Parameter Encoding

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).