For my geophysics class I am trying to illustrate the fact that it is possible to increase the S/N ratio of a seismic signal data set corrupted with zero mean random noise by adding a number of independent data sets from the same reflector where noise is uncorrelated from set to set. The expected improvement in S/N is proportional to sqrt(N) where N is the number of independent data sets. Thus adding 4 sets together should improve the S/N by a factor of 2, 3 db where S/N in db = 10log(rms signal squared/rms noise squared).

To illustrate this, I use Excel to generate four data sets of 100 points each with zero mean random noise. I compute the rms squared value of a single data set and compare it to the rms squared value of the summed and normalized data set.

The resulting improvement in S/N consistently computes to 6db insead of 3db. This being the square of the expected value leads me to suspect I am doing something wrong.

Once again, 4 independent data sets of zero mean random noise. These four data sets are added together sample by sample and divided by four. The rms value of one unsummed data set is compared to the summed data set. The expected improvement in S/N is 2; what I get is 4.

Any explanations?

Vic