Download - Prestack Migration MigrationIntuitive Least Squares Green’s Theorem

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


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


RTMRTM


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

Prestack RTM vs One-way Wave Equation Prestack RTM vs One-way Wave Equation MigrationMigration

OutlineOutline


RTMRTM


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

RRTM vs KM MigrationRRTM vs KM Migration

Prestack RTM vs One-Way Mig.Prestack RTM vs One-Way Mig.

OutlineOutline


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


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

Download - Prestack Migration MigrationIntuitive Least Squares Green’s Theorem

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