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Ordinary and simple kriging

I'm performing ordinary and simple kriging from a set of non-negative
values:
krige.conv: model with constant mean
krige.conv: Kriging performed using global neighbourhood

and
krige.conv: model with constant mean
krige.conv: Kriging performed using global neighbourhood

where my.variogram.model is gaussian fitted through variofit with
"cressie" weigths.

I'm getting the same predicted values for both models, 12%  of them
being negative. Is it because simple and ordinary kriging predictions
are not including the overall mean? If this is the case what mean should
I use?
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