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Seismic waves and earthquake epicenters

Use the S–P arrival-time differences at three stations to estimate hypocentral distances, then locate the epicenter where the surface-distance circles intersect.

    E02 · Seismic waves and earthquake epicentersReady
    Find the distance to the epicenter based on the time difference between P and S waves from the three observatories, and find the epicenter where the three circles meet. You can also experiment with the numbers and controls below.

    Earth Science · Geology · Earth Interior / Principles and Exploration

    Seismic waves and earthquake epicenters — principles and investigation

    The difference between P-wave and S-wave arrival times estimates the distance to an earthquake’s hypocenter. Change the station positions and focal depth to find where the distance circles meet. Distinguish the underground hypocenter from the epicenter directly above it, and hypocentral distance from surface distance.

    How does it work?

    The epicenter is estimated using surface circles from three different observatories. When placing a straight line, the intersection point calculation is unstable.

    Key relationship

    d=8.4Δt (km), r=√(d²−h²)

    Try this investigation

    1. Drag or select three observatories and move them using the horizontal and vertical sliders. After executing the earthquake, check the P·S arrival mark and the intersection of the three circles.
    2. Run and record depths of 0 km and 30 km from the same epicenter, respectively, and compare the epicenter distance and surface radius.
    3. Check whether the intersection point of the circle points to the same epicenter even if you move observation station 3 from a depth of 0 km.

    Interpreting your results

    If Vp = 6 km/s, Vs = 3.5 km/s, and the S–P interval is 10 s, what is the hypocentral distance?

    d=Δt×6×3.5/(6−3.5)=8.4Δt. This distance is the distance to the hypocenter and the surface radius is √(d²−h²).

    Assumptions and limitations

    Assume a homogeneous medium and straight propagation with Vp=6 km/s and Vs=3.5 km/s. It is a model that knows the depth in advance and obtains an accurate arrival time. The actual layer structure, refraction, and time errors are omitted, and the waveform amplitude is a virtual relative value.