Prestack Migration Least Squares Migration Greens Theorem Intuitive

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Prestack Migration Least Squares Migration Green’s Theorem Intuitive

Prestack Migration Least Squares Migration Green’s Theorem Intuitive

3 D Prestack Diffraction Stack Migration Motivation: ZO only good if no lateral vel

3 D Prestack Diffraction Stack Migration Motivation: ZO only good if no lateral vel change s g x

3 D Prestack Diffraction Stack Migration Trial image pt x = m(x) = s,

3 D Prestack Diffraction Stack Migration Trial image pt x = m(x) = s, g d(x’, sx+ xg ) s g x

Outline Prestack DS Migration Theory RTM vs Poststack vs Prestack MATLAB Code

Outline Prestack DS Migration Theory RTM vs Poststack vs Prestack MATLAB Code

Prestack Migration Question: Why Prestack when poststack migration seems good enough? Answer: Stacking to

Prestack Migration Question: 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.

Diffraction Stack Migration: Prestack Down time T(s, g) = sx + Up time xg

Diffraction Stack Migration: Prestack Down time T(s, g) = sx + Up time xg Where is scatterer? g s sx xg d(s, g, sx + xg ) s, g Narrow band case: direct wave correlated with data x

115. Diffraction Stack Modeling: Prestack T m d=Lm d ~ d(s, g) = 2

115. Diffraction Stack Modeling: Prestack T m d=Lm d ~ d(s, g) = 2 x ~ ) W( e i sx A(s, x) ~ m(x) e i xg A(g, x)

115. Diffraction Stack Migration: Prestack T ò m=Ld d ò 2 ~ m(x) =

115. Diffraction Stack Migration: Prestack T ò m=Ld d ò 2 ~ m(x) = d . . ~* ) W( s, g m(x) = d(s, g, + sx xg s, g -i sx - i xg e ~ e d(s, g) A(s, x) ) A(g, x) Broadband case ~ W( )=1 A(s, x) A(x, g) Narrow band case: direct wave correlated with data

Outline Prestack DS Migration Theory RTM vs Poststack vs Prestack MATLAB Code

Outline Prestack DS Migration Theory RTM vs Poststack vs Prestack MATLAB Code

Prestack RTM vs One-way Wave Equation Migration

Prestack RTM vs One-way Wave Equation Migration

Prestack RTM vs One-way Wave Equation Migration

Prestack RTM vs One-way Wave Equation Migration

ZO Diffraction Stack Migration Trial image pt x m(x) = d (g, xg )

ZO Diffraction Stack Migration Trial image pt x m(x) = d (g, xg ) g x

ZO Diffraction Stack Migration Trial image pt x m(x) = d (g, xg )

ZO Diffraction Stack Migration Trial image pt x m(x) = d (g, xg ) g 2 D dot product of migration Operator and d(g, t) x Migration Image

ZO Reverse Time Migration Trial image pt x m(x) = d (g, xg )

ZO Reverse Time Migration Trial image pt x m(x) = d (g, xg ) g ~Scattered RTM x Super-resolution

ZO Reverse Time Migration Trial image pt x m(x) = d (g, xg )

ZO Reverse Time Migration Trial image pt x m(x) = d (g, xg ) g ~Scattered RTM x Super-resolution

Prestack RTM vs One-way Wave Equation Migration

Prestack RTM vs One-way Wave Equation Migration

Outline Prestack DS Migration Theory RTM vs Poststack vs Prestack MATLAB Code

Outline Prestack DS Migration Theory RTM vs Poststack vs Prestack MATLAB Code

Types of Traveltimes Shortest Traveltime or Shortest Raypath Maximum Energy Traveltimes Shortest path ray

Types of Traveltimes Shortest Traveltime or Shortest Raypath Maximum Energy Traveltimes Shortest path ray Maximum energy ray Shortest traveltime ray

Poststack vs Prestack Migration

Poststack vs Prestack Migration

Poststack vs Prestack Migration

Poststack vs Prestack Migration

RRTM vs KM Migration

RRTM vs KM Migration

RRTM vs KM Migration

RRTM 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.

Outline Prestack DS Migration Theory RTM vs Poststack vs Prestack DS MATLAB Code

Outline Prestack DS Migration Theory RTM vs Poststack vs Prestack DS MATLAB Code

MATLAB Prestack Migration

MATLAB Prestack Migration

MATLAB Inefficient Prestack Migration for isx=1: nx % Loop over shot for igx=1: nx

MATLAB Inefficient Prestack Migration for 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

MATLAB Prestack Migration

MATLAB Prestack Migration

Prestack Migration 1. No assumption about velocity model 2. More sensitive to velocity model

Prestack Migration 1. No assumption about velocity model 2. More sensitive to velocity model errors compared to poststack migration 2 6 3. More than 10 – 10 times slower than poststack migration 4. More sensitive to velocity model than time migration

Poststack vs Prestack Migration

Poststack vs Prestack Migration

Poststack vs Prestack Migration

Poststack vs Prestack Migration