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In last section, we have described how to estimate the relative time-shift
through the non-linear optimization. Although our method has several nice properties,
yet it also has a defect: the accuracy of the estimation is
limited to the time-sampling interval. This is because data is available
only at the integer multiples of the sampling interval. One way to solve the problem
is to interpolate data along time axis before the algorithm is
applied to it. However, in addition to the cost of interpolation,
the computational cost of the non-linear optimization algorithm increases much
faster than does the accuracy of the estimation. For example, let *k* be the
ratio of the new sampling interval to the original sampling interval,
the computational cost will increases by a factor of *k*^{2} while the accuracy
increases only by a factor of *k*. Another way is to interpolate the computed
objective function. But the solutions obtained by using this method will
depend on the choice of interpolation algorithms.
In this section, we will describe an elegant algorithm that does not require
heavy computation, and yet has the potential to find the exact solution.

** Next:** Objective function
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Stanford Exploration Project

1/13/1998