[email protected] wave-equation migration velocity analysis beyond the born approximation paul...
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![Page 1: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/1.jpg)
Wave-equation migration velocity analysis
beyond the Born approximation
Paul Sava* Stanford University
Sergey Fomel UT Austin (UC Berkeley)
![Page 2: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/2.jpg)
Imaging=MVA+Migration
• Migration• wavefield based
• Migration velocity analysis (MVA)• traveltime based
• Compatible migration and MVA methods
![Page 3: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/3.jpg)
Imaging: the “big picture”
• Kirchhoff migration
• traveltime tomography
wavefronts
• wave-equation migration
• wave-equation MVA (WEMVA)
wavefields
![Page 4: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/4.jpg)
Agenda
Theoretical background
WEMVA methodology
Scattering
Imaging
Image perturbations
Wavefield extrapolation
Born linearization
Alternative linearizations
![Page 8: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/8.jpg)
Agenda
Theoretical background
WEMVA methodology
Scattering
Imaging
Image perturbations
Wavefield extrapolation
Born linearization
Alternative linearizations
![Page 9: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/9.jpg)
Imaging: Correct velocity
Background velocity
Migrated image
Reflectivity model
What the data tell us...What migration does...
location
depth
location
depth
depthdepth
depth
![Page 10: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/10.jpg)
Imaging: Incorrect velocity
Perturbed velocity
Migrated image
Reflectivity model
What the data tell us...What migration does...
location
depth
location
depth
depthdepth
depth
![Page 11: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/11.jpg)
Wave-equation MVA: Objective
Velocity perturbation
Image perturbation
slownessperturbation(unknown)
WEMVAoperator
imageperturbation
(known)
sLΔRminΔs
location
depth
location
depth
![Page 12: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/12.jpg)
– migrated images
– moveout and focusing– use amplitudes
– parabolic wave equation– multipathing
– slow
– picked traveltimes
– moveout– ignore amplitudes
– eikonal equation
– fast
Comparison of MVA methods
• Wave-equation MVA • Traveltime tomography
![Page 13: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/13.jpg)
Agenda
Theoretical background
WEMVA methodology
Scattering
Imaging
Image perturbations
Wavefield extrapolation
Born linearization
Alternative linearizations
![Page 14: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/14.jpg)
What is the image perturbation?
Focusing Flatness Residual process:• moveout• migration• focusing
slownessperturbation(unknown)
WEMVAoperator
imageperturbation
(known)
sLΔRminΔs
location
depth
angle
![Page 15: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/15.jpg)
Agenda
Theoretical background
WEMVA methodology
Scattering
Imaging
Image perturbations
Wavefield extrapolation
Born linearization
Alternative linearizations
![Page 16: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/16.jpg)
Double Square-Root Equation
Wikdz
dWz
Δsds
dkkk
0
0
ss
zzz
Fourier Finite DifferenceGeneralized Screen Propagator
Δzikz
Δzzze
W
W
Wavefield extrapolation
βΔsΔzz
0
Δzz
eW
W
βΔsΔzikΔzik0zz
![Page 19: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/19.jpg)
1eWΔW βΔs0
slownessperturbation
backgroundwavefield
wavefieldperturbation
ΔW
Δs
Wavefield perturbation
z
Δzz0s Δss0
![Page 20: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/20.jpg)
Agenda
Theoretical background
WEMVA methodology
Scattering
Imaging
Image perturbations
Wavefield extrapolation
Born linearization
Alternative linearizations
![Page 21: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/21.jpg)
Born approximation
iei 1
ie
Small perturbations!
Born linearization
Non-linear WEMVA
1eWΔW βΔs0
βΔsWΔW 0slowness
perturbation(unknown)
WEMVAoperator
imageperturbation
(known)
sLΔRminΔs
Unit circle
![Page 22: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/22.jpg)
sLΔRminΔs
Does it work?What if the perturbations are not small?
Location [km]
Depth [km
]
![Page 25: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/25.jpg)
Agenda
Theoretical background
WEMVA methodology
Scattering
Imaging
Image perturbations
Wavefield extrapolation
Born linearization
Alternative linearizations
![Page 26: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/26.jpg)
Wavefield continuation
Wikdz
dWz βΔs
0
eW
W
Bilinear
Implicit
βΔs2
βΔs2
W
W
0
βΔs1
1
W
W
0
Explicit βΔs1W
W
0
(Born approximation)
![Page 27: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/27.jpg)
Exponential approximations
ξβΔs1
βΔsξ11eβΔs
0,1ξ
0ξ
1ξ
0.5ξ
Wikdz
dWz βΔs
0
eW
W
Unit circle
![Page 28: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/28.jpg)
1eWΔW βΔs0
A family of linearizations
ξβΔs1
βΔsξ11eβΔs
0,1ξ
βΔsξΔWWΔW 0Linear WEMVA
slownessperturbation(unknown)
WEMVAoperator
imageperturbation
(known)
sLΔRminΔs
![Page 30: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/30.jpg)
Agenda
Theoretical background
WEMVA methodology
Scattering
Imaging
Image perturbations
Wavefield extrapolation
Born linearization
Alternative linearizations
![Page 31: Paul@sep.stanford.edu Wave-equation migration velocity analysis beyond the Born approximation Paul Sava* Stanford University Sergey Fomel UT Austin (UC](https://reader030.vdocuments.site/reader030/viewer/2022032800/56649d375503460f94a1046c/html5/thumbnails/31.jpg)
Summary
• Wave-equation MVA• wavefield-continuation• improved focusing • image space (improve the image)• interpretation guided
• Improved WEMVA• better approximations• no additional cost• further refinement