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## Splitting again

The customary numerical solution to the x-domain 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 kx and clear from the denominators to get Table .6.

 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 x-variable if the model is x-variable. The second arises in a mathematical transformation, namely, equation (), so it is purely a matter of definition.

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12/26/2000