Many of us still dread our high school days, when the math teacher talked about logarithms. Who understood then and who can remember now the alien concept of grouping numbers not in their natural sequence, but by some funny exponent applied to an arbitrary base. Well, here is a quick refresher on the simplest logarithms, those of base 10. Look at the number 100 and ask how often you have to multiply the number 10, our base, by itself to get 100. The answer is 2 - and that is the logarithm of 100. If you look at the number 1000 and ask again how often you have to multiply our base number 10 by itself to get 1000, the answer is 3. Hence the logarithm of 1000 is 3. You therefore can use logarithms to easily deal with really big numbers, as the logarithm of one million is six and the latest bail-out figure for Wall Street, 100 billion, is reduced to a mere 11 when you determine its logarithm.

Richter scaled his earthquakes using such a logarithmic method (see blog November 18, 2008). A magnitude 3 earthquake therefore has ten times larger amplitudes than a 2; a magnitude 4 is ten times bigger than a 3 and hence one hundred times bigger than a 2. In Richter's day, the seismograph's recordings were on light sensitive paper, which was illuminated by a light beam artfully reflected from the moving mass of a Wood-Anderson seismograph, its mirror. Once the film was developed, the ground movement was represented by a dark line on that paper.

But even with a magnifying glass you were not able to see fine details of the ground movement. As a consequence, with the original Richter scale it was impossible to classify either the really big quakes (see blog December 1, 2008) or the tiniest microtemblors.

With today's electronic seismometers, however, the lower limit of the first Richter scale has been all but eliminated. These instruments are so sensitive that they can register earthquakes a hundred or even a thousand times smaller than an event of magnitude 2. But how do we label such tiny quakes? That is again where the ingenuity of a logarithmic scale comes in. An earthquake ten times smaller than a 2 would have a magnitude of 1; a hundred times smaller would be zero on the logarithmic scale. And if an event is thousand times smaller, its size would be "minus 1" on the Richter scale. And we do indeed measure such nanosized earthquakes regularly, for instance in a borehole, which penetrates the San Andreas Fault deep below Parkfield in Monterey County (see picture). (hra021)

Recording of a magnitude minus 1 earthquake, measured inside a borehole in Parkfield, CA. (Click to view larger image.)

We have all heard it, we've all read it: When the media talks about earthquakes, invariably someone mentions the "open ended Richter scale." Journalists think they need to differentiate Richter's scale of earthquake magnitudes from other yardsticks of the natural world, say the 12-tier Beaufort scale for wind intensity or the 5-tier Saffir-Simpson scale describing a hurricane's strength. Indeed, the Richter scale is not limited to a certain number of steps. It is a continuous logarithmic scale, but - unfortunately for the media - it is not open-ended. There just are no earthquakes, which measure 8, 9 or even higher on the Richter scale.

	Wood-Anderson seismograph

The media is wrong for two reasons. The first one has to do with the equipment which Richter and Gutenberg used to develop their scale. They utilized seismographs of the Wood-Anderson type 18, 2008). These instruments were developed more than 75 years ago, and they are just not made to withstand the shaking of a really strong quake. Instead they become, as seismologsts put it, non-linear. Measuring strong quakes is therefore beyond the reach of these sensors.

The other reason lies in the physics of earthquakes themselves. In a sense, earthquakes are like musical instruments, each having a characteristic frequency which depends on its size. The smallest temblors have a high pitch like a piccolo. Stronger quakes are like trombones with much lower tones. And the biggest shakers sound like the lowest keys on a tuba. During Richter's time, in the early 30's of the last century, seismographs also had their own characteristic frequency. The Wood-Anderson could not pick-up the lower sounds and therefore would have been overloaded by a really big quake. Richer knew about the shortcomings of his new yardstick and applied it strictly to earthquakes in Southern California not exceeding a moderate size.

Today's seismometers are, of course, much more sensitive than the instruments of Richter's days. They are broadband, which means that they can pick-up the sounds of a whole orchestra, small and big earthquakes alike. They are also much more sensitive that the Wood-Andersons ever were. Broadband sensors can therefore register even the tiniest earthquakes. In a future blog, we will describe how such micro- or even nano-earthquakes can be measured on the Richter scale. (hra020)

Two events coincide, according to the Merriam-Webster's dictionary, when they happen at the same time. Nowhere does it say however, whether these two events need to be related or not, or if one can be the consequence of the other. That's why we speak of a "pure coincidence" when two completely unrelated events happen simultaneously. An example could be, when my car gets a flat tire in the Caldecott Tunnel at the same time my daughter in Boston wins the lottery. Some pure coincidences can be very unlikely, say that the A's win the World Series in the same year that the Raiders clinch the Superbowl.

Pure coincidence was at play on Saturday morning when two earthquakes occured that had nothing to do with each other. Within 39 seconds, the earth was shaken by two earthquakes of the same magnitude, 6.4. The epicenters of these two quakes were both in the ocean. The first one occured at 8:01 am PST in the Indian Ocean off the coast of the Indonesian island of Sumatra. The other one happened a little bit more than half a minute later in the South Pacific east of New Caledonia near the Loyalty Islands (see map).

