True Amplitude WEM arising from True Amplitude One-way Wave Equations

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# True Amplitude WEM arising from True Amplitude One-way Wave Equations - PowerPoint PPT Presentation

True Amplitude WEM arising from True Amplitude One-way Wave Equations. Yu Zhang, GuanQuan Zhang and Norman Bleistein. Basic Plan. Derive dynamically correct one-way wave equations. Migrate data with the new equations. Apply imaging condition to dynamically correct migrated data.

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### True Amplitude WEM arising from True AmplitudeOne-way Wave Equations

Yu Zhang, GuanQuan Zhang

and Norman Bleistein

Basic Plan
• Derive dynamically correct one-way wave equations.
• Migrate data with the new equations.
• Apply imaging condition to dynamically correct migrated data.
• Show computer output.

Forward modeling

Constant wave speed

Fourier transform in t, x, y

What happens when

?

• Kinematics are correct.
• Dynamics are not.
G. Q. Zhang [1993]

Theorem: It works!

• Same eikonal equations
• Same transport equation
Theorem: It Works!

True Amplitude WEM

T Common-shot Kirchhoff Inversion

Summary
• True amplitude one-way wave equations with proof.
• True amplitude common-shot WEM with proof.
• Numerical check for v(z) only.