Scientists have developed a mathematical technique that speeds up seismic simulations by a factor of 1,000, making it easier to map underground layers and assess earthquake risks. Led by Kathrin Smetana from Stevens Institute of Technology, the approach uses model order reduction to handle complex computations more efficiently. While it does not enable earthquake prediction, it could enhance preparedness in vulnerable areas.
Earthquakes strike frequently, with the United States Geological Survey estimating about 55 occurrences daily worldwide, totaling around 20,000 annually. Events of magnitude 7 or higher happen roughly 15 times a year, and one reaches magnitude 8 or above. In 2025, a 7.0 magnitude quake hit Alaska on December 6, while an 8.8 magnitude offshore event near Russia's Kamchatka Peninsula ranked among the strongest ever recorded.
These disasters cause significant damage, costing the United States an estimated $14.7 billion yearly, according to a 2023 report from the USGS and the Federal Emergency Management Agency. Urbanization in seismic zones exacerbates the financial and human toll. Although prediction remains impossible, understanding subsurface structures can improve risk evaluation.
Researchers employ full waveform inversion to image underground layers, simulating seismic waves and comparing them to real data from seismograms. Kathrin Smetana, an assistant professor in mathematical sciences at Stevens Institute of Technology, notes that materials like solid rock, sand, or clay affect wave propagation differently. "You may have layers of solid rock, or you may have sand or clay," she explains.
Traditional simulations, involving millions of variables and repeated thousands of times, can take hours on powerful computers, limiting practical use. To address this, Smetana collaborated with Rhys Hawkins and Jeannot Trampert from Utrecht University, and Matthias Schlottbom and Muhammad Hamza Khalid from the University of Twente. Their method reduces the system size by about 1,000 times while maintaining accuracy. "Essentially we reduced the size of the system that you need to solve by about 1000 times," Smetana says.
Detailed in the paper "Model Order Reduction for Seismic Applications" published in the SIAM Journal on Scientific Computing (2025, volume 47, issue 5), the technique aids in creating detailed subsurface models for better risk assessment. It could also support tsunami simulations, providing time for emergency responses. "There's no way to predict earthquakes at this time," Smetana emphasizes, "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."