Once we have NZ-wide median and sigma vs30 models for Terrain and Geology we can integrate these together to create a combined model.

Median

The two approaches that have been used in previous versions of the code were: Weighting the two models 0.5 each and using geology only.

When using weights a weighting geometric mean was taken.

Sigma

When combining the sigma the below equation is used. The two contributors to the final sigma value are sigma from each model and difference between median values of the model and the final Vs30 value. This means that even if the individual model sigma value is low but the two models give disparate median values then the sigma value would be relatively high.

Improvements

A standard deviation based merge could be considered. Giving the model with a lower standard deviation a relatively higher weight on the median combination. This is indicative of the model with higher confidence of accuracy. This would indicate a w that changes spatially across the country.