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 qq  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 tt dd RR

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 tt dd RR 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 RR RR  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