One of the main ideas in
Fourier analysis is that an impulse function
(a delta function) can be constructed by the superposition of sinusoids
(or complex exponentials).
In the study of time series this construction is used for the
*
impulse response
*
of a filter.
In the study of functions of space, it is used to make a physical point source.

Taking time and space together, Fourier components can be interpreted as monochromatic plane waves. Physical optics (and with it reflection seismology) becomes an extension to filter theory. In this section we learn the mathematical form, in Fourier space, of the Huygens secondary source. It is a two-dimensional (2-D) filter for spatial extrapolation of wavefields.

- Migration improves horizontal resolution
- Rays and fronts
- Waves in Fourier space
- The input-output relation
- Travel-time depth

10/31/1997