Credit to Mr. Redic for calculating the drag force method.
It looks like the Karathen is at least 3,200m long, so I think we can take the VFX designers words at face value. It's upper portion looks like it's around half of its length, while its width is half of that portion, so around 800m wide. Mass-wise, the Karathen had to pull itself onto the seafloor and basically had no buoyancy at all, so it's probably much denser than seawater. Due to its high density and its arms/legs/tentacles adding to its mass, I think we can use a cylinder's likely higher volume of a 400m radius and 3200m height for 1,610,000,000m^3, and a lesser density of 1,000kg, so we can get around 1.61e+12kg or 1,610,000,000 metric tons.
6378.1 km distance and a timeframe of 150 seconds would give it an average speed of 124 mach, or around 42,520 m/s.
Based on this (Pd=Fd*v=1/2ρ*v^3*A*Cd) equation. Its density is around 12,600-13,000kg/m^3, so it's ρ can be said to be 13,000. Its area is basically the front area of the Karathen, let's go with a 800m wide circle/400m radius for an area of 503,000 m^2, it's probably larger but I feel this is good enough.
The drag coefficient is what's tripping me up, since it's based on Reynolds number and viscosity, and the inner core's viscosity ~ 2-7 x 10^14 Pascal*seconds, compared to water's 8.90 x 10^-4 or air's 1.81 x 10^-5. I'm just going with 1 because I don't know how that works.
1/2 x 13000 x 503000 x 42520^3 is 2.5133971e+23 Joules, Country level.
Please be noted though that I haven't checked whether Mr. Redic calculated it correctly, so the result might be inaccurate.
Since we have speed and mass it won't hurt to try KE?
0.5*1.61e12*42520^2 = 1.455400072e21 Joules, Large Island level
Surviving being in the core of Earth
Pascals*m^3 can be converted to Joules. 33-36 gigapascals. I'll use 34.5. The volume of Karathen is 1 610 000 000.
That's 3.45e10*1610000000 = 5.5545e19 Pascals*m^3, 5.5545e19 Joules, Island level
Cannot be calculated like this. To shamelessly copy Mr Redic again:
"For the inner core pressure, I assumed the Karathen is around half as wide as her upper half, which looked around half her height of 3,200m, so I plug in a 400m radius and a 3,200m height for the surface value of as a cylinder (9,050,000m^2), then divide the result by the result of an average man's height and radius plugged in to a cylinder's surface area divided by their actual surface area of 1.9m^2 (it was only around 1.22x smaller, but still feel it might be more accurate), which give me a surface area of 7379828.3262m^2. When I apply the inner core's 360 gigapascals, I got 2.6567382 × 10^18 newtons, or 270,911,900,826,622 metric tons of force on her.
Jason Momoa's surface area of 2.37m^2 in comparison gets 853,200,000,000 newtons of force on Aquaman, or around 87,002,187 metric tons."
Idk how that is useful though.
Actually we can calc it like DontTalkDT's sun feat.
Temperature of the inner core is 5430 degrees Celcius.
Surface area is 7 379 828.3262 m^2 for Karathen.
I'll use emissivity of lava, or 0.55 to 0.85. I'll use 0.55 for such high temperatures.
Now conduction. I'm just assuming human values of 3 mm, 0.209 and 33 degrees cuz there's literally no way to find out values for Karathen. That's 2.774749032196264e12 Watts.
Adding together that's 2.4624796060712626e14 Watts.