Transcript 23. Reverse-Time Migration

Reverse-Time
Migration
Geol 757
Advanced Seismic Imaging
and Tomography
1
References

Paul Sava and Stephen J. Hill, Tutorial: Overview
and classification of wavefield seismic imaging
methods: The Leading Edge, February 2009, v.
28, p. 170-183, doi:10.1190/1.3086052.

Edip Baysal, Dan D. Kosloff, and John W. C.
Sherwood, Reverse time migration: Geophysics, v.
48, no. 11 (Nov. 1983), p. 1514-1524.

Matthew H. Karazincir and Clive M. Gerrard,
Explicit high-order reverse time pre-stack depth
migration: Expanded Abstracts, Soc. Explor.
Geophys. New Orleans 2006 Annual Meeting, p.
2353-2357.
2
From Sava & Hill, 2009
 What
defines a WE migration?
 Classification based on:



Assumptions of algorithms
Domain of implementation
Imaging Principle
3
WEM Classifications

Single Scattering – no multiples in data


Born approximation
Wave-Equation Solutions – acoustic forward modeling



Not Kirchhoff summation
The acoustic equation cannot get close to Zoeppritz
Not full-wave inversion
4
WEM Classifications
 Imaging


and Wavefield Reconstruction
Shot record migration – sequential,
independent
Survey-sinking migration - simultaneous
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WEM Classifications
 Implementations
in
Sava & Hill:



Shot record, 2-way in
time, time domain
Shot record, 1-way in
depth, frequency
domain
Survey-sinking, 1-way
in depth, frequency
domain
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The Wavefield
 2D
world
 Constant velocity
 Impulse source



at t=0
at z=0
red dot
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The Wavefield
 Constant-depth
slices
 Hyperbolas
 Diffractions
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The Wavefield
 Constant-time
slices
 Semicircles
 Wave
propagation
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Migration
 Migration
=
Wavefield
continuation +
Imaging
condition
 Continuation of
full multidimensional
wavefields
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Migration
 Two
different
imaging conditions:
1. Shot record,
sequential imaging
2. Survey-sinking,
simultaneous
imaging
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Shot Record, Sequential Imaging
 Constant
velocity
 Examine:



Data
Wavefields
Image
 At:


Source
Receiver
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Shot Record, Sequential Imaging (a)

Model that generates
data:


Flat reflector above
Dipping reflector below

2D Survey in x:


Split spread
Look at one shot
record
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Shot Record, Sequential Imaging (b)

Fire impulsive source:


t=0
z=0
 Shot


gather data:
Two reflections
Impulsive waves
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Shot Record, Sequential Imaging (c)

Source impulse data:


Single red impulse
t=0, z=0

Data at source,
just like receiver
data
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Shot Record, Sequential Imaging (d)

Exploding reflectors:


Blue = horizontal
Green = dipping


Cones in const.-V
From t=0 at recorded
depth point
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Shot Record, Sequential Imaging (e)
 Source

radiation:
Wavefield cone


From t=0
From source x
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Shot Record, Sequential Imaging (f & g)

Imaging condition – Ws-R-Wr model:

Scatterer exists at the spatial coordinate (x and z) that
contains coincident, nonzero wavefield amplitudes in both
the source and the receiver wavefields
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Shot Record, Sequential Imaging (f & g)

Imaging condition – Ws-R-Wr model:

Reflectors exist where incident and reflected
wavefields are coincident in time and space
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Shot Record, Sequential Imaging (f & g)

Imaging condition – Ws-R-Wr model:


Ws and Wr coincide (nonzero) at some time t
Doesn’t matter what t it was - only the coincidence
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Shot Record, Sequential Imaging (h)


(g) Ws(t) contains one nonzero value (red) at (x*, z*)
(f) Wr(t) has two non-0 values (blue, green) at (x*, z*)
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Shot Record, Sequential Imaging (h)


This (x*, z*) is on upper reflector
Ws(t) • Wr(t) gives non-0 at reflector
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Shot Record, Sequential Imaging (h)
Post nonzero Ws(t) • Wr(t) at (x*, z*) in (x, z)
image
 Correlate at other (x, z) points and post their
nonzero amplitudes
 Add in migrated sections for other shot gathers

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Shot Record, Sequential Imaging
 Ws-R-Wr
model, Berkhout (1982)
 Need the source and scattered wavefields


Source wavefield carries energy to the
reflector
Scattered wavefield carries energy away from
the reflector
 For

W(x, z, t)
 For

2D data, the wavefields are 3D
3D data, the wavefields are 4D
W(x, y, z, t)
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Sequential Imaging Needs
1. Wavefield reconstruction that generates
the source and scattered wavefields, WS
and Wr, at all locations in space x, z and all
times t from data recorded at the surface,
and
2. An imaging condition that extracts
reflectivity information, i.e. the image I, from
the reconstructed source and scattered
wavefields WS and Wr.
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Imaging Principle
 Single-scattering
assumption
 The incident and scattered wavefields are
identical at the scatterer, except for:

The reflection coefficient.
 Kinematically
accurate- timing & structure
 Dynamically inaccurate- poor R,
impedance, AVO
 Scattering cannot change wave phase.
 If there are multiples, the cross-correlated
amplitude will be too high.
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Wavefield Reconstruction
 Velocity




Model
Must be known a priori.
In a smooth-velocity area, uncertainty will not
prevent imaging.
In the presence of strong lateral velocity
contrasts, their complete characterization is
essential.
Code the velocity model into a procedure for
generating wavefields from sources.
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Wavefield Reconstruction

Generating the Source Wavefield Ws


Simulate each shot gather’s source, forward in
time from its true position.
Generating the Receiver Wavefield Wr



Simulate each shot gather trace’s receiver
position as a virtual source, at that receiver’s true
position.
Feed each receiver’s recorded data into each
receiver “source,” as a source time function.
Produces a “reversed time” wavefield from the
data, projecting recorded amplitudes back onto
the scatterers.
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Wavefield Reconstruction
 Successful
wavefield reconstruction relies
on the single-scattering assumption for
seismic imaging, i.e.,


Recorded wavefields have scattered only
once in the subsurface (there are no multiples
in the data), and
No scattering occurs in the process of
wavefield reconstruction.
 Full-wave
modeling methods may not work
well, since they always implement
scattering with propagation.
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Wavefield Reconstruction
 One-way
Paraxial wave-propagation
modeling will work well, since it cannot
create reflections. Paraxial is also faster.
 Two-way modeling procedures can work
so long as they do not introduce scattering
– downward continuation, WKBJ ray
tracing, deterministic traveltimes, etc.
 Any modeling method capable of handling
lateral variations will introduce scattering.
 More reasons RTM is kinematic, not
dynamic
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Wavefield Reconstruction Axis
 Depth


Downward continuation
Paraxial wavefield
extrapolation in the
frequency domain
 Time

marching
marching
Reverse-time migration
with acoustic finitedifference modeling in the
time domain
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Extended Imaging Conditions
 Zero-lag,
 Space
h=0 cross-correlation:
and time shifts λx, λy, λz, τ:
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Extended Imaging Conditions
 Create


a multidimensional image
I(x, y, z, λx, λy, λz, τ)
Try amplitude-vs.-angle analysis
 Determine





wavefield reconstruction error
from very approximate wavefield
reconstructions (one-way, low-order)
from velocity error
from multiples in the data
from problems with acquisition coverage
from incomplete subsurface illumination
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Marmousi Model
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Marmousi Model
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Marmousi Model
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