Striking without warning, earthquakes can collapse buildings and launch colossal waves, killing thousands all within a span of minutes.

Because of the immense number of variables and unknowns that lie behind every quake, researchers cannot accurately predict exactly when the next one will hit. Yet better understanding of where temblors are likely to occur, along with the level of havoc they are likely to wreak, is a chief and realizable goal for current seismologists.

To aid in this endeavor, Kathrin Smetana is conducting pioneering work in speeding up computational run times for earthquake-related simulations. As an assistant professor of mathematics in the Charles V. Schaefer, Jr. School of Engineering and Science at Stevens, Smetana is leveraging her mathematical skills and background to make models smaller and thus less computationally intensive.

In a recent study in the SIAM Journal on Scientific Computing, Smetana and colleagues demonstrated a way to slash the number of unknowns in a model by a factor of 1,000, dramatically lowering cost and duration for simulation runs. The upshot: Scientists can now hone their models by being able to run far more of them, improving maps of subsurface areas and tools for seismic monitoring.

“What we did is reduce the size of the system you have to solve,” says Smetana. “The seismologists I’m working with are really excited.”

For their study, Smetana and her collaborators started by considering the challenges researchers face in computing seismograms. These spiky graphs are captured by seismographs and serve as visual records of the ground motion caused by earthquakes. Local swaying is fundamentally influenced by the composition of underlying ground layers, which range from solid rock to clay, sand and other materials.

In earthquake-prone areas especially, researchers analyze seismograms for the information they contain about those substrata. “Basically, you run synthetic earthquakes on your computer and then you compare with real seismograms to get an idea of how good your model is, and you do this iteratively,” says Smetana.

Constructing these models often involves creating 3D grids of the subsurface, then evaluating and approximating a continuous model in the grid points to obtain matrices that can be numerically processed. Smetana and colleagues realized much of the information in such constructs is unnecessary for ultimately producing an accurate wave field — the full description of an earthquake’s ground motion through time and space.

The team employed this winnowed approach to a model of the subsurface of the Groningen region in northeastern Netherlands, one of the largest natural gas fields on Earth, where gas extraction since the 1960s (phased out by 2023) altered the shape of the subsurface, triggering damaging earthquakes. Focusing on just the most pertinent data points, the reduced models delivered the same accuracy as time-consuming conventional models.

Smetana aims to continue honing this computational mathematical accelerant. “It’s enjoyable and beneficial to engage in interdisciplinary work,” she says.

– Adam Hadhazy