Transcript Extended Diffraction-Slice Theorem for Wavepath Traveltime
Multi-source Least Squares Migration and Waveform Inversion
Wei Dai, Ge Zhan, Xin Wang, and G. Schuster KAUST and University of Utah
Outline
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Fast Multisource+Precond. Theory
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Multisource Least Squares Migration
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Multisource Waveform Inversion
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Conclusion
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RTM Problem & Possible Soln.
Problem: RTM computationally costly
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Partial Solution: Multisource LSM RTM Preconditioning speeds convergence by factor 2-3 LSM reduces crosstalk 3
Multisource Least Squares Migration
d L
Forward Model:
d +d =[
L +L ]m 1 2 2 1
Multisource Migration:
m
mig
=L
T
d
Multisrc-Least Sq. Migration :
m =[L T L] -1 L T d multisource preconditioner multisource modeler+adjoint f T [Lm - d] Preconditioned Steepest Descent f ~ [L T L] -1
Outline
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Fast Multisource+Precond. Theory
•
Multisource Least Squares Migration
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Multisource Waveform Inversion
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Conclusion
0
SEG/EAGE Salt Model
4500 4 0
CSG
X (km)
Multisource CSG
16 1500
X (km) X (km)
9
Multisource Least Squares Migration Workflow
Generate ~200 CSGs, Born approx:
d and d 1 2
Random Time Shifted CSG and Add :
d =d + d 1 2
Compute Preconditioner : f =
[L T L] -1
Iterate Preconditioned Regularized CG:
f T [Lm - d] + reg .
*f =
0
Model, KM, and LSM Images
Model 90x LS M (30 its) 1x Kirchhoff Migration 3
1.5
1.5x
0 3km
LSM 10 srcs (5 its) 9x LSM 10 srcs (30 its) 0.1x
KM 10 Srcs 8
0
Model, KM, and LSM Images
Model 90x LS M (30 its) 1x Kirchhoff Migration 3
1.5
1.5x
0 3km
LSM 10 srcs (5 its) LSM 40 srcs (30 its) 2.5x
0.02x
KM 40 Srcs 9
1.4
Did Deblurring Help?
Standard precond. CG
0 0
CG deblurring
Iteration #
30
Conclusions
1. Empirical Results: Multisrc. LSM effective in suppressing crosstalk for up to 40 source supergather, but at loss of subtle detail. Did not achieve breakeven 2.5x > 1x. 2 2. Deblurring precond. >> Standard 1/r precond.
3. Blending Limitation: Overdetermined>Undetermined T -1 4. Future: Better deblurring [L L] and regularizer
Outline
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Fast Multisource+Precond. Theory
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Multisource Least Squares Migration
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Multisource Waveform Inversion
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Conclusion
Multiscale Waveform Tomography
1. Collect data d(x,t) syn .
2. Generate synthetic data d(x,t) by FD method syn .
4. To prevent getting stuck in local minima: a). Invert early arrivals initially mute b). Use multiscale: low freq. high freq.
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Multi-Source Waveform Inversion Strategy (Ge Zhan)
144 shot gathers
Generate multisource field data with known time shift Initial velocity model Generate synthetic multisource data with known time shift from estimated velocity model Multisource deblurring filter Using multiscale, multisource CG to update the velocity model with regularization
Acoustic Marmousi Model and Multiscale Waveform Inversion m/s 5000 0 0 X(m) X(m) 2000 1910 12x 1910 m/s 5000 50 iterations 2000
12-Source Misfit Gradient vs Deblurred Gradient Standard 12-Src Gradient 19.5% Error Deblurred 12-Src Gradient 2000 7.1% Error 2000
Residual Gradient vs # of Shots
Summary
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Multisource+Precond. +CG Reduces Crosstalk
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Multisource Waveform Inversion: reduces computation by 12x for Marmousi
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Multisource LSM: Reduces LSM computation $$ but still costs > standard mig.
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Problem: Need Formulas for S/N vs dx
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Potential O(10) speedup with 3D
Outline
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Fast Multisource+Precond. Theory
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Multisource Least Squares Migration
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Multisource Waveform Inversion
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Multisource MVA
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Conclusion