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The stationary phase method is an approach for solving integrals analytically by evaluating
the integrands in regions where they contribute the most. This method is specifically
directed to evaluating oscillatory integrands, where the phase function of the integrand is multiplied
by a relatively high value. In our case, this value corresponds to the frequency and thus
our approximation is asymptotically exact as the frequency approaches .
Integrals of the form
are approximated asymptotically () when
by
| |
(149) |
where t0 is the ``stationary point'' in which the derivative of
the phase is zero. The approximation described in equation () assumes the
second derivative is non-zero, which is the case here.
D
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Stanford Exploration Project
7/5/1998