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.

Constant wave speed

Fourier transform in t, x, y

Forward modeling

What happens when ?

• Kinematics are correct.

• Dynamics are not.

G. Q. Zhang [1993]

Theorem: It works!

Same eikonal equations

Same transport equation

Wave equation migration

Imaging condition

True amplitude WEM

Imaging condition

Theorem: It Works!

True Amplitude WEM

Common-shot Kirchhoff Inversion

Image: U/D

Image: pU/pD

Summary

• True amplitude one-way wave equations with proof.

• True amplitude common-shot WEM with proof.

• Numerical check for v(z) only.