INTRODUCTION

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

$${p_{1}(t_{1})} = {p(\alpha t)}.$$ (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.