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_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_min a dark matter particle must have to impart a recoil energy E_R to a target nucleus. It is widely

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... ved that the modulation expressed as a function of v_min is common to all experiments, irrespective of the dark matter distribution. We point out that the annual modulation as a function of v_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.