  Antiquark nuggets are hypothetical compact composite objects conjectured to
account for a significant fraction of dark matter in the Universe. In contrast
to quark nuggets, these objects consist of antimatter. They may remain
undetected if they possess a sufficiently small cross section relative to their
mass. In this paper, we investigate the allowed region in the parameter space
of this model that is consistent with the observed neutrino flux from the Sun
and the Earth, and the non-observation of seismic events with specific
signatures of dark matter particles. We found the allowed values of the
antibaryon charge number in this model to be in the interval $2\times
10^{24}<A<8\times 10^{25}$, while the probability of nucleon annihilation upon
collisions with the antiquark core is constrained by $0.1\lesssim \kappa<0.25$.
Although very large values of the antibaryon charge, $A>10^{33}$, are not fully
excluded by the present study, we show that they conflict with the
non-observation of rare catastrophic explosion-like events on the Earth.
