Generalized Diffraction Stack Migration with Wavelet Compression

Ge Zhan, Yi Luo, and G. T. Schuster Jan. 7, 2010

Outline

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Motivation

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Theory

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Numerical Results

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Conclusions

Motivation

  Problem Kirchhoff (diffraction-stack) migration is efficient but with a high-frequency approximation.

 WEM method (RTM) is accurate but computationally intensive compared to KM.

 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.

Outline

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Motivation

•

Theory

•

Numerical Results

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Conclusions

Theory



Reverse Time Migration

Trial image pt.

 Interpretation: Calc. GF by FD solver  

G s x

* Direct wave   ( | ) * |

t

 0 Back-propagated traces 

GDM

    Generalized Kirchhoff Kernel Migration Operator ( | ) * *

d r

Interpretation: Dot product of the hyperbola with data

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.

Theory

s

Migration Operator  ( , , )  ( | ) * * Size = nx*nz*ns*ng*nt = 645*150*323*176*1001*4 = 20 TB Too big to store.

x r

G

2D Wavelet Transform appropriate threshold 10x compression  ( , , )  ( | ) * *

G

Theory

Can Scatterers Beat the Resolution Limit ?

Green’s Function            

direct multiple

 trace

Outline

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Motivation

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Theory

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Numerical Results

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Conclusions

Numerical Results

SEG/EAGE Salt Model 0

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

3 0 0 X (km) Zoom View 3 0 X (km) 15 15 km/s 4.5

3.5

2.5

1.5

Numerical Results

Wavelet Transform Compression

0 Calculated GF Reconstructed GF 1.5

Trace Comparison 4 1 Trace #

200 MB

401 1 Trace #

20 MB

401 4 1 101 201 301 Trace# 401

Numerical Results

Multiples 0 Early-arrivals 4 1 Trace# 401 1 Trace# 401

0

Numerical Results

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

Outline

•

Motivation

•

Theory

•

Numerical Results

•

Conclusions

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