Hydrodynamic Analysis of Seismic Noise:
A New Look at Silence

Based on materials from pianoscript.ru

1. What This Article Is About

Every day, an earthquake occurs somewhere on Earth. Sometimes weak, sometimes catastrophic. Seismic stations around the world record ground vibrations around the clock. But most of these records are considered "noise" — random interference that carries no useful information. Usually, they are discarded so as not to interfere with analysis.

We looked at this noise differently. Not as interference, but as a meaningful signal. We built a model that extracts parameters from noise — much like engineers study turbulence in liquids or gases. It turned out that noise does not behave randomly. It contains patterns that repeat from station to station.

In this article, we will explain how our approach works, what we saw in data from real seismic stations, and what patterns we managed to discover. We wrote this text so that any reader can understand it — without specialized education or complex formulas.

2. How We Usually Listen to the Earth

Imagine you are standing on a bridge over a river. You want to understand what is happening underwater. You throw a stone and watch the ripples. If the circles are smooth — the water is calm. If the circles are torn and disappear quickly — there is an underwater current or whirlpool.

Seismologists do roughly the same thing. They listen to the Earth.

Seismic stations are placed all over the world — very sensitive instruments that record the slightest ground vibrations. A person cannot feel these vibrations. But the instrument can. It records everything: the steps of an animal a kilometer away, the wind, ocean waves, and real earthquakes.

The data flows continuously. Day after day. Year-round. For decades.

When a strong earthquake occurs, a seismologist opens the recording, finds the moment of the shock, and studies the waves. From them, they determine where the strike was, how strong, and at what depth. This works well. But it is a backward look: the event has already happened.

What about what came before? Silence. Noise. Usually, it is cut away and ignored. It is believed that there is no useful information there. It is just interference.

We thought: what if there is something in this noise? What if the Earth is not just "making noise" but transmitting signals that we have not yet learned to read?

And so we looked at noise differently.

3. What We Did Differently

The usual approach: noise is garbage, it must be thrown away. Our approach: noise is a conversation, it must be understood.

We borrowed an idea from hydrodynamics — the science of the motion of liquids and gases. When water flows through a pipe, it can flow smoothly (laminar), or with vortices and chaos (turbulent). Engineers describe this with the Navier-Stokes equation. We thought: why not apply a similar logic to seismic noise?

Imagine a crowd of people in a square. If everyone stands calmly — it is silence. If people start looking at each other, gathering in groups, moving synchronously — that is structure. Outwardly, it looks like random movement, but in reality, the system is preparing for something. Our model searches for exactly such moments: when order emerges in apparent chaos.

We take a recording from a seismic station. We break it into 60-second segments. And for each segment, we calculate several parameters:

• Chaos force — how strongly the data "rushes about."
• Turbulence — whether the recording resembles a turbulent flow.
• Coherence — how chaos and turbulence are related to each other.
• Determinism — whether there is a hidden structure in the data.
• Nonlinearity — how far the system is from equilibrium.

This is similar to measuring temperature, pressure, and humidity for a weather forecast. We do not know exactly where and when lightning will strike. But we see that clouds are gathering, pressure is dropping, wind is increasing. The system is sending signals.

And so it is here. We do not predict earthquakes. We describe the state of the environment. And this state, as it turned out, changes long before strong events. Moreover, it changes in a similar way for different stations and different regions.

4. What We Saw

We ran thousands of hours of recordings from different stations through the model. We looked at calm days, days before strong events, and days after. And here is what we discovered.

Silence Can Be Dangerous

The first thing that surprised us: silence is not always good. When a station records a very smooth, calm signal, this often means that the system is accumulating energy. Chaos drops almost to zero. Everything freezes. This happened before all the major events we studied.

And vice versa: when there is a lot of chaos around, when the station is "noisy" — that is a normal, healthy state. The system releases stress little by little. Nothing terrible is happening.

We called this the "background paradox": silence = danger, chaos = safety.

Turbulence in Silence — A Strong Signal

Sometimes, against a background of general silence, a burst of turbulence suddenly appears. Imagine a smooth river in which a whirlpool suddenly arises. It spins, boils, and disappears. And all around is quiet again.

We called such bursts markers. They do not appear randomly. The larger the future event, the earlier and more clearly the markers are visible. For small events — minutes or tens of minutes. For large ones — hours or even tens of hours.

Three Orders of Markers

Markers come in different strengths. The stronger the marker, the further it stands from the event:

• First order: weak. Appear hours or tens of minutes before. Visible before events from magnitude 4.5.
• Second order: stronger. Tens of minutes or hours before. For magnitudes 7 and above.
• Third order: the strongest. Can appear a day or more before. Before magnitudes 8 and above.

