LEAST SQUARES WAVEPATH MIGRATION

Y. Liu and H. Sun Geology and Geophysics Department University of Utah

Outline

. Objective . Wavepath Migration . Least Squares Wavepath Migration . Numerical Results . Field Data Results . Conclusions

Objective

•

Least-Squares Migration a. Advantages:

• • •

Apply to Incomplete data Reduce acquisition footprint Improve Image resolution b. Disadvantage: Need more calculation time

Objective

Least Squares Migration:

•

Forward Modeling: fast

•

Migration: slow

Objective

Wavepath Migration :

Advantages:

• •

Save calculation time Suppress artifacts

Objective

Least-Squares Wavepath Migration:

• • • •

Advantages:

Apply to Incomplete data Reduce acquisition footprint Improve resolution Save calculation time

Outline

. Objective . Wavepath Migration . Least Squares Wavepath Migration . Numerical Results . Field Data Results . Conclusions

Wavepath Migration

( Xg, 0 ) Fat Ellipsoid Fat Ray KM : Fat Ellipsoid, 3-D CPU WM: Hatched Area, 1.5-D CPU

Traveltime + Ray Direction

True Reflection point Small Migration Aperture

Fewer Artifacts Less Expensive

4

SEG Overthrust Model Results

0 0 KM Image (CPU:

1.0

) Offset (km) 18 0 0 WM Image (CPU:

0.78

) Offset (km) 18 B A B A 4

CPU Comparison in 3-D SEG/EAGE Salt Data

KM:

1

WM:

1/33 West Texas Field Data

KM:

1

WM:

1/14

Outline

. Objective . Wavepath Migration . Least Squares Wavepath Migration . Numerical Results . Field Data Results . Conclusions

Least Square Wavepath Migration

Forward Migration: :

d=Lm

(1) T

m

st

=L d

(2)

Objective Function:

P(m)=|| Lm-d ||

0 2 (3)

LSWM:

T

m

st

=

[

LL

]

-1 T

Ld

(4)

Least Square Wavepath Migration

Iteration process: Field Data Wavepath Migration Forward Synthetic Data Wavepath Migration Y/N Stop Criteria

Outline

. Objective . Wavepath Migration . Least Squares Wavepath Migration . Numerical Results . Field Data Results . Conclusions

4 0 0

Point Scatterer model

X (km) 4 0 0 X(km)

.

4 2.5

0 0 X (km)

Scatterer Image

4 0 X (km) 4 0 X (km) 4 .

4 KM image WM image LSWM image

Outline

. Objective . Wavepath Migration . Least Squares Wavepath Migration . Numerical Results . Field Data Results . Conclusions

CSG for Mobil Data

Trace 0 1

GEOMETRY Shots: 668 Trace: 120 Total: 80160 Ns=1500 Dt=4ms Ds=25m Dg=25m Min/Offset=262m

5 120

Velocity Model

CDP Number 0 0 Dx=12.5

Dz=12.5

Nx=1594 Nz=281 CDP=12.5

3.5

19.9

3.5

1.5

3.4

4.8

X(Km)

WM vs. LSWM

19.0

X(Km) 19.0

After 15 iternations

WM Image for Mobil Data

12.0

X(m) 18.0

2.8

12.0

WM image (0) 18.0

2.8

LSWM image (15)

Outline

. Objective . Wavepath Migration . Least Squares Wavepath Migration . Numerical Results . Field Data Results . Conclusions

Conclusions

• •

Suppress artifacts Improve Resolution

•

Computation time (Mobil Data)

WM CPU 1.0

LSWM CPU (15): 8.5

•

Slightly sensitive to velocity

Acknowledgements

We thank 2001 UTAM sponsors for their financial supports