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