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A straightforward solution to (1) is trace interpolation.
But because of the very simple form of stretch, there are elegant
alternatives to explicit trace interpolation.

After logarithmic and Fourier transformation of the time function *p*(*t*)
the original stretch can be performed by a simple multiplication^{}:

| |
(2) |

For brevity, we will refer to this ourier transformed ogarithmic domain
as domain.
denotes the variable in the domain after stretching.
To prevent the time trace from being undersampled, the trace after
logarithmic transformation will have to have *n*_{s} samples^{}, where

| |
(3) |

is the maximum frequency of *p*(*t*),
, are the upper and lower limits of the section of
*p*(*t*), that
the logarithmic trace of *n*_{s} points resamples
correctly. In practice the logarithmic trace is often found to be
extremely long.

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Stanford Exploration Project

11/18/1997