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