How to get consistent standard deviation of GRF's when running simulation in ERT/FMU simulation box grid model
There are currently a weakness in the FMU mode implementation of APS when using GRF's in FMU/ERT/AHM.

The problem: The variance will in general be different for the GRF's created in ERT simulation box and in RMS simulation box for the same zone. The number of grid cells in the ERT simulation box is in general larger than the number og grid cells in the same geomodel grid zone. The standard deviation is calculated by sigma = [Max(trend) - Min(trend)] * relative standard deviation. This means that the actual standard deviation will be different since Min(trend) and Max(trend) is not in general the same for the trend in the ERT simboks grid and the RMS simulation box for the same zone. Note that Min(trend) and Max(trend) are min and max value over all active grid cells of the trend and that number is different for the ERT simbox grid and the RMS geogrid simbox for the same zone.

Solution: Ensure that Min(trend) and Max(trend) is calculated ONLY over the grid cell that are active in the RMS grid model. This can be done by mapping/copying the Zone parameter values from the geogrid zone to the ERT simbox and use that as a variable to filter out the grid cells in the ERT simbox grid that are actually corresponding to active grid cells for the zone it belongs to in the geogrid. This requires a function top map FROM geogrid zone til ERT simulation box grid.

Compare trends from ERT simbox grid for a given zone and RMS geogrid simbox for the same zone : The effect of rescaling (multiply all values buy a constant) or shift (subtract all values by a constant) does not change the sorting order of the values of the active grid cell values. It therefore does not have any effect on the output facies realization, but this can have the effect that comparing GRF trends created in ERT simbox (after it is mapped over to the RMS geogrid) and GRF trend created directly in the geogrid may differ. One ways of ensuring the same values, one should rescale and shift the values by the same amount in trend calculation both in RMS geogrid and ERT simulation box grid. This means calculate rescaled/shifted values by: new_trend_values(i,j,k) = [trend_values(i,j,k) - min(trend over active cells]/[max(trend over active cells)] - min(trend over active cells)]. This will ensure that for all cells that are active( physical cells i RMS geomodel for the zone) will get values between 0 and 1. All values in cells that are not present or inactive in the geomodel but exists in the ERT simbox will and should also be rescaled to be consistent. This approach will ensure that trends created in ERT simulation box grid and in RMS simulation box for the same zone will get the same values if calculated correctly. Then it is possible to compare them after the trend created in the ERT simulation box is mapped over to the RMS geogrid. Finally, note that the gaussian residual values simulated in ERT simbox and in RMS simbox for the same zone in general always will differ since the number of grid cells used in the simulation algorithm for these two cases differs. So it is not possible to use a comparison of GRF's with both trend and residuals created in ERT simbox grid and RMS simbox as criteria for consistency. But by running with 0 relative standard deviation, trends can be compared when taken into account that the active cell values are rescaled/shifted consistenty in the algorithm applied to the two grids as mentioned above.