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The problem at hand is stretching a time series *p*(*t*). The amount of
stretch is to be proportional to time t:
| |
(1) |

This task occurs frequently when performing dip moveout correction (DMO)
Bolondi et al. (1982); Forel and Gardner (1988); Notfors and Godfrey (1987). Constant velocity DMO stretches
each input trace for a range of alpha values. All the stretched
traces are added into the final zero offset data.
After applying logarithmic resampling and Fourier transform to a time series
the stretching expressed by equation (1) reduces to a
multiplication. Unfortunately, this frequently used logarithmic
transformation requires long traces, in order to prevent data
aliasing. We propose a variation of the logarithmic resampling
which results in shorter series in the transformed domain.

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Stanford Exploration Project

11/18/1997