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Generalized Diffraction Stack Migration with Wavelet Compression

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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