Atmospheric focusing
Atmospheric focusing is a phenomenon occurring when a large shock wave
Shock wave
A shock wave is a type of propagating disturbance. Like an ordinary wave, it carries energy and can propagate through a medium or in some cases in the absence of a material medium, through a field such as the electromagnetic field...

 is produced in the atmosphere
Earth's atmosphere
The atmosphere of Earth is a layer of gases surrounding the planet Earth that is retained by Earth's gravity. The atmosphere protects life on Earth by absorbing ultraviolet solar radiation, warming the surface through heat retention , and reducing temperature extremes between day and night...

, as in a nuclear explosion
Nuclear explosion
A nuclear explosion occurs as a result of the rapid release of energy from an intentionally high-speed nuclear reaction. The driving reaction may be nuclear fission, nuclear fusion or a multistage cascading combination of the two, though to date all fusion based weapons have used a fission device...

 or large extraterrestrial object impact. The shock wave is refracted
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

 horizontally by density variations in the atmosphere so that it can have impacts in localized areas much further away than the theoretical extent of its blast effect. In large bombs, some effects may thus be found hundreds of kilometers from the blast site (such as in the case of the Tsar Bomba
Tsar Bomba
Tsar Bomba is the nickname for the AN602 hydrogen bomb, the most powerful nuclear weapon ever detonated. It was also referred to as Kuz'kina Mat , in this usage meaning "something that has not been seen before"....

 test, where damage was caused up to approximately 1,000 km away).

This effect operates similarly to the patterns made by sunlight on the bottom of a pool, the difference is that the light is bent at the contact point with the water while the shock wave is distorted by density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

 variations (e.g. due to temperature variations) in the atmosphere. Variations of wind
Wind is the flow of gases on a large scale. On Earth, wind consists of the bulk movement of air. In outer space, solar wind is the movement of gases or charged particles from the sun through space, while planetary wind is the outgassing of light chemical elements from a planet's atmosphere into space...

 can cause a similar effect. This will disperse the shock wave at some places and focus it at others. For powerful shock waves this can cause damage farther than expected; the shock wave energy density will decrease beyond expected values based on uniform geometry
Inverse-square law
In physics, an inverse-square law is any physical law stating that a specified physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity....

( falloff for weak shock or acoustic waves, as expected at large distances).
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