reverse-time migration geol 757 advanced seismic imaging and tomography 1
TRANSCRIPT
Reverse-Time Migration
Geol 757
Advanced Seismic Imaging
and Tomography
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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.
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From Sava & Hill, 2009 What defines a WE migration? Classification based on:
Assumptions of algorithms Domain of implementation Imaging Principle
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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
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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 multi-dimensional 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
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2D Survey in x: Split spread Look at one shot
record
Shot Record, Sequential Imaging (b) Fire impulsive source:
t=0 z=0
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Shot gather data: Two reflections Impulsive waves
Shot Record, Sequential Imaging (c) Source impulse data:
Single red impulse t=0, z=0
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Data at source, just like receiver data
Shot Record, Sequential Imaging (d) Exploding reflectors:
Blue = horizontal Green = dipping
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Cones in const.-V From t=0 at
recorded depth point
Shot Record, Sequential Imaging (e) Source radiation:
Wavefield cone
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From t=0 From source x
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 2D data, the wavefields are 3D W(x, z, t)
For 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.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.
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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 marching Downward continuation Paraxial wavefield
extrapolation in the frequency domain
Time marching Reverse-time migration
with acoustic finite-difference modeling in the time domain
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Extended Imaging Conditions
Zero-lag, h=0 cross-correlation:
Space 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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