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Page 1: Slide #1 biondo@stanford

Slide #1 [email protected]

Page 2: Slide #1 biondo@stanford

Slide #2

(156990) Claerbout = 2003 KX18

[email protected]

     Jon Claerbout (b. 1938) is a prolific contributor to the theory and art of exploration seismology.  He was the first to demonstrate a practical method for imaging the Earth's interior using wavefields modeled in a computer.  He also pioneered seismic interferometry, a method now used to probe the sun - Joe Dellinger (May 2011)

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Slide #3

(156990) Claerbout = 2003 KX18

[email protected]

  ``I chose this asteroid`` because among those I have discovered solo it has a particularly inclined orbit (23 degrees), and "KX" in the designation, which makes me think of Fourier transforms.’’ Joe Dellinger

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Slide #4

Wave-equation migration velocity analysis by residual

moveout fitting

Biondo Biondi

SEP 142 pp. 25-32 SEP 143 pp. 59-66

Page 5: Slide #1 biondo@stanford

Slide #5 [email protected]

Yaxun Tang’s thesis

Initial

Final

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Slide #6

Claudio Guerra’s thesis

[email protected]

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Slide #7

Ready for ``prime time’’?

§  Convergence – DSO gradient artifacts slows down convergence.

§  3D WAZ – Poor source sampling causes artifacts in subsurface CIGs (offset or angle).

§  Resolution – Can we improve resolution by exploiting velocity information contained in back-scattered waves, and improve global convergence?

[email protected]

Page 8: Slide #1 biondo@stanford

Slide #8

Ready for ``prime time’’?

§  Convergence – DSO gradient artifacts slows down convergence.

§  3D WAZ – Poor source sampling causes artifacts in subsurface CIGs (offset or angle).

§  Resolution – Can we improve resolution by exploiting velocity information contained in back-scattered waves, and improve global convergence?

[email protected]

Page 9: Slide #1 biondo@stanford

Slide #9

Ready for ``prime time’’?

§  Convergence – DSO gradient artifacts slows down convergence.

§  3D WAZ – Poor source sampling causes artifacts in subsurface CIGs (offset or angle).

§  Resolution – Can we improve resolution by exploiting velocity information contained in back-scattered waves, and improve global convergence?

[email protected]

Page 10: Slide #1 biondo@stanford

Slide #10 [email protected]

Synthetic example – Velocity model

Page 11: Slide #1 biondo@stanford

Slide #11 [email protected]

Velocity information in the data

Transmission kinematics & amplitudes

Page 12: Slide #1 biondo@stanford

Slide #12 [email protected]

Velocity information in the data

Transmission kinematics & amplitudes

Yang Zhang’s & Ali Al-Momin’s

talks

Page 13: Slide #1 biondo@stanford

Slide #13 [email protected]

Velocity information in the data

Transmission kinematics & amplitudes

Reflections kinematics & amplitudes

Ali Al-Momin’s talk

Yang Zhang’s & Ali Al-Momin’s

talks

Page 14: Slide #1 biondo@stanford

Slide #14 [email protected]

Prestack image with constant background velocity

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Slide #15

Non-parametric objective function

[email protected]

Symes & Carazzone,

Geophysics 1991

Chavent & Jacewitz,

Geophysics 1995

Page 16: Slide #1 biondo@stanford

Slide #16 [email protected]

Gradients with non-parametric objective functions

Stacking power maximization

Differential Semblance Optimization (DSO)

Gradients courtesy of Ali Al-Momin

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Slide #17

Parametric objective function

[email protected]

Page 18: Slide #1 biondo@stanford

Slide #18 [email protected]

Example with angle-domain RMO

Biondi & Symes, Geophysics 2004

Page 19: Slide #1 biondo@stanford

Slide #19 [email protected]

Gradient evaluation

Page 20: Slide #1 biondo@stanford

Slide #20 [email protected]

Gradient evaluation – Δρ

Page 21: Slide #1 biondo@stanford

Slide #21 [email protected]

