Why is there a logarithmic grid on this plot?
It's a mistake.

You probably know this, but for anyone who's interested, these wireline logs are:


DRHO — density ('RHO') correction (delta, or 'D') in g/cc.
DPHI — porosity ('PHI') from density ('D'), as a fractional proportion.
NPHI — porosity from the neutron log ('N'), as a fractional proportion.


All of these logs are usually displayed on a linear scale. Indeed it wouldn't make sense to display them on a log scale, which is mainly for displaying resistivity logs, e.g. the induction log. Even if they were, it wouldn't make sense to show the usual 4 octaves (0.2 to 2000 for resistivity), given the range of the data and the scale of porosity values geologists are interested in.

It's not clear if the data have actually been displayed on a log scale, or if it's just that the grid has been erroneously added. I would treat the data with suspicion.