Question regarding Inverse Square Law

[LaserPrecision]

I'm quite confused about how to handle finding the power of the origin of a blast based on the damage it causes at the edge. For example, this calc here. Is this formula the same even on a much smaller scale, or is it different? On the Inverse Square Law page, this is the method given:

Example 1: Finding energy based on something destroyed within an explosion​

A ground explosion with a radius of 5 meters has exactly enough energy so when it hits a brick with an area of 0.07116953508 square meters and a volume of 0.0010692559 cubic meters, it vaporizes it. How much energy does this explosion hold?

• First we use the known value for vaporization onto the brick, which is 25700 joules per cubic centimeter. It requires 27.4798773 megajoules to vaporize said brick.
• When dealing with ground explosions, one should use a hemisphere as a basis for the explosion’s shape. The area of a hemisphere with a radius of 5 meters is 157.08 square meters
• 157.08 square meters/0.07116953508 square meters * 27.4798773 megajoules
• If we plug in these numbers, it results in 60.651501 gigajoules, or 14.496 tons of tnt, which is City Block level

But I also stumbled into another page that has a different method:

An omnidirectional attack executed 200 meters above a concrete surface carved 75 meters into the ground, leaving a 230 meter diameter crater and everything pulverized. The volume is 1.590e6 m³, and the pulverization energy of concrete is 40 j/cc. Using these numbers, the intensity at 75 meters is 6.36e13 joules.

The energy of the source is then P = 4π•75²•6.36e13, and P = 4.496e18 joules.

Those are three separate methods. One uses a 4 times multiplication factor and ^2 exponent at the end. The one on the official page has neither, and the third one uses a 4 times multiplication factor and pi without a ^2 exponent at the end.

So my question is what method should be used depending on the scale of the explosion. If it helps, I'm planning to use this method to calculate an explosion that destroyed a city but we only see the edge of the explosion (Had it actually occurred), so I want to find the yield of the epicenter given the power required to destroy a building at the edge of a city (or several kilometers away from the omnidirectional epicenter).

 

[LaserPrecision]

Bump

 

[GodlyCharmander]

Bump, I'd like this to be explained.

 

[KLOL506]

Ah yes, reverse-inverse-square law.

Incredibly useful to find the true yield of an explosion at the epicenter with nothing but the energy intensity left at a distance and the distance itself. The bane of every calc member's existence.

Incredibly handy if you know how to use it, almost everything from 4-B and above was made using this formula.

You could try asking Executor N0, he's one of our two remaining cosmos specialists after DontTalkDT.