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 Bolondi, C. D., Loinger, E., and Rocca, F., 1982, Offset continuation of seismic sections: Geophysical Prospecting, 30, 813828.

 Forel, D., and Gardner, G. H. F., 1988, A three dimensional perspective on twodimensional dip moveout: Geophysics, 53, 604610.

 Notfors, C. D., and Godfrey, R. J., 1987, Dip moveout in the frequencywavenumber domain: Geophysics, 52, 17181721.

The time stretch (1) amounts to time stretch
proportional to time:
 
(7) 
The logarithmic resampling is defined by:
 
(8) 
After logarithmic variable transformation from t to s
the time stretch of equation (1) and
(A1) is:
 
(9) 
 
(10) 
Having Fourier transformed the time series p'(s) this constant shift
translates to a complex scaling:
 
(11) 
denotes the stretched variable of the domain.
After Fourier transformation from variable t to
the original stretch relation (1) becomes
 
(12) 
After logarithmic transformation (A2) of the frequency trace
we find relationships equivalent to equation (A3)
and (A4):
 
(13) 
 
(14) 
describes the new variable in the logarithmic domain.
An additional Fourier transformation allows us
to express the intended
time stretch as a simple scaling (4) of the transformed trace.
We want to map our input trace onto a logarithmic mesh. How many
samples do we need in the logarithmic domain?
According to equation (A2) the relation between interval
and is:
 
(15) 
is the sampling interval for which the time trace is properly
sampled. is the maximum time of p(t). At is at a minimum:
 
(16) 
where is the Nyquist frequency corresponding to .The number of sample points in the log domain has to be
 
(17) 
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Stanford Exploration Project
11/18/1997