I am not sure if any supervillain has ever proposed such a scheme but it does sound a bit like one. Dr Conrad Zimsky (played by Stanley Tucci) in “The Core” discovered how to focus seismic waves onto city targets; but blowing the earth up by injecting oxygen into the mantle – no. Allow me to suggest a few reasons why not.
“earth’s molten mantle”
This is a bit pedantic perhaps, but the Earth’s mantle isn’t molten. It would be, if the pressure were the same as it is at surface – and it’s the release of pressure that causes rock to become molten at volcanoes, for example. But elsewhere the mantle is solid. It is plastic, like many things that are solid: ice and pitch for example. But although it flows with time it is still solid. Solid solid solid.
“over many years”
Well, how many exactly? The Mantle already receives a steady supply of oxygen from the surface via subduction zones – the oxygen being mainly in the form of water. This does not tend to blow the Earth apart, thought he water is important in lubricating the subduction engine. Subduction works at the usual sorts of geodynamic rates, say 10cm per year to make the sums easier. So if the distance to the mantle from the bottom of the Marianas Trench is say 10km, that’s 100,000 years for the total transit time. A bit long for a plot.
“easily and quietly”
Well, the easy quiet approach takes 100,000 years and it’s happening already without adverse effects. Doing it quickly and in greater quantity would be possible I suppose, but there would be a price to pay, in that it would be neither easy nor quiet. First it would involve drilling a deeper borehole than has ever been drilled into rocks so hot and pressured that completely new drilling technology would probably be required. The Russians did something like this on the Kola Peninsula in the 1960s. They got to about 12km, and it was an operation of at least the scale and expense of their space programme. I think “easily and quietly” is a boundary condition too far for this project.
Also, oxygen at those pressures and temperatures would not behave as we might expect it to at surface. However this is not to say that pumping liquid oxygen down a superdeep borehole into superhot rocks would be a walk in the park. I can see H&S being difficult to about it; though supervillains tend to pay scant respect to workplace safety, I have noticed.
“directly to the core”
Drilling to the core – which is an awfully long way away – is likely to remain impossible until and possibly beyond the invention of phasers and starships. The Enterprise (all of them except Captain Archer’s vessel) seems capable of superdeep geological drilling, but alas the nature of the technology remains a closed book. When I asked how the phasers worked, I was told as most people are, “very well, thank you”. The same explanation also works for warp drives, tractor beams, force fields, replicators and dematerialisation technology.
Finally there’s a question of scale.
The atmosphere is MINUTE on the scale of the Earth, and only the bottom bit of it has a mere 16% or so Oxygen – the rest of the air is, as the song says, rarified. If your car did “up” you could drive to space in about 30 minutes. It’s really really thin. The Mantle, on the other hand, is over 90% of the Earth’s volume and thousands of miles across. This is all algebra to me, but using Wikipedia values for the radii of core, mantle and atmos, feeding that into “Pi R cubed” and taking one from another, you can easily compare the volumes of the Mantle and the atmosphere. You will find that the ENTIRE atmos, not just the 16% of it that’s oxygen (and presumably your plot wouldn’t wish to use all of it) could disappear into the Mantle and nobody would be able to find it.
(Love to read this story, incidentally.)