This simple math trick could transform earthquake science

On December 6, 2025, a powerful 7.0 magnitude earthquake struck Alaska. While quakes of that size draw attention, earthquakes occur far more often than many people realize. The United States Geological Survey (USGS) estimates that roughly 55 earthquakes happen every day worldwide, adding up to about 20,000 each year. Typically, one earthquake per year reaches a magnitude of 8.0 or higher, while around 15 others fall within the magnitude 7 range on the Richter scale, which measures the amount of energy released. In 2025 alone, an offshore 8.8 earthquake near Russia's Kamchatka Peninsula ranked among the 10 strongest earthquakes ever recorded, according to USGS.

Earthquakes can cause loss of life, destroy buildings and roads, disrupt economies, and leave lasting emotional scars on those affected. Their financial impact is also increasing. A 2023 report from USGS and the Federal Emergency Management Agency (FEMA) found that earthquake damage now costs the United States an estimated $14.7 billion each year. One major reason is that more people are living in regions where seismic activity is common.

Being able to forecast when and where a major earthquake will strike would greatly improve preparedness and reduce harm. Despite decades of research, scientists still cannot predict earthquakes with reliable accuracy.

While timing remains unpredictable, understanding what lies beneath the Earth's surface can significantly improve risk assessments. Kathrin Smetana, Assistant Professor in the Department of Mathematical Sciences at Stevens, explains that underground materials vary widely. "You may have layers of solid rock, or you may have sand or clay," she says. Because seismic waves move differently through each material, the type of subsurface strongly influences how shaking is felt at the surface.

To map these underground layers, researchers use a method known as Full Waveform Inversion. This seismic imaging technique helps reconstruct the structure of the subsurface by combining simulations with real earthquake data. Scientists first generate computer-based earthquakes and track how seismic waves travel through the Earth. They then analyze the simulated wave patterns at seismograph locations and compare them with real seismograms, which are graphical records of ground motion from actual earthquakes. After many rounds of refinement, the simulated data begins to closely match real observations, offering a clearer picture of underground conditions.

In practice, researchers begin with an initial estimate of the subsurface in a given area. They repeatedly adjust this model, running new simulations each time, until it aligns with real earthquake measurements.

"You compare the data from your computer simulation with actual data that you got from earthquakes," says Smetana. "This allows you to find out what the subsurface looks like and what effect an earthquake has on the composition of the subsurface -- and that ultimately, helps determine the risk for an earthquake at a certain location."

This approach plays a crucial role in improving earthquake monitoring and risk assessment tools. However, it comes with a major drawback. Each simulation can involve millions of variables and must be repeated thousands of times. According to Smetana, a single simulation using traditional methods can take several hours even on advanced computing clusters. Running enough simulations to support ongoing monitoring can quickly become too expensive and time consuming.

To overcome this barrier, Smetana teamed up with computational seismologists Rhys Hawkins and Jeannot Trampert from Utrecht University, along with Matthias Schlottbom and Muhammad Hamza Khalid from the University of Twente in the Netherlands. Together, they developed a streamlined model that dramatically reduces the computational burden while preserving accuracy.

"Essentially we reduced the size of the system that you need to solve by about 1000 times," Smetana says. "It was a very interdisciplinary project, and we found a clever way to construct the reduced model while still maintaining the accuracy of the prediction. I really enjoy interdisciplinary collaborations and this one in particular because you learn to see things with a new perspective, which, in my opinion, ultimately helps finding creative and novel approaches to solve a problem in an interdisciplinary team."

Their research is detailed in a paper titled "Model Order Reduction for Seismic Applications," published in the SIAM Journal on Scientific Computing.

Improving Risk Assessment, Not Prediction

The new model does not make it possible to predict when earthquakes will occur. Instead, it offers a more efficient way to evaluate earthquake risk in different locations. "If you get a good picture of the subsurface, you have a better idea of assessing the risk of future earthquakes," Smetana explains.

The same modeling approach could eventually help scientists simulate tsunamis triggered by undersea earthquakes. In many cases, tsunamis take at least an hour to reach land after an earthquake, depending on where the rupture occurs. That time window could allow researchers to run rapid simulations that inform emergency responses.

Accurate images of the subsurface are key to understanding how earthquakes affect different regions. "There's no way to predict earthquakes at this time," Smetana says. "But our work can help generate a realistic view of the subsurface with less computational power, which would make our models more practical and help us be more earthquake resilient."