Recent theoretical work has explored dark matter accumulation in the Earth and its drift toward the center of the Earth that, for the current age of the Earth, does not necessarily result in a concentration of dark matter (χ) in the Earth's core. We consider a scenario of long-lived $(τ_χ∼10^{28}s)$, superheavy $(m_χ=10^7-10^{10} GeV)$ dark matter that decays via $χ→ν_τ\overline{ν}_τ$ or $χ→ν_μ\overline{ν}_μ$. We show that an IceCube-like detector over 10 years can constrain a dark matter density that mirrors the Earth's density or has a uniform density with density fraction ϵρ combined with the partial decay width $B_{χ→ντ\overline{ν}_τΓ_χ}$ in the range of $(ϵρ/10^{-10})B_{χ→ν_τ}Γ_χ≲1.5×10^{-29}-1.5×10^{-28} s^{-1}$. For $χ→ν_μ\overline{ν}_μ, m_χ=10^8-10^{10} GeV$, and $E_μ>10^7 GeV$, the range of constraints is $(ϵρ/10_{-10})B_{χ→ν_μ}Γ_χ≲3×10^{-29}-7×10^{-28} s^{-1}$.