wave-equation mva using partial stack-power-maximization

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Wave-equation MVA using partial stack-power-maximization

Yang Zhang* and Guojian Shan June, 2013

SEP—149, p51


Outline

  Wave equation MVA (WEMVA) background –  Common Image Gather in angle and offset domain

–  WEMVA workflow

  Partial image-stack power objective function

2


WEMVA characteristics

  Wave-equation migration velocity analysis

•  Is a reflection tomography method

•  Optimizes objective function defined in image domain (Common image gathers)

•  Uses wave-equation operator to compute images & velocity updates (wave path not ray path).

3


Common-image gather in reflection angle domain

  Imaging the same reflector with different incident angles (same in reflection ray-tomography)

  In ideal case, the more correct the velocity model, the more the gathers are flat

  More expensive to compute using wave-equation

4


Common-image gather in subsurface offset domain

  Different from surface offset-gathers used frequently in Kirchhoff migration

  In ideal case, the more correct the velocity model, the gathers are more focused on h=0 (rather than being flat)

  Computationally easy to implement

5


Zero-subsurface offset domain

6

v(z) image

true image

0 1000

2000 3000

0 1000

2000 3000


Subsurface offset gathers

7

v(z) gather

true gathers

0 1000

2000 3000

0 1000

2000 3000

hX hX hX


General WEMVA flow

8

Migrateandgenerate

subsurfaceADCIG

Measureimagefocusing

(e.g.flatnessofADCIGs)

Updatevelocitymodelusing

wave‐equaConoperators

iterate

Z

angle

Z

X

Gerritsen et.al, SEG 2011


WEMVA objective functions

9

 Stack‐power‐maximizaCon(SPM)

 DifferenCalsemblanceopCmizaCon(DSO)


WEMVA objective functions

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 Stack‐power‐maximizaCon(SPM)(Gratacous,2005)

 DifferenCalsemblanceopCmizaCon(DSO),(Shen&Symes,2008)

• Globalconvergenceproblems

• SensiCvetoimageamplitudes• SensiCvetoCIGsarCfactsiiProblemsin3D


Outline

  Wave equation MVA background

  Partial Image-stack power objective function

11


Partial stack power maximization

  Existing stack power maximization

12


Partial stack power maximization

  Existing stack power maximization

  Using partial stack –  is a low-pass filtering kernel

•  Box function / triangular function / Gaussian function

  Properties of partial stack –  More robust against cycle-skipping problem as in previous stack-power

maximization method

–  Is a generalization of the previous method

13


Partial stacking avoids cycle-skipping

14

Full stack Partial stack

∆z ∆z

angle

depth


WEMVA objective functions in angle domain

15

Stack Power Maximization (SPM)

Partial SPM

DSO

Angle-domain Convolution kernel

angle


Comparison of WEMVA objective functions (graphic)

16

SPM

Partial SPM

DSO

Angle-domain, convolution

Offset-domain, multiplication

Global convergence

Integration rather than differentiation

High resolving power

Flexibility with wt function

angle offset

(a) (b)


Comparison of WEMVA objective functions (equation)

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Stack Power Maximization (SPM)

Partial SPM

DSO

Angle-domain Offset-domain

Global convergence

Integration rather than differentiation

High resolving power

Flexibility with G(h)


Energy Normalized WEMVA objective functions

18

Partial SPM

DSO

From Tang, Ph.D Thesis, 2011


Marmousi model: true velocity

19

0 1000

2000 3000

4000 0 2000 6000 8000

velo

city

(m/s

)


Starting velocity

20

0 1000

2000 3000

4000 0 2000 6000 8000

velo

city

(m/s

)


Partial-SPM without normalization (20 iterations)

21

0 1000

2000 3000

4000 0 2000 6000 8000

velo

city

(m/s

)


Partial-SPM without normalization

22

Final image Display clip 4x

Initial image

0 1000

2000 3000

0 1000

2000 3000


Normalized Partial stack power (40 iterations)

23

4000 0 2000 6000 8000

0 1000

2000 3000

velo

city

(m/s

)


Marmousi test, normalized partial SPM method, starting model

24

0 1000

2000 3000

4000 0 2000 6000 8000

velo

city

(m/s

)


First update, Normalized partial stack power

25

4000 0 2000 6000 8000

0 1000

2000 3000


First update, Normalized DSO

26

4000 0 2000 6000 8000

0 1000

2000 3000



27

4000 0 2000 6000 8000

0 1000

2000 3000

velo

city

(m/s

)



28

4000 0 2000 6000 8000

0 1000

2000 3000

velo

city

(m/s

)


Normalized DSO (40 iterations)

29

4000 0 2000 6000 8000

0 1000

2000 3000

velo

city

(m/s

)


True image

30

4000 0 2000 6000 8000

0 1000

2000 3000


Normalized Partial SPM

31

4000 0 2000 6000 8000

0 1000

2000 3000


Normalized DSO

32

4000 0 2000 6000 8000

0 1000

2000 3000


Conclusion & Discussion

  Partial SPM merges the merits of both SPM and DSO objective functions, also more flexible

  Normalization for reflector amplitude is not only preferred but necessary

  Remaining question: –  Compared to data-domain, image-domain is easier to look at, but we are

still missing the ultimate correct objective function

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Conclusion & Discussion

  Partial SPM merges the merits of both SPM and DSO objective functions, also more flexible –  Normalization for reflector amplitude is not only preferred but necessary

  Steering filters helps improves convergence speed and reduces the null space of the inverse problem –  Most effective if the model is poorly constrained along the dipping

direction

  Question Remained: –  Compared to data-domain, image-domain is easier to look at, but we are

still missing the ultimate correct objective function.

–  Is the steering filter always desirable? What if the geometry of the velocity model does not follow the reflectors’, like BP 2004 model?

34


Acknowledgement

  Chevron ETC, Imaging & Velocity model building group

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wave-equation mva using partial stack-power-maximization

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