A Bayesian Parametric Ground-Motion Prediction Model: Response Spectra of Shallow Crustal Seismicity in Europe

When the ground shakes, the violence of the tremor at any specific location is not just a matter of how big the earthquake was or how far away it happened. It is also a story of the path the energy took through the Earth and the specific nature of the ground beneath a building. Scientists who study these shaking patterns use mathematical models to predict how strong the ground motion will be at a given spot. These predictions are vital for designing buildings that can survive a quake and for understanding the risk to communities. However, Europe presents a unique challenge. Unlike regions with frequent, massive earthquakes, much of Europe experiences smaller, less frequent tremors. This scarcity of large events makes it difficult to build accurate prediction models, forcing scientists to rely on data from smaller quakes and try to scale them up. The problem is that the ground in France or Belgium behaves differently than the ground in Italy or Greece, and a model that works for one region often fails in another.

A team of researchers based in Grenoble, France, has developed a new way to predict these ground motions that better accounts for these regional differences. They created a model that combines data from three distinct sources: a massive European database of earthquake recordings, a specialized dataset from France, and another from Belgium. By merging these records, they built a comprehensive picture of how seismic waves travel across the continent, covering everything from tiny tremors to major events. The result is a tool that can predict the shaking intensity of shallow earthquakes anywhere in Europe with greater accuracy than previous methods, particularly in areas where large earthquakes are rare but still possible.

The researchers started by gathering a vast collection of seismic records. They combined data from over 55,000 recordings of ground shaking, capturing events that occurred between 1976 and 2026. These recordings came from sensors placed across a wide swath of Europe, from the high-seismicity zones of Italy and Greece to the quieter regions of France and Belgium. A key part of their work involved cleaning and standardizing this data. Earthquake magnitudes, which measure the size of the event, had been calculated in different ways by different groups. The team replaced these varied estimates with a single, consistent set of magnitude values. This step was crucial because inconsistent measurements can distort the relationship between the size of an earthquake and the shaking it produces. They also ensured that the data included a wide range of earthquake sizes, from very small events with magnitudes around 1.6 up to large ones near 7.7, allowing them to study how shaking scales across the entire spectrum.

Once the data was prepared, the team built a new prediction model using a sophisticated statistical approach known as Bayesian regression. Unlike older methods that treated every location as a generic point, this new model recognizes that the Earth is not uniform. It divides Europe into a grid of small squares, each measuring half a degree by half a degree. For every square on this grid, the model learns how the ground attenuates, or weakens, seismic waves. This is a significant shift from previous models, which often assigned a single, broad region a uniform set of rules. By using a grid, the new model can detect subtle variations. For instance, it can distinguish between the high-attenuation zones of the Pyrenees, where waves die out quickly, and the low-attenuation zones of the lower Rhine Graben, where waves travel further with less loss.

The model also separates the effects of the earthquake source from the effects of the recording site. It calculates how much shaking is caused by the specific characteristics of the earthquake itself, such as its location and depth, and how much is caused by the local geology where the sensor is placed. This separation allows the model to be more precise. For example, it can identify that a specific valley in France consistently amplifies shaking more than a nearby hill, even if they are close together. The researchers found that this level of detail reduced the uncertainty in their predictions. The new model produces smaller margins of error compared to the previous best model used across Europe, meaning engineers and risk assessors can have more confidence in the numbers they receive.

One of the most important findings concerns how the model handles small earthquakes. In the past, models often struggled to predict the shaking from smaller events, sometimes producing unrealistic results where the shaking appeared to increase as the earthquake got smaller. The new model corrects this by using the abundant data from small and moderate earthquakes to establish a reliable baseline. This allows the model to be applied to low-moderate seismicity regions like France and Belgium, where small earthquakes are common but can still cause damage in vulnerable areas like river valleys. The model now behaves in a way that aligns with physical reality, showing that smaller earthquakes produce less shaking, and it can reliably predict the effects of events as small as magnitude 4.

The researchers also discovered that the way seismic waves lose energy depends heavily on the frequency of the shaking. High-frequency waves, which cause rapid, sharp jolts, behave differently than low-frequency waves, which cause slower, rolling motions. The new model captures this frequency dependence by allowing the attenuation rules to change based on the period of the wave. This means the model can predict not just the maximum shaking, but the entire pattern of how the ground moves over time. This is essential for designing different types of structures, as a tall building might respond differently to low-frequency rolling than a short, stiff house does to high-frequency jolts.

The study confirms that the new model is a significant improvement over its predecessor. It covers a wider range of earthquake sizes and distances, from very close to the source to hundreds of kilometers away. It also provides a clearer picture of the uncertainty involved in any prediction. By treating the model as a living system that can be updated with new data, the researchers have created a tool that will become more accurate over time as more earthquake records are collected. This is particularly important for Europe, where the seismic network is constantly expanding. The model is already being adapted for use in national hazard maps for Belgium and France, helping to refine the safety standards for buildings in those countries.

While the model represents a major step forward, the researchers acknowledge that there is still work to be done. Some regions, particularly in the Balkans, remain under-sampled, meaning the model has less data to work with in those areas. Additionally, the depth of earthquakes can be difficult to pinpoint precisely, which introduces some uncertainty. However, the framework they have built is designed to handle these limitations. As new data becomes available, the model can be updated to fill in the gaps and reduce the uncertainty. The ultimate goal is to create a seamless, highly accurate picture of seismic risk across the entire continent, ensuring that communities are better prepared for the ground beneath them.

This work demonstrates that by combining vast amounts of data with advanced statistical techniques, scientists can peel back the layers of complexity that have long obscured our understanding of earthquake shaking. The new model does not just predict numbers; it reveals the hidden patterns of how energy moves through the European crust. It shows that the ground is not a passive backdrop but an active participant in every earthquake, shaping the danger in ways that are now finally becoming clear. For the people living in these regions, this clarity translates into safer buildings and a more informed approach to the ever-present risk of seismic activity.