23. Reverse-Time Migration

Report
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
5
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
6
The Wavefield
 2D
world
 Constant velocity
 Impulse source



at t=0
at z=0
red dot
7
The Wavefield
 Constant-depth
slices
 Hyperbolas
 Diffractions
8
The Wavefield
 Constant-time
slices
 Semicircles
 Wave
propagation
9
Migration
 Migration
=
Wavefield
continuation +
Imaging
condition
 Continuation of
full multidimensional
wavefields
10
Migration
 Two
different
imaging conditions:
1. Shot record,
sequential imaging
2. Survey-sinking,
simultaneous
imaging
11
Shot Record, Sequential Imaging
 Constant
velocity
 Examine:



Data
Wavefields
Image
 At:


Source
Receiver
12
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
13
Shot Record, Sequential Imaging (b)

Fire impulsive source:


t=0
z=0
 Shot


gather data:
Two reflections
Impulsive waves
14
Shot Record, Sequential Imaging (c)

Source impulse data:


Single red impulse
t=0, z=0

Data at source,
just like receiver
data
15
Shot Record, Sequential Imaging (d)

Exploding reflectors:


Blue = horizontal
Green = dipping


Cones in const.-V
From t=0 at recorded
depth point
16
Shot Record, Sequential Imaging (e)
 Source

radiation:
Wavefield cone


From t=0
From source x
17
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
18
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
19
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
20
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*)
21
Shot Record, Sequential Imaging (h)


This (x*, z*) is on upper reflector
Ws(t) • Wr(t) gives non-0 at reflector
22
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

23
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)
24
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.
25
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.
26
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.
27
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.
28
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.
29
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
30
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
31
Extended Imaging Conditions
 Zero-lag,
 Space
h=0 cross-correlation:
and time shifts λx, λy, λz, τ:
32
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
33
Marmousi Model
34
Marmousi Model
35
Marmousi Model
36

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