  According to a scenario in string cosmology, a relic background of light
dilatons can be a significant component of the dark matter in the Universe. A
new approach of searching for such a dilatonic background by observing Earth's
surface gravity was proposed in my previous work. In this paper, the concept of
the geophysical search is briefly reviewed, and the geophysical constraint on
the dilaton background is presented as a function of the strength of the
dilaton coupling, $q_b^2$. For simplicity, I focus on massless dilatons and
assume a simple Earth model. With the current upper limit on $q_b^2$, we obtain
the upper limit on the dimensionless energy density of the massless background,
$\Omega_{DW}h^2_{100} \leq 6 \times 10^{-7}$, which is about one-order of
magnitude more stringent than the one from astrophysical observations, at the
frequency of $\sim$ 7 $\times$ 10$^{-5}$ Hz. If the magnitude of $q_b^2$ is
experimentally found to be smaller than the current upper limit by one order of
magnitude, the geophysical upper limit on $\Omega_{DW}h^2_{100}$ becomes less
stringent and comparable to the one obtained from the astrophysical
observations.
