I was curious about something and crunched some numbers regarding the Japan quake and came upon an astonishing fact.

According to the Global CMT Project moment tensor solution the quake released an energy of 5.31x10^29 dyne-centimeters of energy.[1]

The dyne-cm is equivalent to the erg. There are 100 nano-joules per erg. This means the quake released 5.31x10^22 joules of energy. To put that in perspective, that's that amount of energy from the Sun absorbed by the Earth in only 4 hours and 45 minutes.[2]

Now, the finite fault model on the USGS site [3] shows the fault plane as being +375/-275 x +130/-130 kilometers. That's 650x260 km, or an area of 169,000 kilometers, or 1.69x10^11 square meters.

The finite fault model also models the quake as lasting 200 seconds.

So now let's distribute that energy over the fault plane area and over time.

We have 5.31x10^22 joules across 1.69x10^11 sq-m, giving about 3.14x10^11 joules per square meter.

The joule is one watt per second, so we can divide that value by 200 seconds to get about 1.571x10^9 watts per square meter. There's 1 million square millimeters per square meter, so that leaves us 1,571 watts per square millimeter!!! My soldering iron is only 80 watts and it's tip gets to about 800°F. This quake had nearly 20 times that amount of energy.

But, this calculation has the energy spread out evenly across the fault plane and evenly across time. The quake's maximum instantaneous energy output was about 70 seconds after the quake and peaked at about 8e27 ergs. Further, the finite fault model indicates the bulk of the energy was released in an area of 100x50 kilometers. That's a lot of energy in such a small space.

Now, if I have done my math correctly, I would not be surprised if during this quake some rock was melted.

Brian

[1] http://earthquake.usgs.gov/earthquakes/eqinthenews/2011/usc0001xgp/neic_c0001xgp_gcmt.php
[2] based on the value of 3,850,000 exajoules (EJ) per year from http://en.wikipedia.org/wiki/Solar_energya
[3] http://earthquake.usgs.gov/earthquakes/eqinthenews/2011/usc0001xgp/finite_fault.php