  Galaxies observed today are likely to have evolved from density perturbations
in the early universe. Perturbations that exceeded some critical threshold are
conjectured to have undergone gravitational collapse to form primordial black
holes (PBHs) at a range of masses. Such PBHs serve as candidates for cold dark
matter and their detection would shed light on conditions in the early
universe. Here we propose a mechanism to search for transits of PBHs
through/nearby Earth by studying the associated seismic waves. Using a
spectral-element method, we simulate and visualize this seismic wave field in
Earth's interior. We predict the emergence of two unique signatures, namely, a
wave that would arrive almost simultaneously everywhere on Earth's free surface
and the excitation of unusual spheroidal modes with a characteristic
frequency-spacing in free oscillation spectra. These qualitative
characteristics are unaffected by the speed or proximity of the PBH trajectory.
The seismic energy deposited by a proximal ${M^{PBH} = 10^{15}}$ g PBH is
comparable to a magnitude $M_w=4$ earthquake. The non-seismic collateral damage
due to the actual impact of such small PBHs with Earth would be negligible.
Unfortunately, the expected collision rate is very low even if PBHs constituted
all of dark matter, at ${\sim 10^{-7} {yr}^{-1}}$, and since the rate scales as
${1/M^{PBH}}$, fortunately encounters with larger, Earth-threatening PBHs are
exceedingly unlikely. However, the rate at which non-colliding close encounters
of PBHs could be detected by seismic activity alone is roughly two orders of
magnitude larger --- that is once every hundred thousand years --- than the
direct collision rate.
