Reverse Time Migration

Outline Finding a Rock Splash at Liberty Park ZO Reverse Time Migration (backwd in time) ZO Reverse Time Migration (forwd in time) ZO Reverse Time Migration Code Examples

Liberty Park Lake Rolls of Toilet Paper Time

Find Location of Rock Rolls of Toilet Paper Time

Find Location of Rock Rolls of Toilet Paper Time

Find Location of Rock Rolls of Toilet Paper Time

Find Location of Rock Rolls of Toilet Paper Time

Find Location of Rock Rolls of Toilet Paper Time

Find Location of Rock Rolls of Toilet Paper Time

Outline Finding a Rock Splash at Liberty Park ZO Reverse Time Migration (backwd in time) ZO Reverse Time Migration (forwd in time) ZO Reverse Time Migration Code Examples

ZO Modeling 5 1-way time Reverse Order Traces in Time

Reverse Time Migration (Go Backwards in Time) 1-way time -5 T=0 Focuses at Hand Grenades

Outline Finding a Rock Splash at Liberty Park ZO Reverse Time Migration (backwd in time) ZO Reverse Time Migration (forwd in time) ZO Reverse Time Migration Code Examples

Reverse Time Migration (Reverse Traces Go Forward in Time) 1-way time -5 T=0 Focuses at Hand Grenades

Poststack RTM 1. Reverse Time Order of Traces 5 1-way time -5 1-way time 2. Reversed Traces are Wavelets of loudspeakers

Outline Finding a Rock Splash at Liberty Park ZO Reverse Time Migration (backwd in time) ZO Reverse Time Migration (forwd in time) ZO Reverse Time Migration Code Examples

Forward Modeling Reverse Time Modeling for it=1:1:nt p2 = 2*p1 - p0 + cns.*del2(p1); p2(xs,zs) = p2(xs,zs) + RICKER(it); % Add bodypoint src term p0=p1;p1=p2; end for it=nt:-1:1 p2 = 2*p1 - p0 + cns.*del2(p1); p2(1:nx,2) = p2(1:nx,2) + data(1:nx,it); % Add bodypoint src term p0=p1;p1=p2; end Reverse Time Modeling

Recall Forward Modeling d=Lm d(x) = G(x|x’)m(x’)dx’ ~ ~ ~ ~ ~ ~ ò d=Lm d(x) = G(x|x’)m(x’)dx’ Fourier d(x,t) = G(x,t-ts|x’,0)m(x’,ts)dx’dts ò = G(x,t|x’,ts)m(x’,ts)dx’dts ò Stationarity x z t src Forward reconstruction of half circles

Migration = Adjoint of Data d=Lm d(x) = G(x|x’)m(x’)dx’ ò m=L d m(x’) = G(x|x’)*d(x)dx ò T Fourier t=0 m(x) = G(x,-t+ts|x’,0)d(x’,ts)dx’dts ò Note: t < ts = G(x, ts|x’,t)d(x’,ts)dx’dts ò Stationarity x z t

Migration = Adjoint of Data d=Lm d(x) = G(x|x’)m(x’)dx’ ò m=L d m(x’) = G(x|x’)*d(x)dx ò T Fourier t=0 m(x) = G(x,-t+ts|x’,0)d(x’,ts)dx’dts ò Note: t < ts = G(x, ts|x’,t)d(x’,ts)dx’dts ò Stationarity x z t

Migration = Adjoint of Data d=Lm d(x) = G(x|x’)m(x’)dx’ ò m=L d m(x’) = G(x|x’)*d(x)dx ò T Fourier t=0 m(x) = G(x,-t+ts|x’,0)d(x’,ts)dx’dts ò Note: t < ts = G(x, ts|x’,t)d(x’,ts)dx’dts ò Stationarity x z t

Migration = Adjoint of Data d=Lm d(x) = G(x|x’)m(x’)dx’ ò m=L d m(x’) = G(x|x’)*d(x)dx ò T Fourier t=0 m(x) = G(x,-t+ts|x’,0)d(x’,ts)dx’dts ò Note: t < ts = G(x, ts|x’,t)d(x’,ts)dx’dts ò Stationarity x z t

Migration = Adjoint of Data d=Lm d(x) = G(x|x’)m(x’)dx’ ò m=L d m(x’) = G(x|x’)*d(x)dx ò T Fourier t=0 m(x) = G(x,-t+ts|x’,0)d(x’,ts)dx’dts ò Note: t < ts = G(x, ts|x’,t)d(x’,ts)dx’dts ò Stationarity x z t Backward reconstruction of half circles

Migration = Adjoint of Data d=Lm d(x) = G(x|x’)m(x’)dx’ ò m=L d m(x’) = G(x|x’)*d(x)dx ò T Fourier t=0 m(x) = G(x,-t+ts|x’,0)d(x’,ts)dx’dts ò Let ts = -ts Note: t < ts Note: t > ts = G(x, ts|x’,t)d(x’,ts)dx’dts ò Stationarity - z x t x z t Backward reconstruction of half circles x z t Backward reconstruction of half circles Forward prop. Of reverse time data

m(x’+dx) = d(x) G(x|x’+dx)* Advantages of m(x’+dx) = d(x) G(x|x’+dx)* x Kirchhoff Mig. vs Full Trace Migration Multiples time Multiples Primary 1. Low-Fold Stack vs Superstack 2. Poor Resolution vs Superresolution

Outline Finding a Rock Splash at Liberty Park ZO Reverse Time Migration (backwd in time) ZO Reverse Time Migration (forwd in time) ZO Reverse Time Migration Code Examples

Numerical Examples

3D Synthetic Data 3D SEG/EAGE Salt Model X 3.5 Km Z 2.0 Km Y 3.5 Km 4

3D Synthetic Data 5 W E Kirchhoff Migration Depth (Km) Redatum + KM Depth (Km) Redatum + KM 2.0 Offset (km) 3.5 Offset (km) 3.5 5 Cross line 160

3D Synthetic Data 6 Kirchhoff Migration W E Redatum + KM Depth (Km) Redatum + KM Depth (Km) 2.0 Offset (km) Offset (km) 3.5 3.5 6 Cross line 180

3D Synthetic Data 7 Kirchhoff Migration W E Redatum + KM Depth (Km) Redatum + KM Depth (Km) 2.0 Offset (km) Offset (km) 3.5 3.5 7 Cross line 200

Prism Synthetic Example Numerical Examples GOM Data Prism Synthetic Example

GOM Kirchhoff ?

GOM RTM ?

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Prism Synthetic Example Numerical Examples GOM Data Prism Synthetic Example

Prism Wave Migration Courtesy TLE: Farmer et al. (2006) One Way Migration of Prestack Data RTM of Prestack Data Courtesy TLE: Farmer et al. (2006)

Summary 1. RTM much more expensive than Kirchhoff Mig. 2. If V(x,y,z) accurate then all multiples Included so better S/N ration and better Resolution. 3. If V(x,y,z) not accurate then smooth velocity Model seems to work better. Free surface multiples included. 4. RTM worth it for salt models, not layered V(x,y,z). 5. RTM is State of art for GOM and Salt Structures.

? ? Solution Claim: Image both Primaries and Multiples Methods: RTM A

? ? Piecemeal Methods 2-Way Mirror Wave Migration: Assume Knowledge of Important Mirror Reverse Time Migration A D ? ?