Step 1: Split logs into porosity tools and non porosity tools.
Neutron and density logs are both porosity logs. They are recorded on matched scales so the two curves overlay each other in a normal, gas free zone. Caliper, resistivity, self potential and gamma ray are not porosity logs, they measure hole size, formation resistivity, natural potential and natural radioactivity.
Step 2: Explain why only porosity tools can cross over.
A crossover needs two curves recorded on the same type of scale, moving in opposite directions when gas replaces liquid in the pore space. Gas lowers the hydrogen content, so the neutron curve shifts to a lower apparent porosity, while gas lowers the bulk density, so the density curve shifts to a higher apparent porosity. Because both curves sit on comparable porosity scales, they visibly swap positions and cross. This only happens for the neutron density pair.
Step 3: Test the caliper resistivity pair.
Caliper reads hole diameter in inches, resistivity reads ohm metre values on a logarithmic scale. There is no shared porosity scale, so gas cannot make these two curves cross over one another.
Step 4: Test the neutron self potential pair.
Self potential is a millivolt curve used for shale and bed boundary picking, unrelated to hydrogen content. It does not move in a fixed direction with gas the way the neutron curve does, so no crossover is defined against the neutron log.
Step 5: Test the caliper gamma ray pair.
Gamma ray tracks natural radioactivity from shale minerals, caliper tracks hole size. Gas presence in a clean sand does not systematically move either curve against the other on a shared scale, so again no crossover applies.
Step 6: Conclude.
Since crossover is a porosity log phenomenon, only the neutron density pair shows it. The other three pairs, caliper-resistivity, neutron-self potential and caliper-gamma ray, do not exhibit a gas crossover.
$\boxed{\text{(B), (C) and (D)}}$