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The customary numerical solution to the xdomain forms of the equations
in Tables .4 and .5 is arrived at by splitting.
That is, you march forward a small step alternately
with the two extrapolators
 
(71) 
 (72) 
The first equation, called the
lens equation,
is solved analytically:
 
(73) 
Migration that includes the lens equation
is called depth migration.
Migration that omits this term is called
time migration.
Observe that the diffraction parts
of Tables .4 and .5 are the same.
Let us use them and equation () to
define a table of diffraction equations.
Substitute for i k_{x} and
clear from the denominators to
get Table .6.
Table:
Diffraction equations for laterally variable media.



zero 














You may wonder where the two velocities v(x,z) and came from.
The first arises in the wave equation,
and it must be xvariable if the model is xvariable.
The second arises in a mathematical transformation,
namely, equation (),
so it is purely a matter of definition.
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Previous: Lateral velocity variation again
Stanford Exploration Project
12/26/2000