Epicenter Localization - Hyperbola Method

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True Epicenter / Intersection

Seismic Station

Distance Circle

Hyperbola

📊 Seismic Data

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🎯 Localization Progress

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Triangulate with third station

🧮 How the Hyperbola Method Works

1. Wave Speed Difference

Earthquakes generate two main types of seismic waves:

P-waves (Primary): Faster, arrive first (~6-8 km/s)
S-waves (Secondary): Slower, arrive second (~3-4 km/s)

2. Time-Distance Relationship (Single Station)

The time difference between P and S wave arrivals ( \( \text{t}_S - \text{t}_P \) ) at a station is proportional to the distance from the epicenter. This distance can be calculated using the P-wave velocity ( \( \text{v}_P \) ) and S-wave velocity ( \( \text{v}_S \) ):

distance = (t_S - t_P) × (v_P × v_S) / (v_P - v_S)

With one station, this defines a circle of possible epicenter locations.

3. Hyperbolic Triangulation

The hyperbola method uses the difference in arrival times of a specific seismic wave (e.g., P-wave, or the S-P difference itself) at pairs of stations.

1 station: (Using S-P time) Defines a circle of possible locations.
2 stations: The difference in arrival times of a wave at these two stations is constant for any point on a specific hyperbola. The stations act as foci. This defines one hyperbola.
3 stations: A third station allows the determination of a second, distinct hyperbola. The geometric intersection point of these two (or three) hyperbolas identifies the epicenter.

4. Real-World Application

This method is fundamental to how seismological networks locate earthquakes. This simulation finds the epicenter (the point on the Earth's surface directly above the earthquake's origin). The actual 3D origin is called the hypocenter.

Real seismic data contains noise, and seismologists use many stations and advanced algorithms for precise, reliable locations. Visual intersections on maps can also be affected by map projection and drawing approximations.