Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King...
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![Page 1: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/1.jpg)
Multi-source Least-squares Migration with Topography
Dongliang Zhang and Gerard SchusterKing Abdullah University of Science and Technology
![Page 2: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/2.jpg)
Outline
Summary
TheoryUse ghost extrapolation to reduce stair-step diffractions from irregular surfaces
Numerical ExampleTests on Marmousi model and Foothills model
MotivationIrregular surface problems
![Page 3: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/3.jpg)
Outline
Summary
TheoryUse ghost extrapolation to reduce stair-step diffractions from irregular surfaces
Numerical ExampleTests on Marmousi model and Foothills model
MotivationIrregular surface problems
![Page 4: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/4.jpg)
Irregular Surface Problems
Datuming the data from irregular surface to flat surface
Motivation
![Page 5: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/5.jpg)
Problem: Irregular Surface
Using Ghost extrapolation
Motivation
RTM migrates directly from the irregular surface
Air
Surface
Stair step
Subsurface
Solution: Ghost RTM
![Page 6: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/6.jpg)
Outline
Summary
TheoryUse ghost extrapolation to reduce stair-step diffractions from irregular surfaces
Numerical ExampleTests on Marmousi model and Foothills model
MotivationIrregular surface problems
![Page 7: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/7.jpg)
Least-squares Migration
𝐝=L𝐦f(m)+regularization term
g)
m𝒌+𝟏=m𝒌−𝜶 g𝒌
𝜶=(g𝒌)𝐓 g𝒌
(Lg𝒌)𝐓 Lg𝒌
![Page 8: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/8.jpg)
Workflow of Multisource LSM with Topography
1. 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 topography
• Blended encoded shot gathers
![Page 9: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/9.jpg)
Forward Modeling with Topography
Difficulty :
Implement free surface boundary condition
Calculate the pressure on the points near by the free surface
Acoustic equation:
2 2 2
2 2 2 2
1
0
P P P
x z v tP on the surface
Ghost point
![Page 10: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/10.jpg)
Ghost Extrapolation
Zi,j
Zi-1,j
Zi-2,j
Zi+1,j
Zi+2,j
Surface
Zb
3 2P(z)=az +bz +cz+d
b
i-2,j i-2,j i-1,j i-1,j
i,j i,j
P(z )=P P(z )=P
P(z )=P P(z )=0
G Gi+1,j i+2,jP =P(Δz) P =P(2Δz)
1)i-2,j i-1,j i,j
G Gi+1,j i+2,j
2
2 2
1 4 5- P + P - P1
4 1+ P - P3 1
∂ P≈ (
∂z 2 3 2Δz 2
Taylor Series
![Page 11: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/11.jpg)
Extrapolation in z direction Extrapolation in x direction
Ghost Extrapolation
2 2 2
2 2 2 2
1P P P
x z v t
![Page 12: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/12.jpg)
Example of Dipping Surface
Surface Air
Surface
Stair step
Subsurface
0 X (km) 2
ZoomModel0
1.5
Z (
km
)
![Page 13: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/13.jpg)
Mirror imageCommon Shot Gather
Pi-1,j
Pi-2,j
Pi+2,j=-Pi-2,j
Pi+1,j=-Pi-1,j
Air
Zero velocity layer
V=0
Subsurface
Air
Ghost extrapolation
0 X (km) 2
0
1.5
Z (
km
)
![Page 14: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/14.jpg)
Zoom ViewsConventional method New method
![Page 15: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/15.jpg)
Outline
Summary
TheoryUse ghost extrapolation to reduce stair-step diffractions from irregular surfaces
Numerical ExampleTests on Marmousi model and Foothills model
MotivationIrregular surface problems
![Page 16: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/16.jpg)
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 m
Marmousi Model
0
1
Z (
km
)
0
1
V
(km
/s)
![Page 17: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/17.jpg)
Migration Velocity
Reflectivity Model
Marmousi Model
0 X (km) 2
0
1
Z (
km
)
0
1
Z (
km
)
Ghost FD
0 X (km) 2
Common Shot Gather0
2
T (
s)
![Page 18: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/18.jpg)
0 X (km) 2
Ghost LSRTM Image
Ghost FD
Marmousi Model
Ghost FD Conventional FD
Conventional FD
LSRTM Image
RTM ImageGhost RTM Image
0 X (km) 2
0
1
Z (
km
)
0
1
Z (
km
)
![Page 19: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/19.jpg)
Zoom Views
Ghost FD
Ghost LSRTM Image
Ghost FD Conventional FD
LSRTM Image
RTM ImageGhost RTM Image
Conventional FD
![Page 20: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/20.jpg)
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)
![Page 21: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/21.jpg)
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)
![Page 22: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/22.jpg)
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
)
![Page 23: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/23.jpg)
Ghost LSRTM Image LSRTM Image
Ghost FD
Ghost FD
Ghost RTM Image
Conventional FD
RTM Image
Conventional FD
Zoom Views
![Page 24: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/24.jpg)
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
![Page 25: Multi-source Least-squares Migration with Topography Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology.](https://reader035.fdocuments.us/reader035/viewer/2022062314/56649cc55503460f9498f000/html5/thumbnails/25.jpg)
Thank you!