# prestack migration migrationintuitive least squares green’s theorem

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Prestack MigrationMigration

3D Prestack Diffraction Stack MigrationgsxMotivation: ZO only good if no lateral vel change

Trial image pt xm(x) = 3D Prestack Diffraction Stack Migrationgsx

OutlinePrestack DS Migration TheoryRTMMATLAB CodeRTM vs Poststack vs Prestack

Prestack MigrationQuestion: Why Prestack when poststack migration seems good enough?Answer: Stacking to get stacked section assumes layered medium assumption.Solution: Migrate shot gathers so no layer assumption needed. This is prestack migration.

Narrow band case: direct wave correlated with dataDiffraction Stack Migration: PrestackWhere is scatterer?Down timeUp time

A(s,x)sxiexgieA(g,x)d(s,g) =115.Diffraction Stack Modeling: Prestack~d = L m

A(s,x)sxiexgieA(g,x)m(x) =d(s,g)~*--Narrow band case: direct wave correlated with data..115.Diffraction Stack Migration: Prestack~m(x)

OutlinePrestack DS Migration TheoryRTMMATLAB CodeRTM vs Poststack vs Prestack

Prestack RTM vs One-way Wave Equation Migration

Prestack RTM vs One-way Wave Equation Migration

Trial image pt xZO Diffraction Stack Migration

Trial image pt xMigration ImageZO Diffraction Stack Migration2D dot product of migration Operator and d(g,t)

Trial image pt xZO Reverse Time Migration

Trial image pt xZO Reverse Time Migration

Prestack RTM vs One-way Wave Equation Migration

OutlinePrestack DS Migration TheoryRTMMATLAB CodeRTM vs Poststack vs Prestack

Types of TraveltimesShortest Traveltime or Shortest Raypath Maximum Energy Traveltimes

Poststack vs Prestack Migration

Poststack vs Prestack Migration

RRTM vs KM Migration

RRTM vs KM Migration

Prestack RTM vs One-Way Mig.

Prestack RTM vs One-Way Mig.

OutlinePrestack DS Migration TheoryRTMDS MATLAB CodeRTM vs Poststack vs Prestack

MATLAB Prestack Migration

MATLAB Inefficient Prestack Migrationfor isx=1:nx % Loop over shot for igx=1:nx % Loop over receivers for ix=1:nx % Loop over model x for iz=1:nx % Loop over model z t=timer(ix,iz,isx)+timer(ix,iz,igx) sample=gather(isx,igx,t) % Shot gather has 2 time derivatives mig(ix,iz)=mig(ix,iz)+sample end end endend

MATLAB Prestack Migration

Prestack Migration1. No assumption about velocity model2. More sensitive to velocity model errors compared to poststack migration3. More than 10 10 times slower than poststack migration4. More sensitive to velocity model than time migration26

Poststack vs Prestack Migration

Poststack vs Prestack Migration

ZO Reverse Time Migration

Is Superresolution by RTM Achievable?Tucson, Arizona Test60 mThis is highest fruit on the tree..whom dare pick it?(Hanafy et al., 2008)

Is Superresolution by RTM Achievable?Tucson, Arizona Test60 mThis is highest fruit on the tree..whom dare pick it?(Hanafy et al., 2008, TLE)

