A Matrix Profile Based Time Window Selection Method for Microtremors HVSR measurements

The ground beneath our feet is rarely still. Even when we cannot feel it, the Earth hums with a constant, low-level vibration caused by ocean waves, wind, and the distant rumble of human activity like traffic and construction. Seismologists call these faint tremors "microtremors." By listening carefully to this background noise, scientists can map the hidden layers of rock and soil below the surface without digging a single hole. This technique, known as the Horizontal-to-Vertical Spectral Ratio method, works by comparing how much the ground shakes side-to-side versus up-and-down. The ratio between these two movements creates a distinct curve that reveals the natural rhythm, or predominant frequency, of a specific site. This information is vital for engineers designing earthquake-resistant buildings, as different soil layers amplify shaking in different ways. However, the signal is fragile. Because the Earth's hum is non-stationary—meaning it changes constantly over time—and is easily drowned out by sudden bursts of noise, the resulting curves can become distorted. If researchers simply average all the data they collect, these distortions can hide the true rhythm of the ground, leading to inaccurate maps of the subsurface and potentially unsafe engineering decisions.

To solve this problem, researchers Dexiang Kong, Lijing Shi, and Junjie Huang from the China Earthquake Administration have developed a new way to clean up these measurements. Instead of averaging every piece of data they collect, which often includes bad signals, they created a method to automatically identify and remove the noisy, unreliable segments before calculating the final result. Their approach relies on a mathematical tool called the Matrix Profile, which is designed to find patterns and spot anomalies in long sequences of data. Imagine a long string of beads where most are identical, but a few are different colors or shapes; the Matrix Profile acts like a scanner that instantly highlights the odd beads so they can be set aside. In this study, the "beads" are not physical objects but rather the spectral curves generated from short time windows of microtremor recordings. The researchers tested their method using three different levels of verification: simple mathematical signals, computer-simulated ground data, and real-world measurements taken from actual field sites.

The team first tested their algorithm on idealized signals to see if it could distinguish between clean data and data contaminated by noise. They simulated a steady signal and then added varying amounts of random interference, mimicking the way traffic or industrial machinery might disturb a measurement. The results showed a clear, direct relationship: as the noise increased, the algorithm's "anomaly score" rose in perfect lockstep. This proved that the method could quantitatively measure how much a specific time window was disturbed, without needing to know in advance what the noise looked like. It successfully identified the cleanest segments and flagged the most chaotic ones, even when the interference changed gradually or appeared as sudden, sharp spikes.

Next, the researchers moved to a more realistic scenario using computer-generated microtremor data based on known underground structures. In this simulation, they knew the exact "true" frequency of the site because they built the model themselves. When they used the traditional method of averaging all the data, the calculated frequency was off by more than 10 percent, and the shape of the curve was broad and unclear. However, when they applied their new Matrix Profile method to filter out the bad time windows, the error dropped to just 5.1 percent. The resulting curve became much sharper and aligned closely with the known truth. This demonstrated that the method could effectively strip away the distortion caused by non-stationary noise, allowing the true geological signal to emerge with much greater clarity.

Finally, the team took the method to the field, testing it on real microtremor data collected at two different engineering sites. At one location, they had access to deep borehole data, which provided a reliable reference for what the ground's true response should be. At another site, they compared their results against a benchmark derived from strong earthquake records, a standard used when borehole data is unavailable. In the first case, the traditional method produced a result that was nearly 18 percent off from the true value. After filtering the data with the Matrix Profile, the dispersion of the results decreased dramatically, and the curve matched the theoretical model much more closely. At the second site, which lacked deep drilling data, the traditional approach yielded a frequency that was nearly 25 percent higher than the benchmark. By removing the anomalous windows, the new method brought the error down to less than 3 percent, a level of precision that meets strict engineering standards.

The study concludes that this automated screening process offers a robust solution to a long-standing problem in geophysics. By focusing on the overall shape and consistency of the data across the entire frequency range, rather than just looking for a single peak, the method ensures that the final analysis is not skewed by transient noise. It requires no manual inspection by a human expert, no prior knowledge of the local geology, and no complex tuning of parameters. Instead, it relies entirely on the internal consistency of the data itself to separate the signal from the noise. This advancement means that engineers and seismologists can now process vast amounts of microtremor data with greater confidence, ensuring that the maps they create of the Earth's hidden layers are accurate and reliable for protecting communities from seismic hazards.