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"Naturally" is probably not the best term, but I wonder if one chose a random city and poked about with a Geiger Counter, would one find similar figures to those reported here by a civic group and relayed by the South China Morning Post:

The tests were also carried out at the planned site of the Olympic Village and the media centre, with the highest radiation reading - 0.484 microsieverts per hour - detected in undergrowth close to Yumenoshima Stadium, where the equestrian events will be held.

However, an organisation (that I consider to be trustworthy) who monitor levels across Tokyo and the North-East said this:

"It is difficult to have this debate unless we know for sure whether this radiation is from Fukushima or whether it is naturally occurring background radiation," said Pieter Franken, founder of the Japan office of the environmental monitoring organisation Safecast.

Furthermore, the civic group also said:

"We found caesium-137 at almost every place we carried out tests, and there was no caesium here before the accident at Fukushima,"

This would be untrue, I would say, as fallout from South Pacific nuclear tests would have produced caesium-137.

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    You've included too much of your own bias and theory into this question. You should simply quote a claim that you want us to examine. Do you want us to examine the claim that they found 0.484 microsieverts per hour? Or do you want us to examine the claim that they haven't determined that this radiation comes from Fukushima? Or do you want us to examine the claim that they found Cs-137? Or do you want us to examine the claim that there was no Cs present before the accident at Fukushima? – user5582 Oct 14 '13 at 2:23
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    @Articuno: I agree it is unclear, but I read the key claim as that 0.484 microsieverts per hour is an anomalously high level (and hence needs explaining by, for example, the events at Fukushima) – Oddthinking Oct 14 '13 at 3:13
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    0.484 microsieverts per hour is 4.24 millisieverts per year. According to Wikipedia (who cite the Japanese Ministry of Education, Culture, Sports, Science, and Technology), average annual background radiation from natural sources in Japan is 1.5 millisieverts per year (worldwide average is 2.4 and 3.1 in the USA, with most of the difference being radon exposure). So that level does seem to be rather high, though I don't know what the standard deviation from that average is. – Compro01 Oct 14 '13 at 5:41
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    In Cornwall in South West England the average annual dose from radon is 7.8 mSv, though ventialtion has an impact. Chennai [formerly Madras] in south India is higher still. – Henry Oct 15 '13 at 15:44
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It depends what your definition of hotspot is, but some places have much higher levels of radiation than others

Some rocks are much more radioactive than others and if you live in a place built on certain rocks you can easily be exposed to enough radiation to cause notable harm. More than that there have even been natural nuclear reactors.

Here are two examples to illustrate the point.

There is at least one known example where geological conditions created a critical mass that led to a natural nuclear reactor. The best known is Oklo in Gabon. Wikipedia explains:

There is strong geochemical evidence that the Oklo uranium deposit behaved as a natural nuclear fission reactor in Precambrian times: some of the mined uranium was found to have a lower concentration of uranium-235 than expected, as if it had already been in a reactor. Geologists found that it had been in a reactor before—two billion years ago. At that time the natural uranium had a concentration of about 3% 235U, and could have gone critical with natural water as neutron moderator.

Clearly an actual nuclear reactor would count as a natural nuclear radioactive hotspot. Luckily it wasn't in a built up area and occurred a couple of billion years before there were any built up areas.

But people do live in places where the geology exposes them to potential natural radiation. As an example consider the variation in natural radon levels in england. Public Health England have an interactive map here. This clearly shows greater than 30-fold variation in the percentage of houses affected by concerning levels of radiation. People living in high risk areas such as devon and cornwall, for example, are advised to take precautions to reduce the level of indoor radon.

The radon is thought to have significant health effects (from PHE radon website):

A European study, funded by Cancer Research UK and the European Commission showed that radon in the home increases the risk of lung cancer. An independent report, Radon and Public Health estimated that radon is a cause in over 1,100 lung cancer deaths each year in the UK.

So, in short, there are several examples of natural hotspots of radiation.

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