It is like assembling a train: first the signal, then the train starts moving, then it picks up speed. The longer the train, the earlier it begins to move.

The System Can "Collapse"

Sometimes determinism suddenly jumps almost to unity. Noise ceases to be noise — a clear, almost perfect structure appears in the data. As if thousands of random voices suddenly start singing in unison. We called this "wave function collapse." A very strong signal. It appears minutes before sharp changes in the system.

Stations Can Be "Alive" or "Dead"

Not all stations yield a useful signal. Some are located in noisy places: near ports, cities, in ocean surf zones. Their data is so clogged with interference that no patterns are visible. We call such stations "dead" — they are unsuitable for analysis.

Other stations are located in quiet places — far from civilization, on solid rock. They provide a clean signal on which all markers are clearly visible. We call such stations "alive." It is with these that we work.

The rule is simple: if the Hurst exponent is above 0.8 or the calm percentage is below 3% — the station is unsuitable.

5. How We Tested It

Any idea must be tested. There have been many attempts to find patterns in seismic noise. Most were unsuccessful — either the patterns turned out to be random, or they worked on one station and broke on another.

Therefore, we approached testing rigorously.

Data from Different Stations

We took recordings from stations in different parts of the world. We chose those located in quiet places, far from cities and ports. We looked at data over long periods — weeks and months.

Blind Testing

We did not know in advance when or where an event occurred. We simply ran the recording through the model and noted: here is silence, here is a marker, here is a collapse. Then we checked against earthquake catalogs. If there is a marker but no event — the model is wrong. If there is an event but no markers — the model does not work.

What We Found

The model does not predict every event. But there is a clear pattern:

• Before events of magnitude 5.5 and above, markers appear almost always.
• The stronger the future event, the stronger the markers and the earlier they appear.
• The brightest signals appear before the largest events. Chaos drops to anomalously low values, markers appear hours and tens of hours in advance.
• On "dead" stations, the model does not work. This is a good negative result: the model does not extract a signal from nothing.

Reference Database

We now have more than twenty verified cases. For each, we know: the type of behavior, the strength of markers, their lead time, and the level of chaos. These reference points allow us to quickly assess new data.

Limitations

The model does not say: "there will be a magnitude 7.2 earthquake at 14:30." It says: "the system is entering a state that was previously observed before such-and-such events." This is not a prediction in the everyday sense. It is a description of state. Like a barometer does not say when it will rain, but shows that the pressure has dropped.

6. What's Next

We are at the very beginning of the journey. The model works, patterns are visible, but there are still more questions than answers. Here is what we plan to do next.

More Data

Two dozen reference events are enough to see the pattern. But not enough to speak of reliability. We need to run thousands of events from hundreds of stations through the model. Fortunately, all data from the world's seismic stations is openly available — in the IRIS archive. Anyone can download it for free. How to do this is described in the Appendix.

Automation and Speed

Currently, analyzing one station for a day takes time. We want to build a system that works in real time. Data comes from the station, is immediately processed, and we see the state of the system right now. Like a patient monitor in intensive care: parameters are updated continuously, and the doctor immediately notices changes.

Neural Networks

The human eye sees patterns, but a machine can see more. We plan to train a neural network on our reference database. It will be able to find subtle patterns that we miss. And do it around the clock, without fatigue.

Openness

We are publishing this article so that other researchers can test our method. Therefore, we are making the data and description of the method openly available. Let them check. Let them criticize. Let them improve.

Appendix. Technical Details: Equation and Parameters

In this section, we will describe the mathematical basis of the model. There is only one formula. Let's break it down piece by piece.

The Main Equation

Here is what our equation looks like:

At first glance, it looks scary. In reality, it is just a description of how the signal behaves. Let's break it down.

What S Is

$S$ is the signal itself. That very recording from a seismic station. Ground vibrations converted into numbers. We look at how $S$ changes over time ($t$) and across frequencies ($f$). Frequency is how many oscillations per second. Slow waves — low frequency. Fast ones — high frequency. Earthquakes and noise consist of a mixture of different frequencies. The equation describes how energy flows between frequencies and how it changes over time.

Left Side: What Drives the Signal

Three terms on the left:

1. $\frac{\partial S}{\partial t}$ — the rate of change of the signal over time. How fast $S$ is growing or falling right now.
2. $\alpha \cdot S \cdot \frac{\partial S}{\partial f}$ — nonlinear transfer. This is the key part. The coefficient $\alpha$ (alpha) shows how much the signal interacts with itself. If alpha is large — the system is strongly nonlinear. It's like a crowd where each person reacts to their neighbor. Chain reactions occur. Energy is pumped from one frequency to another. This is where the preparation for a major event hides.
3. $\eta \cdot \frac{\partial S}{\partial f}$ — linear transfer. The coefficient $\eta$ (eta) describes the simple, calm movement of energy across frequencies. Like water flowing through a smooth channel.

