Wave-equation MVA by inversion of differential image perturbations Paul Sava & Biondo Biondi Stanford University SEP
Motivation
Wave-equation MVA (WEMVA) Band-limited Multi-pathing Resolution Born approximation –small anomaly Rytov approximation –phase unwrapping
Wave-equation MVA (WEMVA) WE tomography –data space WE MVA –image space
Outline 1.WEMVA overview 2.Born image perturbation 3.Differential image perturbation 4.Example
A tomography problem Traveltime MVA Wave-equation tomography Wave-equation MVA qq t traveltime d data R image L ray fieldwavefield
WEMVA: main idea
Born approximation
WEMVA: objective function slowness perturbation image perturbation slowness perturbation (unknown) Linear WEMVA operator image perturbation (known)
WEMVA: objective function Traveltime MVA Wave-equation tomography Wave-equation MVA tt dd RR
Fat ray: GOM example
Outline 1.WEMVA overview 2.Born image perturbation 3.Differential image perturbation 4.Example
“Data” estimate Traveltime MVA Wave-equation tomography Wave-equation MVA tt dd RR ray tracing data modeling residual migration
Prestack Stolt residual migration Background image R 0 Velocity ratio RR0R0
Prestack Stolt residual migration Image perturbation RR0R0
Born approximation
Residual migration: the problem Correct velocityIncorrect velocity Zero offset image Angle gathers Zero offset image Angle gathers
Born approximation
Outline 1.WEMVA overview 2.Born image perturbation 3.Differential image perturbation 4.Example
Differential image perturbation Image difference Image differential ComputedMeasured
Differential image perturbation RR RR R
Phase perturbation
Differential image perturbation
Born approximation
Example: background image Zero offset image Angle gathers Background image
Example: differential image Zero offset image Angle gathers Differential image
Example: slowness inversion Slowness perturbation Image perturbation
Example: updated image Updated slowness Updated image
Example: correct image Correct slowness Correct image
Outline 1.WEMVA overview 2.Born image perturbation 3.Differential image perturbation 4.Example
Field data example North Sea –Salt environment –Subset –One non-linear iteration Migration (background image) Residual migration (image perturbation) Slowness inversion (slowness perturbation) Slowness update (updated slowness) Re-migration (updated image) location depth
locationdepth
depth velocity ratio
locationdepth
locationdepthlocation
locationdepthlocation
locationdepth
locationdepth
Summary MVA –Wavefield extrapolation methods –Born linearization –Differential image perturbations Key points –Band-limited (sharp velocity contrasts) –Multi-pathing (complicated wavefields) –Resolution (frequency redundancy)
MVA information (a) Traveltime MVAWave-equation MVA Offset focusing (flat ADCIG) z z xx
MVA information (b) Traveltime MVAWave-equation MVA Offset focusing (flat ADCIG) Spatial focusing z z xx
MVA information (c) Traveltime MVAWave-equation MVA Offset focusing (flat ADCIG) Spatial focusing Frequency redundancy
WEMVA cost reduction Full image –Offset focusing –Spatial focusing –Frequency Normal incidence image –Spatial focusing –“fat” rays
Another example
Example: correct model Zero offset image Angle gathers
Example: background model Zero offset image Angle gathers
Example: correct perturbation Zero offset image Angle gathers
Example: differential perturbation Zero offset image Angle gathers
Example: perturbations comparison Differential Difference Correct
Example: differential perturbation Zero offset image Angle gathers
Example: difference perturbation Zero offset image Angle gathers
Example: updated model Zero offset image Angle gathers
Example: correct model Zero offset image Angle gathers