The frequency spectrum of a typical seismic trace is usually bandlimited. and are upper and lower limits of this relatively small, significant part of the spectrum. On the other hand, a seismic time series carries valuable information at early as well as late times. Therefore, and must be close to the extreme ends of the time series. In other words, for seismic traces is usually large, while is comparatively small. Equation (3) and (5) show that the proposed method operating on p(t)'s bandlimited spectrum results in shorter traces. The length ratio of a trace being processed by the proposed versus the standard logarithmic transformation is:
Having applied logarithmic and Fourier transformation to p(t)'s frequency spectrum or to p(t) directly, the desired trace stretching (1) is performed by simple scaling of the trace.
Stretching the input trace by the proposed method is more efficient than the standard methods, if each input trace gets mapped into many output traces. Then the overhead of the initial Fourier and logarithmic transformations are justified by facilitating a fast stretching step which operates on short traces.