[Physics] Can extra-solar gamma rays reach the Earth’s surface

Question

Can gamma rays of high enough energy entering our planet's atmosphere reach the surface (50% probability)?

Or, in other words, is there a window for extremely high-energy gamma rays like for the visible spectrum and radio?

This figure, from Electromagnetic Spectrum, shows that the penetration of gamma rays increases with increasing energy, but it seems to level out at about 25 km altitude:

There are no units on the X-axis, and thus it does not show the energy for the highest energy gamma rays for this figure. This does not rule out a window at even higher energies.

Answer 1

I found a reference through Google Books, Very high energy gamma-ray astronomy by Trevor Weekes, which says that the atmosphere is essentially opaque to high-energy gamma rays, equivalent to a meter-thick wall of lead. We are able to do gamma-ray astronomy with ground-based telescopes by detecting the decay products of the gamma rays' interactions with atmospheric particles, but the photons themselves never (well, essentially never) reach the ground.

From page 13:

The earth's atmosphere effectively blocks all electromagnetic radiation of energies greater than $10\text{ eV}$. The total vertical thickness of atmosphere above sea level is $10^{30}\ \mathrm{g\ cm^{-2}}$, and since the radiation length is $37.1\ \mathrm{g\ cm^{-2}}$, this amounts to more than 28 radiation lengths. This is true up to the energy of the highest known cosmic rays (some of which may be gamma rays).