Geostructures and interpolation from pilot point parameters to model grid

[robinkeegan]

Hi all,
I am just getting started with PyEmu so apologies if this an obvious question. I have been parameterising a model with PyEmu for conditioning with IES. This includes setting up spatially variable K using a constant multiplier and multipliers at pilot points. The pilot points use a variogram geostructure. I have two main questions relating to the geostats and interpolation:

1. Does the sill of the variogram need to be modified to be consistent with the parameter bounds? This notebook (https://github.com/gmdsi/GMDSI_notebooks/blob/main/tutorials/part2_01_pstfrom_pest_setup/freyberg_pstfrom_pest_setup.ipynb) uses a sill of 1, which suggests to me there is an internal calculation in PyEmu that adjusts the covariance from a sill of 1 to the parameter bounds.
2. How are the pilot point parameters interpolated to the grid in a forward run? I found some references to ordinary kriging (OK). If it is OK does that use the same geostructure that was specified for the specific parameter?

Many thanks,
Robin

[jtwhite79]

good questions.

1. internally with PstFrom, we scale the sill of the variogram using the parameter bounds so that the sill equals the variance implied by the bounds when PstFrom.draw() is called. So this is why we want the sill to be 1.0...

2. The interpolation from the pilot points to the grid does use the same geostructure that is supplied when you call PstFrom.add_parameters() just as you suggest.