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Earthquake formula and an alternate method

Mephistus

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Soz I'm gonna model off one of my fav earthquake calcs, to compare this method to a feat I wanted to calc and see how legit this method would be in practiciality and get some feedback.

"Biceptus almost single-handedly suppressed the Great Protein Rebellion of the Vegebrodies. His turgid biceps were said to be infused with a divine power no amount of lifting could match. When he swung his fist earthward, the very ground would tremble for miles at his might. Let the legends record that no clothes would ever fit this Muscle Lord's body. Ever."

Character causes an earthquake felt by peoples in a multiple mile radius when he swings toward the ground and hits it with his big beefy paws.

Gonna assume a magnitude 2 at the bare minimum on the Mercalli scale

2 miles is 3.21869 kilometers

Running this info through the Earthquake formulas we use for quakes with an affected radius less than 60 km:


Magnitude at the epicenter = 2+0.0238*3.21869 = 2.076604822

Energy = 10^[1.5*(2.076604822)+4.8] = 82206703.4458 Joules or 9-A

That's with our normal method. Now, second method is something newish I'm gonna see how much of a difference this makes.

We can estimate this attack's energy by assuming the volume of rock moved in the area affected was moving at the objective speeds recorded by scientists for a magnitude 2 quake , which is the lowest observable ground speed to humans, .1 cm/s or .001 m/s.

The area affected by the shockwave of teh paunch is 2 miles but since its ground capped we are gonna use a hemisphere for the affected volume:

Volume of a sphere with a radius of 3218.69 meters is:

(4/3)*pi*(3218.69^3) = 139677373992 m^3

We are using half that volume since its a ground capped hemisphere so..

139677373992/2= 69838686996 m^3

Density of granite, rock, is 2600 kg/m^3

So the mass moved at .001 m/s from the center meaning its this energetic using the kinetic energy formula:

.5*(.001^2)*(2600*69838686996) = 90790293.0948 joules or like 9-A

Second method gives a higher result and assumes equal energy dispersion from the point of impact and another way to estimate these sort of feats assuming its treated like a omnidirectional, spherical uncontrolled shockwave that moves the rock volume at a speed comparable to listed ground velocities. I think the difference is from assuming the quake is caused by a physical blow and our formula is for natural quakes where just the plates are shifting at any rate.
 
like, for example: 0.1769 km is 2.32E7 meters

(0.034^2)*(2.32e7*2600)*.5 = 34864960 joules

is what this feat yields using this method:

https://vsbattles.fandom.com/wiki/User_blog:Therefir/My_Hero_Academia:_Earthquake

of 360010634701.08 joules

lol, its actually more dependent on the found size affected if anything since the volume of rock is only whats taken into account.

the Earthquake formula is based off of empirical data afaik so its as much of a guess. Also the Earthquake formula probs takes into account the local energy of the shockwave bypassing the resistance to travel through rock and the magnitude scales are based on orders of magnitude energy-wise to cause studied energetic effects at the epicenter, unlike the simple kinetic energy calc.

It looks like this method prolly would matter for the smaller scale quakes like on the 2-3 scale since they don't really radiate out much energy size-wise. Anything on a higher scale quake and its kinda lowballing.
 
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