After checking the literature, the most standard definition of the GFP is the standard deviation across sensors:
- Global field power and topographic similarity | SpringerLink
- Glossary — MNE 1.2.dev0 documentation
- [Eeglablist] get global field power of ERP data
Brainstorm was computing a RMS measure instead (sqrt(sum(x.^2)), and then normalizing by the maximum for display (brainstorm3/figure_timeseries.m at master · brainstorm-tools/brainstorm3 · GitHub). The results is usually very similar or event identical as the STD because the mean of all the sensor values is most of the time close to zero (or IS equal to zero in the case of EEG with an average reference).
But to match the most common definition, I updated the code and documentation to use the STD instead:
- GFP: Changed to STD(F) instead of SQRT(SUM(F.^2)) · brainstorm-tools/brainstorm3@b9dce39 · GitHub
- https://neuroimage.usc.edu/brainstorm/Tutorials/Averaging#Visual_exploration
However, the difference between GFP and POWER(cluster) you reports is normal: the former is the square root of the latter.