$l_a=\frac{\lambda_0 \sqrt{\varepsilon'}}{2 \pi \varepsilon''}$

Where $l_a$ is the penetration depth in ice, defined as the depth at wich the signal power falls to $1/e$, $\varepsilon'$ and $\varepsilon''$ are respectively the real and imaginary parts of the dielectric constant, and $\lambda_0$ is the free space wavelength of the electromagnetic radiation.

And so, the microwave radiation (higher wavelength radiations in the electromagnetic spectrum) used in ground penetrating radar can penetrate through the ice surface, the depth thru which it can penetrate being given by the same equation mentioned above. Cheers.