Gradient evaluation – ΔρèΔI0

Page 22: Slide #1 biondo@stanford

Slide #22 [email protected]

Gradient evaluation – ΔρèΔI0

Page 23: Slide #1 biondo@stanford

Slide #23 [email protected]

Gradient evaluation – ΔρèΔI0

Δz(ρ)

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Slide #24

z

Gradient evaluation – ΔρèΔI0

[email protected]

Background Image ( )

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Slide #25

z

Gradient evaluation – ΔρèΔI0

[email protected]

Δz(ρ)

Better-focused Image (I+)

Background Image ( )

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Slide #26

z

Gradient evaluation – ΔρèΔI0

[email protected]

Δz(ρ)

Background Image ( )

Better-focused Image (I+)

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Slide #27

z

Gradient evaluation – ΔρèΔI0

[email protected]

Image depth derivative (dI0/dΔz)

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Slide #28

z

Gradient evaluation – ΔρèΔI0

[email protected]

Image depth derivative (dI0/dΔz)

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Slide #29

Gradient evaluation – ΔI0èΔs

[email protected]

Biondi & Sava, SEG 1999

Luo & Schuster, Geophysics 1991

Page 30: Slide #1 biondo@stanford

Slide #30 [email protected]

Challenges with one-parameter RMO of full-bandwidth data

Central frequency of 25 Hz

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Slide #31 [email protected]

Moveout is too complex

I0 M(ρ)I0 I0 M(ρ)I0

Page 32: Slide #1 biondo@stanford

Slide #32 [email protected]

Moveout is too large

I0 M(ρ)I0 I0 M(ρ)I0

Page 33: Slide #1 biondo@stanford

Slide #33 [email protected]

Moveout is too complex

I0 M(ρ)I0

Page 34: Slide #1 biondo@stanford

Slide #34 [email protected]

Moveout is too large

I0 M(ρ)I0

Page 35: Slide #1 biondo@stanford

Slide #35 [email protected]

Full-bandwidth (25 Hz)

Central frequency of 25 Hz

Page 36: Slide #1 biondo@stanford

Slide #36 [email protected]

Low Frequency (5 Hz)

Central frequency of 5 Hz

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Slide #37 [email protected]

Smoothed along ρaxis

Central frequency of 25 Hz

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Slide #38 [email protected]

dJ/dρat all horizontal locations

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Slide #39 [email protected]

dJ/dρat all horizontal locations

Good OK

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Slide #40

Summary §  I presented a general methodology for

computing gradients of image-focusing objective functions defined by one (or more) kinematic parameters

§  Global convergence could be achieved in absence of low-frequency signal by properly smoothing objective functions along the axes of kinematic parameters.

[email protected]

Page 41: Slide #1 biondo@stanford

Slide #41

Summary §  I presented a general methodology for

computing gradients of image-focusing objective functions defined by one (or more) kinematic parameters

§  Global convergence could be achieved in absence of low-frequency signal by properly smoothing objective functions along the axes of kinematic parameters.

[email protected]

Page 42: Slide #1 biondo@stanford

Slide #42 [email protected]

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Slide #43 [email protected]

Acquisition footprints

Figure 9.1

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Slide #44 [email protected]

Challenges with single-parameter RMO of full-bandwidth data

Central frequency of 5 Hz

Page 45: Slide #1 biondo@stanford

Slide #45 [email protected]

Acquisition footprints

Figure 9.1

Page 46: Slide #1 biondo@stanford

Slide #46 [email protected]

Acquisition footprints

Figure 9.1

Page 47: Slide #1 biondo@stanford

Slide #47 [email protected]

Acquisition footprints

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Slide #48

z

Gradient evaluation – dI0/dρ

[email protected]

Improved Image (I0+ΔI0)

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Slide #49

z

[email protected]

Improved Image (I0+ΔI0)

Page 50: Slide #1 biondo@stanford

Slide #50 [email protected]

Page 51: Slide #1 biondo@stanford

Slide #51 [email protected]

Acquisition footprints