The semi-variogram is widely used in geostatistical data analyses. It is estimatedby the sample semi-variogram. Although some theoretical work has been done on its sampling distribution for a Gaussian process these results are not of immediate practical usage because of the problems induced by the presence of spatial inter-correlations. In this paper various simulation studies are reported which give overwhelming evidence that a logarithmic transformation of the semi-variogram gives approximate normality for moderately large sample sizes. This result is theoretically expected under certain conditions. A robust estimator of the semi-variogram was also studied using the simulations.