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EDIT: I have closed this question until I have a proper depth for the frozen atmosphere

I'm playing around with setting up an outpost on a rogue planet, and want to scan for deposits of various metals and minerals. Per Isaac Arthur's video on the subject, the original atmosphere will have frozen, covering the planet in layers of ice roughly following:

Original Planet Surface -> Water Ice -> CO₂ -> Argon -> Nitrogen -> LOX lakes/oceans -> He/H atmosphere

Assume:

1. The depth from the LOX lakes/oceans on the new surface, to Original Planet Surface is 2 miles

2. We are scanning the surface from orbit

Per this article, there are many ways to scan for deposits. SHARAD in particular wouldn't even reach 1/3 of the way through the ice. HiRise and CRISM only appear to scan the surface, and are also unsuited to this task.

I think Gamma Ray Spectroscopy is the best candidate, but given how small the wavelength is I don't think it would be able to penetrate 2 miles of ice.

TL;DR: Is there any current (or extrapolated) scanning technology that would be scan for deposits in a planetary crust through 2 miles of ice, from orbit.

EDIT: Thanks to Starfish Prime's answer to this it looks like the atmospheric ice would only be ~16m thick, and the water vapor is a rounding error. I have adjusted the layering to account for their answer.

I'm playing around with setting up an outpost on a rogue planet, and want to scan for deposits of various metals and minerals. Per Isaac Arthur's video on the subject, the original atmosphere will have frozen, covering the planet in layers of ice roughly following:

Original Planet Surface -> CO₂ -> Argon -> LOX aquifers -> Nitrogen -> He/H atmosphere

Assume:

1. The depth from the Nitrogen on the new surface, to Original Planet Surface is ~16 meters

2. We are scanning the surface from orbit

Per this article, there are many ways to scan for deposits. HiRise and CRISM only appear to scan the surface, and are also unsuited to this task. SHARAD in particular would reach, but I'm not sure if the snow, ice, and LOX would appreciably dampen its penetration.

I think Gamma Ray Spectroscopy is the best candidate, but given how small the wavelength is I don't know if it could penetrate the snow, ice, and LOX.

TL;DR: Is there any current (or extrapolated) scanning technology that would be able to scan for deposits in a planetary crust through 16 meters of ice and LOX, from orbit.

I'm playing around with setting up an outpost on a rogue planet, and want to scan for deposits of various metals and minerals. Per Isaac Arthur's video on the subject, the original atmosphere will have frozen, covering the planet in layers of ice roughly following:

Original Planet Surface -> Water Ice -> CO₂ -> Argon -> Nitrogen -> LOX lakes/oceans -> He/H atmosphere

Assume:

1. The depth from the LOX lakes/oceans on the new surface, to Original Planet Surface is 2 miles

2. We are scanning the surface from orbit

Per this article, there are many ways to scan for deposits. SHARAD in particular wouldn't even reach 1/3 of the way through the ice. HiRise and CRISM only appear to scan the surface, and are also unsuited to this task.

I think Gamma Ray Spectroscopy is the best candidate, but given how small the wavelength is I don't think it would be able to penetrate 2 miles of ice.

TL;DR: Is there any current (or extrapolated) scanning technology that would be scan for deposits in a planetary crust through 2 miles of ice, from orbit.

EDIT: I have closed this question until I have a proper depth for the frozen atmosphere

I'm playing around with setting up an outpost on a rogue planet, and want to scan for deposits of various metals and minerals. Per Isaac Arthur's video on the subject, the original atmosphere will have frozen, covering the planet in layers of ice roughly following:

Original Planet Surface -> Water Ice -> CO₂ -> Argon -> Nitrogen -> LOX lakes/oceans -> He/H atmosphere

Assume:

1. The depth from the LOX lakes/oceans on the new surface, to Original Planet Surface is 2 miles

2. We are scanning the surface from orbit

Per this article, there are many ways to scan for deposits. SHARAD in particular wouldn't even reach 1/3 of the way through the ice. HiRise and CRISM only appear to scan the surface, and are also unsuited to this task.

I think Gamma Ray Spectroscopy is the best candidate, but given how small the wavelength is I don't think it would be able to penetrate 2 miles of ice.

TL;DR: Is there any current (or extrapolated) scanning technology that would be scan for deposits in a planetary crust through 2 miles of ice, from orbit.

I'm playing around with setting up an outpost on a rogue planet, and want to scan for deposits of various metals and minerals. Per Isaac Arthur's video on the subject, the original atmosphere will have frozen, covering the planet in layers of ice roughly following:

Original Planet Surface -> CO₂ -> Argon -> Nitrogen -> LOX lakes/oceans -> He/H atmosphere

Assume:

1. The depth from the LOX lakes/oceans on the new surface, to Original Planet Surface is 2 miles

2. We are scanning the surface from orbit

Per this article, there are many ways to scan for deposits. SHARAD in particular wouldn't even reach 1/3 of the way through the ice. HiRise and CRISM only appear to scan the surface, and are also unsuited to this task.

I think Gamma Ray Spectroscopy is the best candidate, but given how small the wavelength is I don't think it would be able to penetrate 2 miles of ice.

TL;DR: Is there any current (or extrapolated) scanning technology that would be scan for deposits in a planetary crust through 2 miles of ice, from orbit.

I'm playing around with setting up an outpost on a rogue planet, and want to scan for deposits of various metals and minerals. Per Isaac Arthur's video on the subject, the original atmosphere will have frozen, covering the planet in layers of ice roughly following:

Original Planet Surface -> Water Ice -> CO₂ -> Argon -> Nitrogen -> LOX lakes/oceans -> He/H atmosphere

Assume:

1. The depth from the LOX lakes/oceans on the new surface, to Original Planet Surface is 2 miles

2. We are scanning the surface from orbit

Per this article, there are many ways to scan for deposits. SHARAD in particular wouldn't even reach 1/3 of the way through the ice. HiRise and CRISM only appear to scan the surface, and are also unsuited to this task.

I think Gamma Ray Spectroscopy is the best candidate, but given how small the wavelength is I don't think it would be able to penetrate 2 miles of ice.

TL;DR: Is there any current (or extrapolated) scanning technology that would be scan for deposits in a planetary crust through 2 miles of ice, from orbit.