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To realize transformation (2) each input trace, *q*(*t*,*m*,*h*), has to
be stretched by the factor *k*/*h*:

| |
(4) |

The differential time moveout of equation (1) is
proportional to time:
| |
(5) |

Logarithmic resampling is defined by:
| |
(6) |

where denotes the frequency variable after Fourier transformation
of the input trace. *T*_{c} is the start of the unmuted frequency trace.
Elsewhere in this report (), I show that
After two Fourier transforms and the intermediate logarithmic
resampling, each trace stretching amounts to a simple
trace scaling:
| |
(7) |

Resampling the *Fourier transformed input trace* rather than
the *trace* itself takes advantage of the band limitation of typical
seismic data ().
The more compact data cube reduces the computation time and
the amount of memory required.

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Stanford Exploration Project

11/18/1997