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Wave-equation migration velocity analysis
Paul Sava* Stanford University
Biondo Biondi Stanford University
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Imaging=MVA+Migration
• Migration• wavefield based
• Migration velocity analysis (MVA)• traveltime based
• Compatible migration and MVA methods
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Imaging: the “big picture”
• Kirchhoff migration
• traveltime tomography
wavefronts
• wave-equation migration
• wave-equation MVA (WEMVA)
wavefields
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Agenda
Theoretical background
WEMVA methodology
Scattering
Imaging
Image perturbations
Wavefield extrapolation
Born linearization
WEMVA applications
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Agenda
Theoretical background
WEMVA methodology
Scattering
Imaging
Image perturbations
Wavefield extrapolation
Born linearization
WEMVA applications
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Imaging: Correct velocity
Background velocity
Migrated image
Reflectivity model
What the data tell us...What migration does...
location
depth
location
depth
depthdepth
depth
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Imaging: Incorrect velocity
Perturbed velocity
Migrated image
Reflectivity model
What the data tell us...What migration does...
location
depth
location
depth
depthdepth
depth
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Wave-equation MVA: Objective
Velocity perturbation
Image perturbation
slownessperturbation(unknown)
WEMVAoperator
imageperturbation
(known)
sLΔRminΔs
location
depth
location
depth
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– migrated images
– moveout and focusing
– amplitudes
– parabolic wave equation
– multipathing
– slow
– picked traveltimes
– moveout
– eikonal equation
– fast
Comparison: WEMVA vs TT
Wave-equation MVA Traveltime tomography
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– migrated images
– interpretive control
– parabolic wave equation
– slow
– recorded data
– two-way wave equation
– slow
Comparison: WEMVA vs WET
Wave-equation MVA Wave-equation tomography
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Agenda
Theoretical background
WEMVA methodology
Scattering
Imaging
Image perturbations
Wavefield extrapolation
Born linearization
WEMVA applications
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Image perturbations
Focusing Flatness Residual process:• moveout• migration• focusing
slownessperturbation(unknown)
WEMVAoperator
imageperturbation
(known)
sLΔRminΔs
location
depth
angle
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Agenda
Theoretical background
WEMVA methodology
Scattering
Imaging
Image perturbations
Wavefield extrapolation
Born linearization
WEMVA applications
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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
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1eWΔW βΔs0
slownessperturbation
backgroundwavefield
wavefieldperturbation
ΔW
Δs
Wavefield perturbation
z
Δzz0s Δss0
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Agenda
Theoretical background
WEMVA methodology
Scattering
Imaging
Image perturbations
Wavefield extrapolation
Born linearization
WEMVA applications
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Born approximation
iei 1
ie
Small perturbations!
Born linearization
Non-linear WEMVA
1eWΔW βΔs0
βΔsWΔW 0slowness
perturbation(unknown)
WEMVAoperator
imageperturbation
(known)
sLΔRminΔs
Unit circle
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Agenda
Theoretical background
WEMVA methodology
Scattering
Imaging
Image perturbations
Wavefield extrapolation
Born linearization
WEMVA applications
![Page 25: Paul@sep.stanford.edu Wave-equation migration velocity analysis Paul Sava* Stanford University Biondo Biondi Stanford University](https://reader035.vdocuments.us/reader035/viewer/2022062715/56649d7e5503460f94a6150a/html5/thumbnails/25.jpg)
Applications
• “Image perturbation”• image difference• image “differential”
• Examples– Structural imaging– Overpressure prediction– 4-D seismic monitoring– Diffraction focusing MVA
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Application 1: Structural imaging
• Velocity analysis in complex areas• multipathing• high velocity contrast
• Full images vs. picked events
• Spatial focusing + offset focusing
• Traveltimes & amplitudes
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Structural imaging: methodology
Data
0R
1R
DV
ImageVelocity
R
Image
perturbationsLΔRminΔs
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Location [km]
Depth [km
]
Location [km]
Depth [km
]
Location [km]
Depth [km
]
Location [km]
Depth [km
]
Structural imaging: example
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Application 2: Overpressure
Overpressure zone
Complicated salt
Complicated propagation
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Overpressure: motivation
• Pressure creates time/moveout changes• cannot be picked with enough accuracy
• Complicated overburden • ray-based methods fail
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Overpressure: methodology
Data
0R
1R
DV
ImageVelocity
R
Image
perturbationsLΔRminΔs
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Application 3: 4D monitoring
• Small traveltime changes• cannot be picked with enough accuracy
• Amplitude variations• ignored by traveltime methods
• Cumulative phase and amplitude effects• mask deeper effects
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4D monitoring: methodology
Data
0R
1R
0D
1DV
ImageVelocity
R
4D difference datasLΔRmin
Δs
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Application 4: Focusing MVA
• Moveout information• missing or• hard to use
• Focusing information• ignored by moveout / traveltime based methods
focusing moveout
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Focusing MVA: methodology
Data
0R
1R
DV
ImageVelocity
R
Image
perturbationsLΔRminΔs
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Agenda
Theoretical background
WEMVA methodology
Scattering
Imaging
Image perturbations
Wavefield extrapolation
Born linearization
WEMVA applications
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WEMVA summary
• Methodology– “wave-equation”– image optimization
• focusing and moveouts
– interpretive control
• Applications – any image perturbation
• repeated images over time• optimized and reference images