Last week, the world was shocked by the news of massive earthquakes and devastating tsunamis in Japan. The event is still unfolding and could become one of the most tragic natural disasters in recent history.
Scientific understanding and modeling of complicated physical phenomena and engineering based on such analysis is imperative to prevent unnecessary loss of life from natural disasters. In this post, we’ll explore the science behind earthquakes to better understand why they happen and how we prepare for them.
Note: The dynamic examples in this post were built using Mathematica. Download the notebook file provided to interact with the simulations and further explore the topics.
First, let’s start with locations. The following visualization is created from the U.S. Geological Survey (USGS) database of earthquakes that occurred between 1973 and early 2011 whose magnitudes were over 5. As you can clearly see, the epicenters are concentrated in narrow areas, usually on the boundaries of tectonic plates. In particular, there are severe seismic activities around the Pacific, namely the “Ring of Fire”. Unfortunately, Japan is sitting right in the middle of this highly active area.
Earthquakes are oftentimes caused at the boundaries of tectonic plates, which form huge faults on the surface. When large enough forces are applied in two different directions, they overcome the friction between the boundary and cause a sudden movement. The phenomenon, also known as strike-slip, is one of many mechanisms that causes earthquakes. The following animation simulates the strike-slip at a fault and seismic waves caused by it.
The scale of an earthquake is measured by the amount of released energy during the seismic activity. The magnitude scale is logarithmic. The following chart shows the relation between the scale and the energy released by the event, with a few recent major earthquakes indicated.
Mouse over the image to see the logarithmic graph. 
PJ, or petajoule, may not be the most familiar measurement unit of energy for many people. We can use Wolfram|Alpha to convert it to more popular measures, such as megatons of TNT explosive. The Sendai earthquake was measured at magnitude 9, and the energy released was approximately 2000 petajoules:
To put it into some context, the largest nuclear explosive ever tested (Tsar Bomba) was roughly 58 megatons. We are talking about an order of magnitude more energy than that of the largest nuclear bomb.
The magnitude scale is a base-10 logarithmic scale. For instance, the difference in energy released between the current Sendai earthquake (magnitude 9) and the Haiti earthquake in 2010 (magnitude 7) is:
Thus, the energy released during the Sendai earthquake is 1000 times more than that of the Haiti.
So, how is all the energy from earthquakes transferred? Most of the energy is converted into heat generated by friction, but some of it is transformed and radiated as seismic waves. There are two types of seismic waves: body waves and surface waves.
Body waves travel through the earth and can be differentiated by the direction of oscillation during propagation. In P-waves, the particles vibrate in the same direction as wave propagation, similar to sound waves. On the contrary, particles move perpendicular to the direction of the propagation in S-waves.
Surface waves travel only through the crust or the surface of the Earth. However, they are responsible for much destruction due to their properties. Again, the surface waves can be divided into two: Love and Rayleigh waves.
Love waves create motions similar to S-waves, but horizontally. This horizontal movement is particularly damaging to the foundations of buildings.
Rayleigh waves traverse the way that waves roll across lakes or oceans. During propagation, particles move in elliptical paths. Sometimes called ground rolls, Rayleigh waves are low frequency (less than 20 Hz) and oftentimes are detected by animals, but not humans.
Understanding seismic waves is essential for minimizing or preventing structural damages to buildings during earthquakes. So the question is, what you can do?
If external forces are applied, buildings will sway. The structural dynamics are quite complex and depend on a lot of parameters. But as an example, I used a simple damped harmonic oscillator equation to simulate the sway of a building in the following animation (the gray cylinders represent the foundations of the building):
The sway helps to dissipate energy from the seismic waves. Through structural design, material selection, and construction techniques, engineers have tried to reduce the effect of earthquakes on buildings. One such example is a tuned mass damper, a device installed in buildings to reduce harmonic resonance.
Tuned mass damper on display in Taipei 101. Photo courtesy of Armand du Plessis.
Another option that is widely considered today is a technique called base isolation, or seismic isolation. In nutshell, you put some devices, such as a lead rubber bearing, at the base of a building to isolate the building structure from the vibration from earthquakes.
This technique can help reduce structural stress significantly. It is also considered to be a good option for short buildings with high stiffness, or for retrofitting existing structures. In fact, many historical monuments in the U.S. have already been retrofitted with base isolation systems to reduce the damage from earthquakes.
We are providing the downloadable notebook for the post. Most examples are dynamic, and you can interact with simulations. Feel free to use Mathematica or Wolfram CDF Player to explore the content.
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