Calculating the Epicenter of Earthquakes
Main Concept
Seismology is the study of earthquakes, their effects, and seismic waves. The location of an earthquake's epicenter (point on the earth's surface directly above the location of rupture or faulting) can be determined using information about two of these seismic waves.
The first type of wave to consider when determining the epicenter of an earthquake is the P-wave. These waves are also referred to as primary or compressional waves. Important characteristics of P-waves are:
they are the fastest of the seismic waves and are the first to arrive
the particles that the wave passes through move in the same direction as the wave itself (pushing and pulling motion)
they travel through solids, liquids, and gases
The second type of wave to consider when determining the epicenter of an earthquake is the S-wave. These waves are also referred to as secondary or shear waves. S-waves can also be characterized by some unique properties:
they travel slower than P-waves and are the second wave to arrive
they travel perpendicular to the vibration of the particles
S-waves can pass through solids but not through liquids or gases
The following animation helps to understand the motion of each type of wave.
A seismogram is the graph output from a seismograph, which is used to determine the epicenter of an earthquake. When consulting the seismogram, P-waves always appear before S-waves, as they travel faster and can travel through three states of matter as opposed to one.
To determine the distance of an earthquake epicenter:
Determine the arrival times of the P-wave and the S-wave.
Calculate the difference between the arrival time of the P-wave and the S-wave.
Referring to the Earthquake Time Travel Graph below, determine the location on the graph where the two lines have a difference in their y values equal to the time difference you previously calculated. The x value at this location is the distance to the epicenter of the earthquake.
Earthquake Time Travel Graph
Example
Adjust the sliders to change the arrival times of the P-wave and the S-wave.
Suppose the P-wave arrives at t = 1.0 min and the S-wave arrives at t = 6.0 min. Determine the distance of the earthquake epicenter given the following information.
Solution
To determine the distance of the earthquake epicenter, you can use the steps in the previous section.
1. Determine the arrival times of the P-wave and the S-wave:
Arrival time of P-wave: 1.0 min
Arrival time of S-wave: 6.0 min
2. Calculate the difference between the arrival time of the P-wave and the S-wave.
Time Difference = 6.0 −1.0=5.0 min
3. Refer to the Earthquake Time Travel Graph. Determine the location on the graph where the two curves have a time difference equal to the time difference you previously calculated.
After looking at the Earthquake Time Travel Graph, it is clear that the two curves have a difference of 5 units on the time axis at x = 3.4. Therefore the earthquake has an epicenter distance of 3.4 ⋅ 103 km, or 3,400 km.
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