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Generalized Diffraction Stack Migration with Wavelet Compression

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Generalized Diffraction Stack Migration with Wavelet Compression. Ge Zhan, Yi Luo, and G. T. Schuster Jan. 7, 2010. Outline. Motivation. Theory. Numerical Results. Conclusions. Kirchhoff (diffraction-stack) migration is efficient. but with a high-frequency approximation.

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Generalized Diffraction Stack Migration with Wavelet Compression

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  1. Generalized Diffraction Stack Migration with Wavelet Compression Ge Zhan, Yi Luo, and G. T. Schuster Jan. 7, 2010

  2. Outline • Motivation • Theory • Numerical Results • Conclusions

  3. Kirchhoff (diffraction-stack) migration is efficient but with a high-frequency approximation. • WEM method (RTM)is accurate but computationally intensive compared to KM. Motivation • Problem • Conventional RTM suffers from imaging artifacts. • Solution • Compressed generalized diffraction-stack migration (GDM) . • Wavelet compression of Green’s functions (10x or more). • Least squares algorithm.

  4. Outline • Motivation • Theory • Numerical Results • Conclusions

  5. Interpretation: Back-propagated traces Direct wave • GDM Generalized Kirchhoff Kernel Migration Operator Interpretation: Dot product of the hyperbola with data Theory • Reverse Time Migration Calc. GF by FD solver Trial image pt.

  6. Theory Advantages of GDM • No high-frequency approximation. • Multiple arrivals are included. • Filtering techniques available to KM can be used with GDM. • Same accuracy as WEM method. • Easy to integrate with least squares algorithm.

  7. 2D Wavelet Transform appropriate threshold 10x compression Theory r s Migration Operator x Size = nx*nz*ns*ng*nt = 645*150*323*176*1001*4 = 20 TB Too big to store.

  8. trace Green’s Function Theory Can Scatterers Beat the Resolution Limit ?

  9. Outline • Motivation • Theory • Numerical Results • Conclusions

  10. km/s 4.5 3.5 0 0 2.5 1.5 Z (km) Z (km) 3 3 0 0 15 15 X (km) X (km) Zoom View Numerical Results SEG/EAGE Salt Model 323 shots 176 geophones peak freq = 13 Hz dx = 24.4 m dg = 24.4 m ds = 48.8 m nsamples = 1001 dt = 0.008 s

  11. Trace Comparison 1.5 0 Time (s) Time (s) 4 1 101 201 301 401 Trace# 4 1 401 Trace # Numerical Results Wavelet Transform Compression Calculated GF Reconstructed GF 1 401 Trace # 200 MB 20 MB

  12. Multiples 0 Time (s) 1 401 Trace# 4 1 401 Trace# Numerical Results Early-arrivals

  13. Numerical Results 0 0 (a) GDM using Early-arrivals (b) GDM using Full Wavefield Z (km) Z (km) 3 3 0 0 15 15 X (km) X (km) 0 15 X (km) (c) GDM using Multiples (d) Optimal Stack of (a) and (c) 0 15 X (km)

  14. Outline • Motivation • Theory • Numerical Results • Conclusions

  15. Conclusions • We presented the theory of GDM with compression • We use the wavelet transform to reach a compression ratio of 10 and greatly reduce storage and computation time • We use multiple scattering to achieve better resolution

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