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Although the samples of a sonic log may not be considered statistically
uncorrelated, I will assume that the samples of the sub-sampled well log are
completely independent from one another. There are, therefore, 99 unknowns
in our problem, one for each sample of the sub-sampled sonic log we wish to
recover. Each model parameter, i.e. sample of the trial sonic log, was
coded as a binary number. Although the model parameters can in principle assume
any real value between some reasonable maximum and minimum values, for the
purpose of representing them as binary numbers we need to discretize them.
Here I used 1024 possible values for each parameter, that is, 10 bits. The
maximum and minimum allowed velocities were in the range between 2200 and
3200 m/s. This means a resolution just under 1 m/s for the inversion of each
parameter (each sample of the sonic log).

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Stanford Exploration Project

11/11/2002