
Surface
Stair
step
Subsurface
0
X (km)
2Zoom
M
odel
0
1.5
Z (km)Slide13
Mirror image
Common Shot Gather
P
i-1,j
P
i-2,j
P
i+2,j
=-
P
i-2,j
P
i+1,j
=-P
i-1,j
Air
Zero velocity layer
V=0
Subsurface
Air
Ghost extrapolation
0
X
(km
)
2
0
1.5
Z (km)Slide14
Zoom Views
Conventional method
New methodSlide15
Outline
Summary
Theory
Use
ghost
extrapolation
to reduce stair-step diffractions from
irregular
surfaces
Numerical Example
Tests on
Marmousi model and Foothills model
Motivation
Irregular surface problemsSlide16
0
X (km)
2
Grids size: 201
x 400 dx=
dz=5 m Peak Freq.: 25 Hz Shots: 200 Receiver: 400
Max difference of elevation: 180 mMarmousi Model0
1
Z (km)
01V (km/s)Slide17
Migration Velocity
Reflectivity Model
Marmousi
Model
0 X
(km)
2
0
1
Z (km)01
Z (km)
Ghost FD
0 X (km)
2
Common Shot Gather
0
2
T (s)Slide18
0
X
(km)
2
Ghost LSRTM Image
Ghost FD
Marmousi
Model
Ghost FD
Conventional FD
Conventional FD
LSRTM Image
RTM Image
Ghost RTM Image
0
X (km)
2
0
1
Z (km)
0
1
Z (km)Slide19
Zoom Views
Ghost FD
Ghost LSRTM Image
Ghost FD
Conventional FD
LSRTM Image
RTM Image
Ghost RTM Image
Conventional FDSlide20
0 X (km) 8
Grids size: 333
x 833 dx=
dz
=10 m Peak Freq.: 15 Hz Shots: 208 Receiver: 833
Max difference of elevation: 500 m
Foothills
Model
0
3
Z (km)0
6
V (km/s)Slide21
Migration Velocity
Reflectivity Model
0 X
(km)
8
0 X (km)
2
Common Shot Gather
Ghost FD
Foothills Model
0
3
Z (km)
0
3
Z (km)
0
2
T (s)Slide22
0 X
(km)
8
Ghost LSRTM Image
0 X
(km)
8
LSRTM Image
Ghost FD
Ghost FD
Ghost RTM Image
Conventional FD
RTM Image
Conventional FD
Foothills
Model
0
3
Z (km)
0
3
Z (km)Slide23
Ghost LSRTM Image
LSRTM Image
Ghost FD
Ghost FD
Ghost RTM Image
Conventional FD
RTM Image
Conventional FD
Zoom ViewsSlide24
Summary
MLSM can produce high quality images efficiently:
MLSM
with topography produces high quality image,
multi-source
saves the
computational time
Ghost extrapolation can
reduce stair-step
diffraction
artifacts
Future work:
Using 2D ghost extrapolation
Test on field data
High accuracy for the free surface boundary
condition
Elastic Slide25
Thank you!