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According to the classic rules of mathematical physics, the
solution of the kinematic equations (15) and (16)
can be obtained by solving the following system of ordinary
differential equations:
 

 (20) 
Here m stands for either v or ,=, . To trace the v and rays, we must first
identify the initial values x_{0}, , , and
from the boundary conditions. The variables x_{0} and
describe the initial position of a reflector in a
timemigrated section, describes its migrated slope, and
is simply .
Using the exact kinematic expressions for f results in rather
complicated representations of the ordinary differential equations.
The linearized expressions, on the other hand, are simple and allow
for a straightforward analytical solution.
Next: From kinematics to dynamics
Up: Alkhalifah and Fomel: Anisotropy
Previous: Linearization
Stanford Exploration Project
11/11/1997