Can I "stack" semivariogram data?

Question

I have several synoptic measurements (every few months) of a gravity field I would like to interpolate by kriging. Each group of measurements comprises about 45 measurement locations, and spatial correlation is relatively poor. I would like to use a single semivariogram model for all of the interpolated surfaces, rather than fitting a unique model for each measurement time. I think this is appropriate because the changes over time are caused by the same underlying phenomena (groundwater level change), and the spatial correlation should be unchanging with time.

Is there any problem with "stacking" the semivariogram data? I would have to calculate the semivariance-distance pairs independently for each measurement time, but could then combine all of them on a single semivarogram plot and fit my model to all of the data pairs. I'm primarly an arc user, but I think I could create the semivariogram model outside of arc (e.g., MATLAB) and simply specify the nugget/sill/major range for spatial analyst. Thanks-

Answer 1

This is perfectly legitimate. It is based on the assumption that the covariance structure of the random field does not change from time to time. One way to see that this is OK (without writing complicated statistical formulas) is to suppose that the data at each time have the same relative locations--leaving the distances and bearings unchanged--but have been displaced by such a large distance that you would not want to pair values at one time with values at another due to their large spatial displacement. The spatial stationarity assumption in this hypothetical case is implied by the assumptions of (a) spatial stationarity at each individual time and (b) no change over time; and the data pairs used for the variogram estimation are identical in both cases.

(I have used this technique to krige groundwater monitoring data, most recently in a successfully defended US federal court case.)