anti-aliasing filter for reverse-time migration · anti-aliasing ˜lter for kirchho˚ migration but...

Anti-aliasing Filter for Reverse-time MigrationG. Zhan* and G.T.Schuster

We develop an anti-aliasing �lter for reverse-time migration (RTM). It is similar to the traditional antialiasing �lter used for Kirchho� migration(KM) except it is applied to both primary and multiple re�ection events.

01

INTRODUCTION

RTM operation can be interpreted as a dot-product of the kernel �ngerprint G(g|x)G(x|s) with the common-shot-gather�ngerprint D(g|s)

and the result m(x) is the RTM image. If the trial image point is at an actual scatterer, then the �ngerprints ofthe CSG and migration kernel will be a good match and the dot-productwill return a large value.

If the trial image point is far from any re�ector, then the CSG and kernel �ngerprints will be mismatched and the dot-product will yield a low magnitude.

This description de�nes the dot-product interpretation of migration,and we will now refer to G(g|x)G(x|s) and D(g|s) as kernel and data �ngerprints, respectively.

Migration as Fingerprint Matching

METHOD

Kirchhoff migration operator

t

x

Primary migration operator

t

x

Multiplemigration operators

t x t

x

Anti-aliasing Filter

KM Fingerprint Matching RTM Fingerprint Matching

x

t

Compute the migration kernel �ngerprint and measure the local dip;step1

Apply low-pass-�lters to every time sample of the kernel so that theanti-aliasing condition is satis�ed;

Take dot-products of the �ltered migration kernel with recorded datato get the image. The resulting image will be free of aliasing artifacts.

step2

step3

RESULTS

Synthetic Model and Shot-gather

CONCLUSIONS

An anti-aliasing �lter for RTM is proposed. It is similar to the traditionalanti-aliasing �lter for Kirchho� migration but accounts for both primaryand multiples.

The resulting RTM image is free of aliasing artifacts.Advantage

Migration Fingerprint

Kirchho� Migration Image

Reverse-time Migration Image

Disadvantage

The main disadvantage of applying this anti-aliasing �lter is the increasedcomputational cost compared to standard RTM.

KM RTM

aliased anti-aliased

aliased anti-aliased