What is Zion's depth in the Matrix?

Tank says that Zion is...

"Deep underground, near the earth’s core where it’s still warm."

... but surely that would put it deep in the liquid mantle, and I seriously doubt the city is submerged in magma.

Did the planet's mantle solidify due to heavy geothermal energy extraction, or did he just make a mistake and meant the city is close to the liquid mantle and not the core? Does he just mean "really deep underground"?

• It's deeeeep, maaaaaan Commented Sep 10 at 6:53

Zion is approximately 9000m below the Earth's surface

Notwithstanding Tank's hyperbole about Zion being 'close to the Earth's core', in the third film the Machines are drilling down toward Zion from the surface. At the meeting of the captains, Ghost and Niobe give us more than enough info to effectively pinpoint Zion's depth.

The Machines are already at a depth of (approx.) 2000m.

Soren: How deep are they?

Niobe: Almost two thousand meters.

Their current rate of digging is (approx.) 100 m/h.

ICE: How fast are they moving?

NIOBE: Control estimates their descent at one hundred meters an hour.

The Machines will be inside Zion in (approx.) 72 hours.

GHOST: And if Niobe's right, in seventy two hours, there's going to be a quarter-million more.

From here we can do some simple maths: 72hours x 100m/h = 7200m. If we add the current 2000(ish)m depth, we get a rough estimate of 9000m and pocket-change.

At that depth the temperature of the rock would be (approx.) 150°C. More than enough to keep the place toasty-warm and hidden from any machine scans for heat sources.

• According to NatGeo, "The core is found about 2,900 kilometers (1,802 miles) below Earth's surface." 9K m is 9 km. If we do a little more maths: 9 / 2900 = 0.003103448276. That is, Zion is 0.3103448276% close to the core from the surface, nowhere near the Earth's core. Commented Sep 3 at 14:43
• Don't forget sigfigs! If it's "about 2,900 km", then you can't really say a percentage that's precise to 12 digits since the actual distance could be anywhere from 2850 to 2950 km. You can only confidently say at most two digits. :D Commented Sep 3 at 16:33
• Tank was right. Zion was closer to the Earth Core. We can also assume it's a lack of geographical knowledge on the character. Commented Sep 3 at 19:01
• @Idran You’re really tempting me to delete and repost with more correct info right now… :) Commented Sep 3 at 22:48
• @kwc "Hold on, Neo. Before we visit the machine city, we need to remain in these pressure chambers for days…" Commented Sep 4 at 10:06