  Due to Earth's revolution around the Sun, the expected scattering rate in
direct dark matter searches is annually modulated. This modulation is expected
to differ between experiments when given as a function of recoil energy
$E_\text{R}$, e.g. due to the gravitational focusing effect of the Sun. A
better variable to compare results among experiments employing different
targets is the minimum speed $v_\text{min}$ a dark matter particle must have to
impart a recoil energy $E_\text{R}$ to a target nucleus. It is widely believed
that the modulation expressed as a function of $v_\text{min}$ is common to all
experiments, irrespective of the dark matter distribution. We point out that
the annual modulation as a function of $v_\text{min}$, and in particular the
times at which the rate is maximum and minimum, could be very different
depending on the detector material. This would be an indication of a scattering
cross section with non-factorizable velocity and target material dependence.
Observing an annual modulation with at least two different target elements
would be necessary to identify this type of cross section.
