Two papers you should look at, one is by Andre Journel and is in Mathematical Geology (circa 1980)  and the other is by Noel Cressie  in the proceedings of the Banff conference on geostatistics (circa 2004). You could also find them by searching Google for the authors

A few cautions, to obtain the relationship between the (theoretical) variograms for a random function with a multivariate log normal distribution and the corresponding normal distribution see Journel. However a univariate transformation does not ensure that the transformed distribution is normal.

Empirical variograms do not have any parameters, only the theoretical model does. For a given data set the empirical variogram is not unique, it depends on several user choices such as the width of the distance classes, the smallest lag distance, maximum lag gistance, whether it is an omnidirectional variogram or a directional variogram.  The linear variogram model does not have a range, it does not have a sill.

You can't use a spherical variogram with a log normal distribution, see a paper by Georges Matheron.

While it is common to refer to the range of a gaussian or an exponential variogram, neither has a true range. Most softwares use what is called the "effective" range which is the lag distance at which the value of the variogram is 95% of the sill. In constrast a spherical model does have a true range.

If you use an automatic fitting algorithm then you need to recognize that there is no unique/best possible choice for optimizing the fit of the model to the empirical variogram or to the variogram cloud (gstat has several choices for the weighing in the least squares fitting.

Finally, the geostatistical model is based on the assumption that the data is a NON RANDOM sample from one partial realization of the random function. Random selection of the data locations is not the same as random sampling from a distribution. Common tests for normality are not really valid.

This doesn't really answer your question but there is no simple unique answer. Do you need to re-transform the kriged values? If so this complicates the question

First, I think your variogram for raw data does not have a spherical shape, but rather a linear shape. You may not fit a spherical model on an experimental variogram if it does not reach (or seems to tend towards) a sill in the available range of distances. I think that's the main reason why range parameter differs between raw vs. log-transf. variogram models.

To check if I'm right about my latter hypothesis, you may do the same exercise with a dataset which has an experimental variogram that actually fits well with a spherical model.

Also, I think the difference might be due to the automatic fitting process: don't forget that log(d) has a derivative (~slope) decreasing with increasing d; consequently, at large distances d, log(d) will look like it has almost reached  a sill.

Finally, I suggest you to consider also the great gstat package for R. I've used it many times, and it works nicely, and is well documented.

Cheers.

Two papers you should look at, one is by Andre Journel and is in Mathematical Geology (circa 1980)  and the other is by Noel Cressie  in the proceedings of the Banff conference on geostatistics (circa 2004). You could also find them by searching Google for the authors

A few cautions, to obtain the relationship between the (theoretical) variograms for a random function with a multivariate log normal distribution and the corresponding normal distribution see Journel. However a univariate transformation does not ensure that the transformed distribution is normal.

Empirical variograms do not have any parameters, only the theoretical model does. For a given data set the empirical variogram is not unique, it depends on several user choices such as the width of the distance classes, the smallest lag distance, maximum lag gistance, whether it is an omnidirectional variogram or a directional variogram.  The linear variogram model does not have a range, it does not have a sill.

You can't use a spherical variogram with a log normal distribution, see a paper by Georges Matheron.

While it is common to refer to the range of a gaussian or an exponential variogram, neither has a true range. Most softwares use what is called the "effective" range which is the lag distance at which the value of the variogram is 95% of the sill. In constrast a spherical model does have a true range.

If you use an automatic fitting algorithm then you need to recognize that there is no unique/best possible choice for optimizing the fit of the model to the empirical variogram or to the variogram cloud (gstat has several choices for the weighing in the least squares fitting.

Finally, the geostatistical model is based on the assumption that the data is a NON RANDOM sample from one partial realization of the random function. Random selection of the data locations is not the same as random sampling from a distribution. Common tests for normality are not really valid.

This doesn't really answer your question but there is no simple unique answer. Do you need to re-transform the kriged values? If so this complicates the question

Don't try to interpret the parameters of the variogram estimated and modeled using log transformed data as being simply a transform of the parameters if the variogram were estimated and modeled using the original data. It is not that simple, see the paper by Journel reference above.

I suspect you did a univariate transform, simply replaced each original data value by its logarithm, You need a transform that will generate a multivariate gaussian distribution for it to be really useful.

You say the frequency distribution of the transformed data "looks more normal", that is a meaningless statement, just having a sort of bell shaped curve is not enough.

If you are going to use the transformed data and the variogram estimated and modeled using that data for kriging then you have a problem, you can't back transform the kriged values by simply using an exponential. If on the other hand you use those kriged values without back transforming you might get useful results. Note the comment by Laurencelle