# Modeling Seismic Wave Propagation on a 156GB PC Cluster

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California Institute of Technology builds a ground-shaking, 156-box, dual-processor cluster.
Bolivia Shakes and Moves

On June 9, 1994, a huge earthquake with a magnitude of 8.2 on the open Richter scale occurred in Bolivia, at a depth of 641 km (400 miles). Most earthquakes occur at much shallower depths, usually less than 30 kilometers. This event in Bolivia was one of the largest deep earthquakes ever recorded. Due to its unusual characteristics, this earthquake has become the subject of numerous studies in the seismological community. We tried to simulate this event on our cluster.

Figure 7 shows a still of the ground shaking (displacement of the Earth at a given location due to the passage of a seismic wave generated by the earthquake). The epicenter in Bolivia is indicated by the purple triangle. The waves travel inside and along the surface of the Earth. They can be seen propagating across the United States, for instance. A permanent displacement is visible at the surface of the Earth around Bolivia, extending as far as the Amazon river to the north. This effect, which was recorded by several seismic stations in Bolivia, is called the “static offset”. The earthquake was so big that it moved the ground permanently by a few millimeters. The vertical displacement reached up to 7mm, i.e., ¼“ to the south). It is correctly reproduced by our code.

Figure 7. Seismic Waves during the 8.2 Bolivia Earthquake

Due to the fact that the waves travel all around the globe, seismic recording stations in other countries were able to detect the Bolivia earthquake. Figure 8 shows an actual record from a station in Pasadena, California and the corresponding record simulated by our method. Again, the agreement is satisfactory. At each time step, this simulation required solving a system of equations with 500 million unknowns (also called the degrees of freedom of the system). Simulating the propagation of seismic waves for an hour and a half after the earthquake took 48 hours on the cluster using half of the nodes (150 processors).

Figure 8. Vertical Velocity as Recorded in Pasadena

Needless to say, our research has benefited tremendously from the power and the reliability of Linux and from the open-source philosophy. Using a large cluster of PCs, we are able to simulate the propagation of seismic waves resulting from large earthquakes and reach unprecedented resolution.

Acknowledgements

Luis Rivera provided invaluable information and help for this project. We thank Jan Lindheim, Tom Sterling, Chip Coldwell, Ken Ou, Jay Nickpour and Genevieve Moguilny for discussions regarding the structure of the cluster. Matt Massie added several options to his nice Ganglia package to help us monitor more parameters on our cluster. Rusty Lusk provided some useful insight about running MPICH on large clusters.

Resources

Dr. Dimitri Komatitsch is a senior researcher in the Division of Geological and Planetary Sciences at the California Institute of Technology. His interests are applied mathematics, numerical analysis and the application of computer science to problems in geophysics and seismology.

Dr. Jeroen Tromp is a professor in the Division of Geological and Planetary Sciences at the California Institute of Technology. He is interested in theoretical seismology, in particular seismology at the scale of the Earth. Recently he has focused on numerical modeling of seismic wave propagation.

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