Transcript No Slide Title

Wave-equation
migration velocity analysis
Paul Sava*
Biondo Biondi
Stanford University
Stanford University
[email protected]
Imaging=MVA+Migration
• Migration
• wavefield based
• Migration velocity analysis (MVA)
• traveltime based
• Compatible migration and MVA methods
[email protected]
Imaging: the “big picture”
wavefronts
wavefields
• Kirchhoff migration
• wave-equation migration
• traveltime tomography
• wave-equation MVA
(WEMVA)
[email protected]
Agenda
Scattering
Theoretical background
Imaging
Image perturbations
Wavefield extrapolation
WEMVA methodology
Born linearization
WEMVA applications
[email protected]
Wavefield scattering
[email protected]
Wavefield scattering
[email protected]
Scattered wavefield
Wavefield
perturbation
Medium
perturbation
[email protected]
Agenda
Scattering
Theoretical background
Imaging
Image perturbations
Wavefield extrapolation
WEMVA methodology
Born linearization
WEMVA applications
[email protected]
Imaging: Correct velocity
location
depth
depth
Background
velocity
location
Reflectivity
model
depth
depth
What migration does...
What the data tell us...
depth
Migrated
image
[email protected]
Imaging: Incorrect velocity
location
depth
depth
Perturbed
velocity
location
Reflectivity
model
depth
depth
What migration does...
What the data tell us...
depth
Migrated
image
[email protected]
Wave-equation MVA: Objective
location
depth
Velocity
perturbation
WEMVA
operator
min ΔR  L  s
Δs
image
perturbation
(known)
slowness
perturbation
(unknown)
location
depth
Image
perturbation
[email protected]
Comparison: WEMVA vs TT
Wave-equation MVA
Traveltime tomography
– migrated images
– picked traveltimes
– moveout and focusing
– amplitudes
– moveout
– parabolic wave equation
– multipathing
– eikonal equation
– slow
– fast
[email protected]
Comparison: WEMVA vs WET
Wave-equation MVA
– migrated images
Wave-equation tomography
– recorded data
– interpretive control
– parabolic wave equation
– two-way wave equation
– slow
– slow
[email protected]
Agenda
Scattering
Theoretical background
Imaging
Image perturbations
Wavefield extrapolation
WEMVA methodology
Born linearization
WEMVA applications
[email protected]
Image perturbations
location
angle
WEMVA
operator
depth
min ΔR  L  s
Δs
image
perturbation
(known)
Focusing
Flatness
slowness
perturbation
(unknown)
Residual process:
• moveout
• migration
• focusing
[email protected]
Image perturbations
 1
 1
 1
[email protected]
Agenda
Scattering
Theoretical background
Imaging
Image perturbations
Wavefield extrapolation
WEMVA methodology
Born linearization
WEMVA applications
[email protected]
Wavefield extrapolation
dW
  ik z W
dz
Double Square-Root Equation
Fourier Finite Difference
Generalized Screen Propagator
z  Δz
W
ik z Δz
e
z
W
W
z  Δz
z  Δz
0
W
dk z
 kz 0ik z0 Δz  βΔs
Δs
 ikk z Δz
ds s s0
e
βΔs
[email protected]
“Wave-equation” migration
z
s0
z Δz
z  Δz
0
W
[email protected]
Slowness perturbation
z
s0
s 0  Δs
z Δz
z  Δz
0
W
z  Δz βΔs
0
W
e
[email protected]
Wavefield perturbation
z
s 0  Δs
s0
z Δz
background
wavefield

ΔW
ΔW Δs
 W0 e
wavefield
perturbation
βΔs

1
slowness
perturbation
[email protected]
Agenda
Scattering
Theoretical background
Imaging
Image perturbations
Wavefield extrapolation
WEMVA methodology
Born linearization
WEMVA applications
[email protected]
Born approximation

ΔW  W0 e
βΔs
WEMVA
operator

1
Non-linear WEMVA
i
e  1  i
e
min ΔR  L  s
ΔWΔs  W0βΔs
image
perturbation
Born
linearization
(known)
slowness
perturbation
(unknown)
i
Small perturbations!
Unit circle
[email protected]
Agenda
Scattering
Theoretical background
Imaging
Image perturbations
Wavefield extrapolation
WEMVA methodology
Born linearization
WEMVA applications
[email protected]
Applications
• “Image perturbation”
• image difference
• image “differential”
• Examples
– Structural imaging
– Overpressure prediction
– 4-D seismic monitoring
– Diffraction focusing MVA
[email protected]
Application 1: Structural imaging
• Velocity analysis in complex areas
• multipathing
• high velocity contrast
• Full images vs. picked events
• Spatial focusing + offset focusing
• Traveltimes & amplitudes
[email protected]
Structural imaging: methodology
Data
Velocity
Image
R0
D
V
R
R1
min ΔR  L  s
Image
perturbation
Δs
[email protected]
Structural imaging: example
Location [km]
Depth [km]
[email protected]
Application 2: Overpressure
Complicated
propagation
Complicated
salt
Overpressure
zone
[email protected]
Overpressure: motivation
• Pressure creates time/moveout changes
• cannot be picked with enough accuracy
• Complicated overburden
• ray-based methods fail
[email protected]
Overpressure: methodology
Data
Velocity
Image
R0
D
V
R
R1
min ΔR  L  s
Image
perturbation
Δs
[email protected]
Overpressure: proof of concept
[email protected]
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
[email protected]
4D monitoring: methodology
Data
Velocity
D0
Image
R0
V
D1
min ΔR  L  s
R
R1
4D difference
data
Δs
[email protected]
4D monitoring: proof of concept
[email protected]
Application 4: Focusing MVA
• Moveout information
• missing or
• hard to use
moveout
focusing
• Focusing information
• ignored by moveout / traveltime based methods
[email protected]
Focusing MVA: methodology
Data
Velocity
Image
R0
D
V
R
R1
min ΔR  L  s
Image
perturbation
Δs
[email protected]
Focusing MVA: proof of concept
[email protected]
Agenda
Scattering
Theoretical background
Imaging
Image perturbations
Wavefield extrapolation
WEMVA methodology
Born linearization
WEMVA applications
[email protected]
WEMVA summary
• Methodology
– “wave-equation”
– image optimization
• focusing and moveouts
– interpretive control
• Applications
– any image perturbation
• repeated images over time
• optimized and reference images
[email protected]