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I am attempting to create surfaces of strata via Kriging in Arc GIS from borehole data. In addition to the predicted surface I also want surfaces showing 95% confidence above and below the predicted surface. The issue I'm having is with these 95% surfaces.

The surfaces are very "tight" to the known surface when within a couple of meters of a known value/ borehole but standard errors immediately become high once a few meters away from the borehole.

enter image description here I have included a cross-section of our 3 surfaces. The predicted surface is represented by the middle line with the lower dashed and upper line the lower and upper 95% confidence limits. Please note how steeply we lose confidence at a very close distance to a known borehole.

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In fact, in your case, you are not losing confidence: you are gaining confidence (because you told your model to trust the observed values). So what you observe is a confidence interval at 95 % that becomes very small (in other words there is no uncertainty, so the confidence is high on the valueat this location).

If there is no nugget effect, your kriging will be an exact estimator (meaning that the interpolated surface is equal to the observed values where they are available).

That being said, it seems to me that your model did not catch the spatial autocorrelation near the boreholes (probably because you don't have enough pairs of points located at close distances). I suggest that you try with another model than the spherical model (e.g. gaussian or cubic) in order to have something smoother (variance increases slower at short distances of the observation with those models). Maybe a small nugget effect could also help in your case if there are reasons to believe that the borehole measurements could be unprecise. However, my advices should be taken with care because a good understanding of the underlying phenomenom is necessary to select the best model when there are no pairs of points for all types of distances.

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