Question

On the seismogram of an earthquake recorded at a seismic station in Paris, France, the S-wave arrives 6 minutes after the P-wave. On the seismogram recorded at a station in Mumbai, India, for the same earthquake, the difference between the P-wave and S-wave arrival times is 4 minutes. Which station is closer to the epicenter? From the information provided, can you pinpoint the location of the epicenter? Explain. (D)

Short answer

From the given arrival times, we can conclude that the Mumbai seismic station, with a 4-minute difference between the P- and S-waves, is closer to the epicenter than the Paris seismic station, which has a 6-minute difference. However, we cannot pinpoint the exact location of the epicenter with the given information, as we need data from at least three seismic stations and the knowledge of how the waves change their speed in different Earth layers for precise location.

Step-by-step solution

Analyze the given arrival times of P-waves and S-waves

For the seismic station in Paris, France, the S-wave arrives 6 minutes after the P-wave. For the seismic station in Mumbai, India, the difference of the arrival times of the P- and S-waves is 4 minutes. Keep in mind that P-waves travel faster than S-waves.

Compare the arrival time differences

Since the S-wave took 6 minutes longer to reach the seismic station in Paris and only 4 minutes longer to reach the seismic station in Mumbai, we can say that it took longer for the S-wave to travel the distance from the epicenter to the station in Paris than it did to travel to the station in Mumbai.

Determine which station is closer to the epicenter

Since the difference in arrival times of P-waves and S-waves is lesser for Mumbai (4 minutes) compared to Paris (6 minutes), the Mumbai seismic station is closer to the epicenter of the earthquake. This is because the closer a seismic station is to the epicenter, the lesser the time it takes for the slower S-wave to cover the distance after the faster P-wave has reached the station.

Can we pinpoint the location of the epicenter?

With the information provided, we cannot pinpoint the exact location of the epicenter. We can only conclude the relative distances of the seismic stations from the epicenter, as we lack enough data to determine the actual distances or the angles formed between the stations and the epicenter. Additionally, we would need data from at least three seismic stations (triangulation) and the knowledge of how the waves change their speed within different layers of the Earth to more accurately locate the epicenter.

Key concepts

Seismic Waves

Seismic waves are the ripples of energy that travel through the Earth's layers after a disturbance, such as an earthquake, occurs beneath the surface. These waves are the primary method by which we can learn about earthquakes and the interior of the Earth. There are two main types of seismic waves: Primary waves, or P-waves, and Secondary waves, or S-waves.

P-waves are the fastest seismic waves and can travel through solids, liquids, and gases. They arrive first at a seismic station. Their speed can vary depending on the material they move through, but typically they can travel anywhere from 5 to 8 km/s. What makes P-waves unique is their ability to compress and expand the material they travel through; in this process, the material moves in the same direction as the wave is traveling.

S-waves, on the other hand, are slower than P-waves, typically moving at about 3 to 4 km/s and can only pass through solids. Their movement is characterized by shearing the material perpendicular to the direction of wave propagation. Knowing the unique properties and behavior of these waves is crucial for scientists when it comes to locating earthquake epicenters and understanding Earth's inner structure.

P-wave and S-wave Arrival Times

The arrival times of P-waves and S-waves are pivotal in seismology as they help in determining the distance of a seismic station from an earthquake epicenter. During an earthquake, P-waves are the first to be detected, followed by the slower S-waves. The difference in arrival times is due to the varying speeds of the waves; P-waves are faster and thus take less time to be recorded by a seismic station.

The time gap between the arrival of the P and S-waves – known as the S-P interval – increases with the distance from the epicenter of the earthquake. So, by measuring this interval at different seismic stations, scientists can estimate how far away the earthquake occurred. This method proves extremely useful when there aren't any direct measurements available to determine the distance to the epicenter. However, it does not provide the exact location; instead, it establishes a radius within which the epicenter can be found. This lack of precision is why multiple stations are required for a more accurate pinpointing of the epicenter.

Seismic Station Triangulation

Triangulation is a fundamental process in geophysics used for locating the epicenter of an earthquake. This method requires data from at least three different seismic stations. By calculating the distance of each station from the epicenter using the P-wave and S-wave arrival times, as previously explained, seismologists draw circles on a map with the radius equal to each station's distance to the epicenter. The point where these circles intersect is where the earthquake has hit – the epicenter.

This technique becomes more accurate with the inclusion of more seismic stations. Unfortunately, with only two stations, like in our example with Paris and Mumbai, you cannot determine the exact location of the epicenter. You would only have two circles on a map intersecting in a curve, which represents a range of possible locations for the epicenter. To truly pinpoint the earthquake’s origin, more data points and a process known as 'triangulation' are necessary. This scientific principle is not only essential for understanding earthquakes but is also applied in various other fields such as navigation and surveying.