There are days you remember. October 17th, 1989 and I was on the phone with a mathematician friend who had just walked out of a meeting with an image processing company in Silicon Valley. We had done a bit of work together and our lab was shopping it around the Bay Area. Our chat had been underway for about ten minutes when he interrupted.

*Steve, I think I need to leave. The building is losing its geometry.*

With that the line went down...

The Loma Prieta earthquake was centered in a section of the San Andreas Fault close to Santa Cruz. The initial reports had its intensity listed as roughly a 7.0, but the USGS scientist was careful to point out that wasn't a Richter scale number and noted the intensity was on yet another scale and this one was probably a IX (roman numeral) indicating extensive property damage. A bit of research was in order.

By the 80s seismologists had abandoned the Richter Scale for a more accurate measure of the energy released. The Moment Magnitude Scale is derived from a different set of calculations than the Richter scale, but is adjusted to yield similar numbers for medium sized quakes. The press and most science classes never got the memo and quakes are still reported in terms of the Richter Scale.

L stick with the old familiar Richter Scale for the time being. It is defined in terms of the log of the amplitude of the shaking. It turns out the energy release scales with the 1.5 power of the shaking amplitude. In simple terms going up one magnitude means 10^{1.5} times more energy is released - about 31.62 times as much.^{1} Go up or down by 2 on the scale and the energy release changes by a factor of 1000. Big numbers imply a lot of energy!

Seismographs can record quakes well under 1.0, but that is past the limit of what a person would notice and there is no property damage. Around 4 some damage can happen. Going over 5 things get serious in a hurry if human populations with poorly built structures are involved. Past 7 or 8 there is extensive damage and anything around 9 can bring down the best structures.

How big can an earthquake be? One in Chile at around 9.5 is often mentioned. 9.5 is often mentioned as a practical limit, but what happens if somehow we release more energy? Certainly the gravitational binding energy of the Earth makes a strict upper limit. A quake that big would cause the planet to fly apart. Adding more energy would just heat up the bits. A magnitude 15 quake works out to about 10^{32} Joules.^{2} Dial it up to about 20 or 21 and you can blow the Sun apart. A bit more and we're in supernova territory.

Smaller numbers are interesting as the amount of energy drops dramatically to levels we can easily comprehend. Since the Richter Scale is a log scale we can go negative. Magnitude 0 is about 63,000 Joules - think of an average car slamming into a solid wall at about 20mph.^{3}

a few more - you can work out the kinetic energy of any number of crashes:-)

-1 2,000 J a person on a bike going into a wall or tree at about 15 mph

-2 63 J your new Macbook zips out the window and falls a floor during an animated chat session

-3 2 J you drop your smartphone from your pocket

-5 .002 J press a key on your laptop

-7 .00000006 J a tiny snowflake flutters to the ground

calculate a few of your own ... sports related ones might be fun or you might think about the animal world from mosquito to elephant.

Technically these aren't earthquakes although with sensitive geophones you can easily measure cars cruising down the road and even joggers running on a nearby concrete path. The Earth has an enormous number of its own microquakes, but the line is sometimes drawn between magnitude 1 and 2. The USGS has a nice map showing recent quakes above 2.5. Dropping to lower energies requires shorter time scales and smaller geographic areas .. here is Southern California down to about 0.1.

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^{1} Roughly R = 2/3 * log_{10}(E/E_{o}) where Eo is 10^{4.8} Joules. So E = 10^{1.5R +4.8} J (I had to look it up. :-) The total seismic moment energy is higher and I'll use that without the detailed discussion for the really big numbers. For quick calculations of smaller shaking I'll use the Richter Scale as it is more direct.

^{2} A back of the envelope number for those of you who are designing your own Deathstar.

^{3} A Joule is a unit of energy that is easily observable on the human scale. An apple falling from a table hits the ground with about a Joule kinetic energy.

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Recipe Corner

Nothing of note during the past week, but a recommendation for eggnog lovers in the NYC metropolitan area. Ronnybrook Farm Dairy Eggnog is **easily** the finest commercial eggnog I've tried. A few years ago the supply dried up just before Christmas and blackmarket prices soared. Their heavy cream is an excellent base for ice cream.

Informative and delightful. Just how I like it. Thank you Steve.

Posted by: Jean Russell | 12/17/2014 at 02:59 PM

I just love this;)

Maybe you can write about what happens if you put the sun in a huge bucket of water. (I'm cheating, remember when I asked?)

Posted by: Jheri | 12/17/2014 at 03:09 PM