Wave-equation migration velocity analysis Biondo Biondi Stanford Exploration Project Stanford University Paul Sava

Fundamental ideas Correct 3-D imaging / attribute analysis require correct velocity –“Everything depends on V(x,y,z)” Jon Claerbout, 1999 Migration and velocity analysis are intrinsically connected –“The major tool to estimate velocity is to migrate the data” Samuel Gray, 1999 Wave phenomena are described by multipathing in complex geology

The goal Estimate 3-D velocity –iterative migration –wave-equation techniques Improve the quality of the migrated image –Exploit residual migration Fit the data

High-frequency vs. finite-frequency migration Kirchhoff Migration WE Migration High-frequencyFinite-frequency migration MVA Traveltime tomography Wave-equation MVA fast & inaccurateslow & accurate

WEMVA theory DATA SLOWNESS IMAGEWAVEFIELD DATA SLOWNESS WAVEFIELDIMAGEWAVEFIELD SLOWNESS perturbation Scattered wavefield WAVEFIELD perturbation IMAGE perturbation WAVEFIELD perturbation Scattered wavefield

WEMVA flow-chart Data Starting image Improved image Perturbation in image Perturbation in slowness Background slowness Background wavefield

Synthetic model

WEMVA theory DATA SLOWNESS IMAGEWAVEFIELD DATA SLOWNESS WAVEFIELDIMAGEWAVEFIELD SLOWNESS perturbation Scattered wavefield WAVEFIELD perturbation IMAGE perturbation WAVEFIELD perturbation Scattered wavefield

What is F? Linear operator –evaluated recursively during depth continuation –incorporates a scattering operator –first-order Born approximation »small perturbations a depth continuation operator the background wavefield

What is  R? What is  S?  S: the slowness perturbation that explains the improvement of the image. –What is an improved image?  R: the difference between the current image and an improved version of it.

What is an improved image? Pre-stack wave-equation migration –Pre-stack images - described by an “offset” axis offset aperture angle Angle-domain Common Image Gathers (CIG) –How to relate velocity and CIGs?

Velocity and CIGs Correct velocity - flat CIGs Incorrect velocity - non-flat CIGs more on angle-domain CIGs: Marie Prucha –(Wednesday, AVO applications) The goal: create an image with flat CIGs at every point

Velocity and CIGs A: original slowness D: true slowness

Velocity and CIGs A: original slowness D: true slowness

How do we flatten CIGs? Residual move-out energy does not move between midpoints Residual migration energy moves between midpoints –3-D pre-stack Stolt residual migration

Pre-stack Stolt residual migration Operates in the  k domain. Fast and robust Velocity-independent –new images do not depend on the new velocity, but on its ratio to the original velocity. Velocity ratio

Stolt pre-stack residual migration RST Original prestack image Extract Improved prestack image Interpretative QC Different ratios

Residual migration Flat CIGs = strong stack along the aperture angle axis. no residual migration for ratio=1

Residual migration Flat CIGs = strong stack along the aperture angle axis. no residual migration for ratio=1

Residual migration Flat CIGs = strong stack along the aperture angle axis. no residual migration for ratio=1

Best focused image –Extract the flattest image from the pre-stack images. depth location ratio –Stack along the angle axis »one stack value for each residual migration ratio –Pick the most energetic value on the stack.

Residual migration - picking For large perturbations scale down the picking ratio scale up the inverted velocity

WEMVA flow-chart Data Starting image Improved image Perturbation in image Perturbation in slowness Background slowness Background wavefield

Image perturbation

WEMVA flow-chart Data Starting image Improved image Perturbation in image Perturbation in slowness Background slowness Background wavefield

Inversion Iteration

Inversion Iteration

Inversion Iteration

Inversion

WEMVA flow-chart Data Starting image Improved image Perturbation in image Perturbation in slowness Background slowness Background wavefield

Image improvement A: original slowness B: updated slowness (first pass) C: updated slowness (second pass) D: true slowness

Image improvement A: original slowness B: updated slowness (first pass) C: updated slowness (second pass) D: true slowness

Image improvement A: original slowness B: updated slowness (first pass) C: updated slowness (second pass) D: true slowness

Image improvement A: original slowness B: updated slowness (first pass) C: updated slowness (second pass) D: true slowness

WEMVA - Conclusion wave-equation techniques iterative migration use the velocity information in CIGs improve the quality of the image interpretative approach