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Prestack MigrationPrestack Migration
Migration Migration
IntuitiveIntuitiveLeast SquaresLeast Squares
Green’s TheoremGreen’s Theorem
3D Prestack Diffraction Stack Migration3D Prestack Diffraction Stack Migration
ggss
xx
Motivation: ZO only good if no lateral vel changeMotivation: ZO only good if no lateral vel change
Trial image pt xTrial image pt x m(m(xx) = ) =
3D Prestack Diffraction Stack Migration3D Prestack Diffraction Stack Migration
ggss
xx
== d(x’d(x’, , + + ))ssxxs,s,gg xxgg
OutlineOutline
Prestack DS Migration TheoryPrestack DS Migration Theory
RTMRTM
MATLAB CodeMATLAB CodeRTM vs Poststack vs PrestackRTM vs Poststack vs Prestack
Prestack MigrationPrestack Migration
Question: Question: Why Prestack when poststack Why Prestack when poststack migration seems good enough?migration seems good enough?
Answer: Answer: Stacking to get stacked section assumes Stacking to get stacked section assumes layered medium assumption.layered medium assumption.
Solution: Solution: Migrate shot gathers so no layerMigrate shot gathers so no layer assumption needed. This is prestackassumption needed. This is prestack migration.migration.
Narrow band case: direct wave correlated with dataNarrow band case: direct wave correlated with data
Diffraction Stack Migration: PrestackDiffraction Stack Migration: Prestack
ssxx xxgg
ss
xx
gg
Where is scatterer?Where is scatterer?
T(s,g) =T(s,g) = ssxx xxgg++
d(s,g, ) d(s,g, ) ssxx xxgg++ ss,g,g
Down timeDown time Up timeUp time
W(W( ) )~~A(s,A(s,xx))
ssxxiiee
xx
xxggiiee
A(g,A(g,xx))
d(s,g) =d(s,g) = m(x)m(x)~~
115.
Diffraction Stack Modeling: PrestackDiffraction Stack Modeling: Prestack
~~ 22
dd = = L L mmm m = = L L ddTT
W(W( ) )~~A(s,A(s,xx))
ssxxiiee
s,gs,g
xxggiiee
A(g,A(g,xx))m(x) =m(x) = d(s,g)d(s,g)dd dd~~
dd(s(s,g, ,g, + + ))ssxx xxgg
A(s,A(s,xx))
s,gs,g A(A(xx,g),g)==
**-- --
Broadband caseBroadband caseW(W( )=1 )=1~~
Narrow band case: direct wave correlated with dataNarrow band case: direct wave correlated with data
....
115.
Diffraction Stack Migration: PrestackDiffraction Stack Migration: Prestack
~~
m(x)m(x)
22
m m = = L L ddTT
OutlineOutline
Prestack DS Migration TheoryPrestack DS Migration Theory
RTMRTM
MATLAB CodeMATLAB CodeRTM vs Poststack vs PrestackRTM vs Poststack vs Prestack
Prestack RTM vs One-way Wave Equation Prestack RTM vs One-way Wave Equation MigrationMigration
Prestack RTM vs One-way Wave Prestack RTM vs One-way Wave Equation MigrationEquation Migration
Trial image pt xTrial image pt x
ZO Diffraction Stack MigrationZO Diffraction Stack Migrationd (d (gg, ) , )
xxggm(m(xx) = ) = gg
xx
Trial image pt xTrial image pt x d (d (gg, ) , ) xxggm(m(xx) = ) =
gg
xx
Migration ImageMigration Image
ZO Diffraction Stack MigrationZO Diffraction Stack Migration
2D dot product of migration 2D dot product of migration Operator and d(g,t)Operator and d(g,t)
Trial image pt xTrial image pt x d (d (gg, ) , ) xxggm(m(xx) = ) =
gg
xx
ZO Reverse Time MigrationZO Reverse Time Migration
~Scattered RTM~Scattered RTM
Super-resolutionSuper-resolution
Trial image pt xTrial image pt x d (d (gg, ) , ) xxggm(m(xx) = ) =
gg
xx
ZO Reverse Time MigrationZO Reverse Time Migration
~Scattered RTM~Scattered RTM
Super-resolutionSuper-resolution
Prestack RTM vs One-way Wave Equation Prestack RTM vs One-way Wave Equation MigrationMigration
OutlineOutline
Prestack DS Migration TheoryPrestack DS Migration Theory
RTMRTM
MATLAB CodeMATLAB CodeRTM vs Poststack vs PrestackRTM vs Poststack vs Prestack
Types of TraveltimesTypes of TraveltimesShortest Traveltime or Shortest Raypath Shortest Traveltime or Shortest Raypath
Maximum Energy TraveltimesMaximum Energy TraveltimesShortest path rayShortest path ray
Shortest traveltime Shortest traveltime rayray
Maximum energy rayMaximum energy ray
Poststack vs Prestack MigrationPoststack vs Prestack Migration
Poststack vs Prestack MigrationPoststack vs Prestack Migration
RRTM vs KM MigrationRRTM vs KM Migration
RRTM vs KM MigrationRRTM vs KM Migration
Prestack RTM vs One-Way Mig.Prestack RTM vs One-Way Mig.
Prestack RTM vs One-Way Mig.Prestack RTM vs One-Way Mig.
OutlineOutline
Prestack DS Migration TheoryPrestack DS Migration Theory
RTMRTM
DS MATLAB CodeDS MATLAB CodeRTM vs Poststack vs PrestackRTM vs Poststack vs Prestack
MATLAB Prestack MigrationMATLAB Prestack Migration
MATLAB Inefficient Prestack MATLAB Inefficient Prestack MigrationMigration
for isx=1:nx % Loop over shotfor isx=1:nx % Loop over shot for igx=1:nx % Loop over receiversfor igx=1:nx % Loop over receivers for ix=1:nx % Loop over model xfor ix=1:nx % Loop over model x for iz=1:nx % Loop over model zfor iz=1:nx % Loop over model z t=timer(t=timer(ix,izix,iz,isx,isx)+timer()+timer(ix,izix,iz,igx,igx)) sample=gather(sample=gather(isxisx,,igxigx,t) % ,t) % Shot gather has 2 time derivativesShot gather has 2 time derivatives
mig(mig(ix,izix,iz)=mig)=mig(ix,iz(ix,iz)+sample)+sample endend endend endendendend
MATLAB Prestack MigrationMATLAB Prestack Migration
Prestack MigrationPrestack Migration
1. No assumption about velocity model1. No assumption about velocity model
2. More sensitive to velocity model errors2. More sensitive to velocity model errors compared to poststack migrationcompared to poststack migration
3. More than 10 – 10 times slower than3. More than 10 – 10 times slower than poststack migrationpoststack migration
4. More sensitive to velocity model than time4. More sensitive to velocity model than time migrationmigration
2 6
Poststack vs Prestack MigrationPoststack vs Prestack Migration
Poststack vs Prestack MigrationPoststack vs Prestack Migration
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