Analytical image perturbations for waveequation migration velocity analysis

Analytical image perturbations for wave-equation migration velocity analysis Paul Sava & Biondo Biondi Stanford University paul@sep. stanford. edu

Wave-equation MVA (WEMVA) • Wavefield-based MVA method • Closely related to – Wave-equation migration – Wave-equation tomography • Benefits – Finite-frequency – Multipathing – Hi resolution paul@sep. stanford. edu

A tomography problem Dq L Traveltime tomography/MVA Wave-equation tomography Wave-equation MVA Dt Dd DR traveltime data image ray field wavefield paul@sep. stanford. edu

Outline 1. WEMVA review 2. Image perturbation 3. Field data example paul@sep. stanford. edu

WEMVA: main idea paul@sep. stanford. edu

Born approximation paul@sep. stanford. edu

WEMVA: objective function Linear WEMVA operator slowness perturbation image perturbation (known) slowness perturbation (unknown) image perturbation paul@sep. stanford. edu

Slowness backprojection slowness perturbation image perturbation paul@sep. stanford. edu

MVA information Traveltime MVA • Wave-equation MVA • • • Offset focusing (flat gathers) Spatial focusing Frequency redundancy g x z z paul@sep. stanford. edu

Outline 1. WEMVA review 2. Image perturbation 3. Field data example paul@sep. stanford. edu

“Data” estimate Traveltime MVA Wave-equation tomography Wave-equation MVA Dt Dd DR ray tracing data modeling residual migration paul@sep. stanford. edu

Prestack Stolt residual migration • Background image • Velocity ratio R 1 r r Rr • Image perturbation paul@sep. stanford. edu

Synthetic model Zero offset image Correct velocity Incorrect velocity Angle gathers paul@sep. stanford. edu

Residual migration: the problem paul@sep. stanford. edu

Differential image perturbation Image difference Image differential Computed Measured paul@sep. stanford. edu

Background image Zero offset image Background image Angle gathers paul@sep. stanford. edu

Differential image Zero offset image Differential image Angle gathers paul@sep. stanford. edu

Image to slowness perturbation Image perturbation Slowness perturbation paul@sep. stanford. edu

Image comparison Zero offset image Correct slowness Updated slowness paul@sep. stanford. edu

Outline 1. WEMVA review 2. Image perturbation 3. Field data example paul@sep. stanford. edu

Field data example • North Sea depth – Salt environment location – One non-linear iteration • • • Migration Residual migration Slowness inversion Slowness update Re-migration (background image) (image perturbation) (slowness perturbation) (updated slowness) (updated image) paul@sep. stanford. edu

Background slowness depth Background image Zero offset image depth location Angle gathers paul@sep. stanford. edu

Semblance depth Angle-gathers velocity ratio paul@sep. stanford. edu

“Ratio” map depth Background image Zero offset image location paul@sep. stanford. edu

Image perturbation depth Background image Zero offset image location paul@sep. stanford. edu

Image perturbation depth Slowness perturbation Zero offset image location paul@sep. stanford. edu

Background slowness depth Background image Zero offset image depth location Angle gathers paul@sep. stanford. edu

Updated slowness depth Updated image Zero offset image depth location Angle gathers paul@sep. stanford. edu

“Correct” slowness depth “Correct” image Zero offset image depth location Angle gathers paul@sep. stanford. edu

Summary • Wave-equation MVA – – Finite frequency Multipathing Hi resolution Image space objective function • Image perturbation – From prestack Stolt residual migration – Differential method – Compliant with the Born approximation paul@sep. stanford. edu