New mathematical shortcuts reduce the core calculations within earthquake shaking simulations by a factor of approximately 1,000, without sacrificing accuracy.

This jump in speed could make it much easier for scientists and cities to model how strongly the ground shakes in the future. earthquakeearthquakes themselves cannot yet be predicted, but can help communities prepare for damage.

The encounter between speed and shaking

In a typical risk investigation, a computer solves millions of linked wave calculations, repeating the calculations for each new guess.

At Stevens Institute of Technology (sit), the math team has built a shortcut that saves you the answer while saving you most of the work.

Dr. Kathryn Smetana, who drove the design, focused on the signal parts that the risk map would actually use and maintain accuracy.

For faster execution, reveal But it can narrow the range of realistic swings a community can plan for.

New model for earthquake simulation

On the surface, the two neighborhoods may be located miles apart, but the ground beneath them can behave very differently.

In January 2026, researchers involved in the project emphasized that hidden materials could change from city block to city block.

“There may be layers of solid rock, or there may be sand or clay,” Smetana said. When waves enter softer sediments from hard rock, they slow down and become larger, increasing the threat to the area.

To map these underground layers, scientists start by: Earthquake recorda record of waves showing seismic motion over time.

Computer models generate their own seismograms, and then subsurface estimates are updated through full waveform inversion, a process that matches simulated and recorded waveforms.

“Compare data from computers. simulation We use real data from earthquakes,” Smetana said.

After enough rounds, the calibrated model can reveal buried zones that direct waves toward some sites and away from others.

slow loop

Because earthquakes occur so frequently, government agencies want to keep their surface models unchanged and up-to-date for years.

Global count from United States Geological Survey On average, about 55 earthquakes occur every day, or about 20,000 earthquakes a year.

With each Full Waveform Inversion update, the computer is forced to solve a huge model and then solve it again.

If each run takes hours on a cluster, your team can’t afford the thousands of iterations required.

maintain bass

Most field data is cleaned before analysis, a step that removes the fastest variations without increasing computing time. match.

To remove this extra motion, seismologists apply a low-pass filter, a tool that removes the highest frequency shaking before comparing events.

By matching only what remains in the filter, this new method eliminates the need to track details that the recorded signal discards.

This trick is best suited for broader patterns used in risk mapping, as high-frequency problems require more calculations.

smaller system

Instead of solving all the equations directly, the team built a small stand-in model that could mimic the full equation.

They called this model order reduction, a shortcut to keep only the most important calculations and reuse them.

During setup, we taught the reduced model what kind of wave behavior is possible through several full simulations.

Subsequent runs used that condensed library and produced new results much faster while remaining stable at various subsurface velocities.

Earthquake simulation test

The researchers used a two-dimensional subsurface model of a seismically active region in the Netherlands as a testing ground.

Across that virtual terrain, they matched seismic records with far fewer unknowns, while changing the expected wave speeds.

Stability was important because if a shortcut dropped the wrong part, the waveform model could explode, producing false motion and timing.

Such results make it easy to try this approach in other regions, even if the geology is very different.

Risk map is faster

Better subsurface models inform shaking predictions that guide renovations, land use regulations, and emergency training.

Earthquakes occur every year in America. loss The average is about $14.7 billion, reflecting the number of people living in risk zones.

When simulations run quickly, analysts can test more disruption scenarios and continue to update local maps as new data arrives.

Cities still need strong building regulations, but faster modeling can show where they can best reduce risk with limited budgets.

The future of earthquake simulation

Even faster models require proper input, so this method still relies on where the sensor captures a clean wave record.

If the observation points are sparse, important rock boundaries can be missed, and that uncertainty can mean that the simulation doesn’t match what people actually feel.

“If we can better understand what’s going on underground, we can better assess the risk of future earthquakes,” Smetana said.

New regions also require careful setup and validation, as shortcuts cannot fix a bad start. model.

fast wave The simulation can make subsurface imaging practical enough for everyday use, rather than something that is rarely run on a shared computer.

Next steps include testing the method in a fully three-dimensional setting, where coastlines and deep basins complicate the waves.

This study SIAM Journal on Scientific Computing.

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