	Map showing locations of 2 earthquakes (red and white "beachball" figures) and station station Matsushiro (MAJO) in Japan (blue square).

On average, about a hundred temblors with magnitudes between 6 and 6.5 occur worldwide every year (see blog September 14, 2008). If they occured regularly, that means if there were some form of physical relationship between them, we would get about two of them per week. But earthquakes here in California are in no way connected to temblors in Japan or terremotos in Chile. In contrast to many a lore, there is no long-distance force associated with one quake that could trigger another equally strong earthquake on another continent.

	Seismogram at station Matsushiro in Japan from November 22 events. Click to view larger image. Data taken from IRIS datacenter

Saturday's two epicenters were 4836 miles apart. If such a hypothetical trigger were to exist, it would have had to traverse this distance in 39 seconds, which corresponds to a speed of roughly 450,000 mph. No tectonic force acts with such a high velocity.

The two coincidental earthquakes made for interesting seismograms, because the seismic waves of the two earthquakes were intermingled, making it difficult for seismologists to identify which phases belong to which quake. An example of the recordings of the seismic station Matsushiro in Japan is shown in the figure, labelled with the correct phases. (hra019)

	Beno Gutenberg
	Charles Richter

How strong is an earthquake? When you stand in a hallway and the shaking begins, some people may lose their balance and fall, while others simply walk away - albeit with a very heavy Texas swagger. Or, in a different temblor, while some buildings might just suffer cracks in the plaster, others will lose their chimneys or hop off their foundations. These examples show that looking at the effects of earthquakes is certainly not an objective way to measure the strength of a temblor. But how do you go about determining the size of a quake if everything around you is shaken as badly as you are?

Seismometers are the tools of choice. They swing in their own rhythm in reaction to vibrations of the ground. And because their response to different kinds of shaking can be described exactly with mathematical formulas, the output of a seismometer is a good way to determine the strength of the shaking. But there is the crux of the matter: How does the strength of the shaking relate to the size of an earthquake? A medium sized earthquake close by can cause the gound to shake more severely than a stronger temblor farther away. Therefore, the distance between the focus of a quake and the location of the seismometer plays an important role in measuring the strength of a quake.

It was almost 75 years ago that two seismologists found a way to overcome these problems. Charles Richter and German-born Beno Gutenberg were both working at Caltech in Pasadena, and their engineers had set up a unique network of identical seismometers in Southern California. They equipped each site with a device called a Wood-Anderson Seismograph. When Richter and Gutenberg looked at one earthquake which was registered at several sites, they could see how the amplitude of a seismic wave decayed with distance from the earthquake source.

After giving their findings some thought, they came up with a simple definition: If an earthquake caused their seismographs to wiggle 1 millimeter (about 1/25th of an inch) and the temblor was 100 km (60 miles) away, then it had a strength of "three." A wiggle ten times that size was called "four," and a "five" was 100 times as strong as a "three," generating wiggles about 4 inches tall. Because Richter was inspired by the astronomers' scheme to classify the brightness of stars, he called his units magnitude, hence the phrase "magnitude on the Richter Scale." In a future blog, we will explore the limits of this logarithmic scale. (hra018)

	Tectonic setting of the earthquake that generated the devastating December 2004 tsunami. Click to view larger image. (Image courtesey of the USGS)

It took a disaster of almost biblical proportions, but finally the Indian Ocean got its own tsunami warning system. Earlier this week, when Indonesia's President Yudhoyono pressed a button in the offices of the Meteorological and Geophysical Survey in Jakarta, he inaugurated a system which will be used to warn people in the coastal communities of Indonesia about the menacing monster waves. While for decades several such systems have existed in the Pacific (i.e in Hawaii, Alaska and Japan), there was no way to warn the people along the coast of the Indian Ocean when the biggest earthquake in forty years struck the area in December 2004. A magnitude 9.2 quake off the coast of the Indonesian island of Sumatra created the largest tsunami the world has seen in historical times. Even thousands of miles away from the epicenter, entire coastal communities were swept away by the killer wave. In the end, the death toll reached more than 230,000 and the physical damage to buildings and infrastructure could hardly be measured.

	German Indonesian Tsunami Early Warning System (Image from www.gitews.org)

In the aftermath of the disaster, many nations generously donated aid to cover the immediate needs of the people affected by the wave. The German government, however, took a different approach. Besides the first aid, it promised the Indonesian government a complete tsunami warning system. Many experts laughed at this proposal, as German science was not known for its expertise in studying these waves. But Berlin put its researchers and engineers to work anyway. At a cost of almost 60 million dollars, a total of 125 scientists put together a complete system in less than four years: they set-up earthquake and GPS stations remote parts of Indonesia. Together with local engineers, they installed tidal gauges and ocean bouys to measure wave heights. In addition, they linked all their sensors to the data center in Jakarta and wrote the programs which calculate the run time and amplitude of a potential tsunami. Finally, they trained local scientists to operate and maintain the system.

Germans and Indonesians tested the system together in many simulated sessions, and most international experts agree that its warnings will be valid. Once it's fully funtional, the system will be upgraded to cover the whole Indian Ocean basin. See a detailed description of the system. (hra017)