Right Side: What Dissipates and Accumulates Energy

Four terms on the right:

1. $\beta \cdot \frac{\partial^2 S}{\partial f^2}$ — diffusion across frequencies. The coefficient $\beta$ (beta) shows how quickly energy spreads across the spectrum. Large beta — energy dissipates quickly. Small beta — energy lingers, accumulates in one frequency region.
2. $\gamma \cdot \frac{\partial^2 S}{\partial t^2}$ — inertia. The coefficient $\gamma$ (gamma) shows how much the system "remembers" its past state. Large gamma — the signal changes smoothly, like a heavy flywheel. Small gamma — the signal jerks.
3. $\kappa \cdot S$ — damping or growth. The coefficient $\kappa$ (kappa) can be negative or positive. If kappa is negative — energy leaves. If positive — energy accumulates. An increase in kappa before an event is one of the signs of preparation.
4. $F$ — external force. This is what comes from outside: a distant earthquake, a train, ocean surf. For our model, $F$ is often interference. We choose stations where $F$ is minimal.

Critical Chaos Drop — The Main Effect

Before major events, |F| drops by tens, sometimes hundreds of times. We call this the critical chaos drop.

Real numbers from our reference events:

• Tohoku M9.0 (2011). Chaos held at 0.002–0.003 for 29 hours before the main shock. This is 100 times below the normal background.
• Kamchatka M8.5 (2025). |F| dropped to 0.0024. Almost complete silence. Markers of the second and third order appeared several hours before the event.
• Sumatra M9.1 (2004). |F| decreased to 0.0025. Silence against the background of a typically noisy region.
• Kumamoto M7.0 (2016). |F| dropped to 0.039. Turbulence (Re) soared to 517 — a giant spike in silence.
• Chile M8.8 (2010). |F| anomalously low, Re reached 1033. An absolute record in our database. Class A — extreme.

Imagine you are bending a branch. While you are just holding it — silence. No cracking. Energy is accumulating. Then the first crack appears — that's a marker. Then a few more cracks. And finally, the branch breaks — that's the main event. Our model sees this silence before the crack.

How Parameters Work Together: A Typical Scenario

1. Days or hours before: Hurst drops to 0.10–0.13. The system becomes persistent. |F| begins to decrease. Silence.
2. Hours or tens of hours before: |F| drops critically low (0.002–0.04). Re gives spikes (50–1000+). Markers of the second and third order appear. |F|/Re moves into class A or B.
3. Tens of minutes before: σα rises above 0.5. The system becomes deeply nonlinear. |α|_max may exceed 2.0.
4. Minutes or seconds before: R² rushes toward unity. The wave function collapses. The event occurs.
5. After the event: |F| sharply soars (sometimes above 3.0 — REJECTED). Chaos returns. The system has discharged.

REJECTED — When the Model Says "No"

Sometimes |F| exceeds 3.0. The model rejects the data — they are so chaotic that they cannot be analyzed. But this is not an error. REJECTED is a sign that the event has already occurred. Energy has been released, the system has entered a discharge state. If REJECTED lasts more than 5 minutes — this is a sign of a major rupture (M7+).

Technical Parameters of the Model

How to Get Data from IRIS

IRIS (Incorporated Research Institutions for Seismology) is the main global archive of seismic data. Tens of thousands of stations, millions of hours of recordings. Everything is openly available. Here's how to work with it.

Via Web Service (URL Request)

Example request for downloading a day of data from one station:

https://service.iris.edu/irisws/timeseries/1/query?net=IU&sta=MAJO&loc=00&cha=BHZ&start=2026-06-30T00:00:00&end=2026-06-30T23:59:00&format=ascii

Let's break it down:

• net=IU — station network (IU — international IRIS network).
• sta=MAJO — station code MAJO.
• loc=00 — location (usually 00).
• cha=BHZ — channel (BHZ — broadband, vertical).
• start=...&end=... — time range in ISO format.
• format=ascii — file format (ascii).

This link can be opened in a browser to download the data.

Important Notes

• The data is free for everyone. No registration required.
• The maximum volume of a single request is about 1 gigabyte. For larger volumes, data is requested in portions (for example, by day).
• The mSEED format is read by our model directly.
• The sampling rate of our model is 20 Hz. IRIS data usually comes at 20, 40, or 100 Hz. If necessary, we perform downsampling (decimation).
• The BHZ channel is the most universal. Broadband, vertical. Best suited for our model.

7. Where the Formula Came From