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Finite-difference migration
THE PARABOLIC EQUATION
SPLITTING AND SEPARATION
The heat-flow equation
Splitting
Full separation
Splitting the parabolic equation
Validity of the splitting and full-separation concepts
FINITE DIFFERENCING IN (omega,x)-SPACE
The lens equation
First derivatives, explicit method
First derivatives, implicit method
Explicit heat-flow equation
The leapfrog method
The Crank-Nicolson method
Solving tridiagonal simultaneous equations
Finite-differencing in the time domain
WAVEMOVIE PROGRAM
Earth surface boundary condition
Frames changing with time
Internals of the film-loop program
Side-boundary analysis
Lateral velocity variation
Migration in (omega,x)-space
HIGHER ANGLE ACCURACY
Another way to the parabolic wave equation
Muir square-root expansion
Dispersion relations
The xxz derivative
END OF CHAPTER FOR NOW
Retardation (frequency domain)
Lateral velocity variation again
Splitting again
Time domain
Upcoming waves
SPLITTING AND SEPARATION APPLICATIONS
Application to 3-D downward continuation
Separability of 3-D migration (Jakubowicz)
Separability in shot-geophone space
THE ACOUSTIC WAVE EQUATION
Reflections and the high-frequency limit
About this document ...
Stanford Exploration Project
12/26/2000