Shockingly complicated

Predicting earthquakes was long thought to be impossible. But thanks to a new TU Delft algorithm, this is no longer so far fetched. For geophysicists it’s a dream come true.

All is quiet above the North Anatolian Fault - for the moment that is. The area around this long, tectonic boundary between the Eurasian Plate and the Anatolian Plate is prone to earthquakes, because the massive African Plateau is slowly sliding underneath these two smaller plates.

As a consequence thousands die. Last time this happened was in 1999: the earthquake at Izmit killed approximately 17,000 people. Wouldn’t it therefore be great to be able to predict exactly where and when earthquakes will occur? For a long time geophysicists dismissed this thought. Modeling the slow creeping motion of the Earth’s rocky mantle in three-dimensions was too tough for all the world’s most powerful computers combined.

Yet now, thanks to an algorithm developed by TU Delft PhD student, Mehfooz ur Rehman, this idea doesn’t seem quite so far fetched. Together with geophysicists from the University of Utrecht, Rehman, and his PhD supervisor, Professor Kees Vuik, of the numerical analysis department, showed that it is theoretically possible to model the underground streams underneath Turkey. The team wrote an article that has been accepted for publication in the magazine 'Geochemistry Geophysics and Geosystems', showing its proof of principle. The lead author of the article is Utrecht University geophysicist Thomas Geenen.

The group in Utrecht will now actually start modeling the underground in Greece and Turkey up to 1,000 kilometers deep, using real seismological data. The model will consist of 100 million underground grid points. “Until recently, the best we could do was one million dots,” says Arie van den Berg, from the Utrecht Geophysicist group. “If we added more, things would completely go astray.”

A model with 1 million dots was nice to play with and for gaining some academic insights, according to Van den Berg, “but it had no practical value.”
But predicting earthquakes will still remain very difficult, since they are linked to underground flows in a very intricate way. Van den Berg: “We will however be able to calculate where the strongest underground stresses are located, and which areas are the most dangerous.”

Solving viscous flow problems means solving mathematical matrices made up of the millions of density and velocity values at millions of different spots in the ground. And, as if this weren’t difficult enough, scaling up the matrix, in order to make the model more accurate, results in an exponential growth in the number of iterations.

The TU Delft formula however makes it possible to scale up the matrix only linearly. That’s something geophysicists have been dreaming about for years. Rehman used a series of multi-grid methods to simplify the matrix. He multiplied the matrix by several other matrices before starting the iterative calculations. “This is called preconditioning the matrix,” Rehman explains. Van den Berg adds, laughing: “A technique so complicated it makes your head spin!”

Another problem Rehman tackled is that of parallel computing. To make the calculations requires many computers calculating simultaneously. Increasing the number of computers would always cause the system to work less efficiently. “It’s like giving instructions to someone,” Rehman says. “It’s easier to explain something to one person - face to face - than to many people at the same time.” According to Rehman, the same goes for computers, in some way. His formula allows computers to work together more efficiently. He has tested this with 500 computers.

For the geophysicists, the world is not enough, now that they have a new calculating tool. After modeling Turkey and Greece, the team in Utrecht wants to model the tectonics of the entire globe. That would involve 1 billion dots. “Next we want to model the inner core of the moon,” says Van den Berg. There are indications that it is partially liquid. Van den Berg wants to calculate whether that is true.

Wouldn’t it be great to predict quakes like the one that struck Turkey in 1999? (Photo: ANP)

All is quiet above the North Anatolian Fault - for the moment that is. The area around this long, tectonic boundary between the Eurasian Plate and the Anatolian Plate is prone to earthquakes, because the massive African Plateau is slowly sliding underneath these two smaller plates.

As a consequence thousands die. Last time this happened was in 1999: the earthquake at Izmit killed approximately 17,000 people. Wouldn’t it therefore be great to be able to predict exactly where and when earthquakes will occur? For a long time geophysicists dismissed this thought. Modeling the slow creeping motion of the Earth’s rocky mantle in three-dimensions was too tough for all the world’s most powerful computers combined.

Yet now, thanks to an algorithm developed by TU Delft PhD student, Mehfooz ur Rehman, this idea doesn’t seem quite so far fetched. Together with geophysicists from the University of Utrecht, Rehman, and his PhD supervisor, Professor Kees Vuik, of the numerical analysis department, showed that it is theoretically possible to model the underground streams underneath Turkey. The team wrote an article that has been accepted for publication in the magazine 'Geochemistry Geophysics and Geosystems', showing its proof of principle. The lead author of the article is Utrecht University geophysicist Thomas Geenen.

The group in Utrecht will now actually start modeling the underground in Greece and Turkey up to 1,000 kilometers deep, using real seismological data. The model will consist of 100 million underground grid points. “Until recently, the best we could do was one million dots,” says Arie van den Berg, from the Utrecht Geophysicist group. “If we added more, things would completely go astray.”

A model with 1 million dots was nice to play with and for gaining some academic insights, according to Van den Berg, “but it had no practical value.”
But predicting earthquakes will still remain very difficult, since they are linked to underground flows in a very intricate way. Van den Berg: “We will however be able to calculate where the strongest underground stresses are located, and which areas are the most dangerous.”

Solving viscous flow problems means solving mathematical matrices made up of the millions of density and velocity values at millions of different spots in the ground. And, as if this weren’t difficult enough, scaling up the matrix, in order to make the model more accurate, results in an exponential growth in the number of iterations.

The new formula however makes it possible to scale up the matrix only linearly. That’s something geophysicists have been dreaming about for years. Rehman used a series of multi-grid methods to simplify the matrix. He multiplied the matrix by several other matrices before starting the iterative calculations. “This is called preconditioning the matrix,” Rehman explains. Van den Berg adds, laughing: “A technique so complicated it makes your head spin!”

Another problem Geenen and Rehman tackled is that of parallel computing. To make the calculations requires many computers calculating simultaneously. Increasing the number of computers would always cause the system to work less efficiently. “It’s like giving instructions to someone,” Rehman says. “It’s easier to explain something to one person - face to face - than to many people at the same time.” According to Rehman, the same goes for computers, in some way. Their formula allows computers to work together more efficiently. They tested this with 500 computers.

For the geophysicists, the world is not enough, now that they have a new calculating tool. After modeling Turkey and Greece, the team in Utrecht wants to model the tectonics of the entire globe. That would involve 1 billion dots. “Next we want to model the inner core of the moon,” says Van den Berg. There are indications that it is partially liquid. Van den Berg wants to calculate whether that is true.