It is often thought that RTM does not enjoy filtering tricks of KM such as U+D separation, obliquity factor, angle gather separation, anti-aliasing filter, etc. This is not true as shown above. The RTM formula is shown above in traditional form: apply adjoint Greens function to data and backpropagate data, then zero-lag correlation with source field. Rearranging brackets gives different interpretation: RTM is just like KM in the sense that you apply a dot product of the hyperbolas to the data to get migration image. In this case the hyperbolas conatin all the scattering events and the Greens functions are computed by FD solves rather than ray tracing.It is often thought that RTM does not enjoy filtering tricks of KM such as U+D separation, obliquity factor, angle gather separation, anti-aliasing filter, etc. This is not true as shown above. The RTM formula is shown above in traditional form: apply adjoint Greens function to data and backpropagate data, then zero-lag correlation with source field. Rearranging brackets gives different interpretation: RTM is just like KM in the sense that you apply a dot product of the hyperbolas to the data to get migration image. In this case the hyperbolas conatin all the scattering events and the Greens functions are computed by FD solves rather than ray tracing.It is often thought that RTM does not enjoy filtering tricks of KM such as U+D separation, obliquity factor, angle gather separation, anti-aliasing filter, etc. This is not true as shown above. The RTM formula is shown above in traditional form: apply adjoint Greens function to data and backpropagate data, then zero-lag correlation with source field. Rearranging brackets gives different interpretation: RTM is just like KM in the sense that you apply a dot product of the hyperbolas to the data to get migration image. In this case the hyperbolas conatin all the scattering events and the Greens functions are computed by FD solves rather than ray tracing.It is often thought that RTM does not enjoy filtering tricks of KM such as U+D separation, obliquity factor, angle gather separation, anti-aliasing filter, etc. This is not true as shown above. The RTM formula is shown above in traditional form: apply adjoint Greens function to data and backpropagate data, then zero-lag correlation with source field. Rearranging brackets gives different interpretation: RTM is just like KM in the sense that you apply a dot product of the hyperbolas to the data to get migration image. In this case the hyperbolas conatin all the scattering events and the Greens functions are computed by FD solves rather than ray tracing.It is often thought that RTM does not enjoy filtering tricks of KM such as U+D separation, obliquity factor, angle gather separation, anti-aliasing filter, etc. This is not true as shown above. The RTM formula is shown above in traditional form: apply adjoint Greens function to data and backpropagate data, then zero-lag correlation with source field. Rearranging brackets gives different interpretation: RTM is just like KM in the sense that you apply a dot product of the hyperbolas to the data to get migration image. In this case the hyperbolas conatin all the scattering events and the Greens functions are computed by FD solves rather than ray tracing.It is often thought that RTM does not enjoy filtering tricks of KM such as U+D separation, obliquity factor, angle gather separation, anti-aliasing filter, etc. This is not true as shown above. The RTM formula is shown above in traditional form: apply adjoint Greens function to data and backpropagate data, then zero-lag correlation with source field. Rearranging brackets gives different interpretation: RTM is just like KM in the sense that you apply a dot product of the hyperbolas to the data to get migration image. In this case the hyperbolas conatin all the scattering events and the Greens functions are computed by FD solves rather than ray tracing.It is often thought that RTM does not enjoy filtering tricks of KM such as U+D separation, obliquity factor, angle gather separation, anti-aliasing filter, etc. This is not true as shown above. The RTM formula is shown above in traditional form: apply adjoint Greens function to data and backpropagate data, then zero-lag correlation with source field. Rearranging brackets gives different interpretation: RTM is just like KM in the sense that you apply a dot product of the hyperbolas to the data to get migration image. In this case the hyperbolas conatin all the scattering events and the Greens functions are computed by FD solves rather than ray tracing.Can RTM achieve superresolution via scattering? Test in Arizona suggests 3x improvement in spatial resolution if RTM is done right. Sources were excited in mine and seismograms recorded at surface. These seismograms were migrated by the EXACT RTM migration operator (Greens functions were recorded so we used these to exactly RTM migrate data..no velocity model needed!). Results show 3x improvement in spatial resolution of RTM scattered image compared to ~KM. The ~KM was achieved by muting out all but first arrival in Greens functions before we formed focusing kernel. See next slide for muted Greens functions. Above should be resolution goal we might all try to achieve,,,above shows the highest fruit on the tree..who dares pick it? Not only can we achieve better resolution but above suggests we can possibly cut aperture width by half.*Can RTM achieve superresolution via scattering? Test in Arizona suggests 3x improvement in spatial resolution if RTM is done right. Sources were excited in mine and seismograms recorded at surface. These seismograms were migrated by the EXACT RTM migration operator (Greens functions were recorded so we used these to exactly RTM migrate data..no velocity model needed!). Results show 3x improvement in spatial resolution of RTM scattered image compared to ~KM. The ~KM was achieved by muting out all but first arrival in Greens functions before we formed focusing kernel. See next slide for muted Greens functions. Above should be resolution goal we might all try to achieve,,,above shows the highest fruit on the tree..who dares pick it? Not only can we achieve better resolution but above suggests we can possibly cut aperture width by half.*