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The frequency will range over .If the *t*-axis is going to be handled by finite differencing
then we will need the *Z*-transform variable equation (50)

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(50) |

and the causal derivative (52)
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(51) |

The data can be subsampled or supersampled before processing,
so is an adjustable parameter.
The causality parameter should be
a small amount less than unity,
say where is an adjustable parameter.
You may want to introduce even if you are migrating
in the frequency domain because it reduces wraparound
in the time domain--it is a kind of viscosity.
The should be about inverse to the data length,
say 1 / *N*_{t} where *N*_{t} is the number of points on the time axis.
(Because I made many plots of synthetic hyperbolas with square root gain,
, time wraparounds were larger than life.
So I had the program default to four times larger).
If you like to adjust free parameters,
you could separately adjust numerator and denominator values of .Subsequently, I'll distinguish between and ,but you can take to be if you don't care to
introduce causality.

** Next:** Retarded Muir recurrence
** Up:** ACCURACY THE CONTRACTOR'S VIEW
** Previous:** Lateral derivatives
Stanford Exploration Project

10/31/1997