Convert EMAG2 GeoTIFF grid to GMT-compatible grid

A relatively new version of the global 2-minute Earth Magnetic Anomaly Grid (EMAG2) grid is available in GeoTIFF grid format at this NGDC URL:

If I run gdal_translate to convert that GeoTIFF grid file to a GMT-compatible grid format, everything looks good although I end up with an old “cf” deprecated GMT format:
% gdal_translate -b 1 -of GMT EMAG2_V3_20170530_UpCont.tif EMAG2_V3_20170530_UpCont.grd

If I then run grdconvert to convert that global “cf” grid to a more modern COARDS-compliant GMT grid and also use -R to chop out a smaller area, I get a very strange minimum Z value:
% grdconvert EMAG2_V3_20170530_Sealevel.grd -GEMAG2_V3_20170530_Sealevel_nf.grd=nf -R0/20/40/60 -V

I do not understand why the Z range will blow up with grdconvert (it also blows up if I simply use grdcut to extract a smaller area from the “cf” grid).

Is there a way to go straight from the GeoTIFF grid to a COARDS-compliant GMT grid without messing up the Z values?

Thanks for any pointers,

GeoTIFFs are GMT-compatible formats de per se. But if want to convert them to netCDF use grdconvert directly on the GeoTIIF. If the Z range problem persists that may indicate something wrong in GeoTIFF metadata.

Whoever made that TIFF decided this was a good idea:

Upper Left  (  -0.0166667,  89.9833333) 
Lower Left  (  -0.0166667, -89.9833333) 
Upper Right (     359.983,      89.983) 
Lower Right (     359.983,     -89.983) 
Center      ( 179.9833333,   0.0000000) 
Band 1 Block=128x128 Type=Float32, ColorInterp=Gray
  NoData Value=-3.4028234663852886e+38

So kind of a pixel grid in latitude and a weird shift pixel grid or gridline with missing repeat in longitude.

Thanks to Joaquim and Paul for responding. With that new knowledge, it was easy to use grdconvert to directly convert the EMAG2 GeoTIFF grids to GMT-compatible COARDS-compliant netCDF grids (commands included below). And, from there, I was able to add the data with no problem to the GeoMapApp menus. Thank you!

% grdconvert EMAG2_V3_20170530_Sealevel.tif -GEMAG2_V3_20170530_Sealevel.grd -V
% grdconvert EMAG2_V3_20170530_UpCont.tif -GEMAG2_V3_20170530_UpCont.grd -V