Question

On the seismogram of an earthquake recorded at a seismic station in Paris, France, the S-wave arrives six minutes after the P-wave. On the seismogram obtained by 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.

Short answer

The Mumbai seismic station is closer to the epicenter, as it has a smaller difference in P-wave and S-wave arrival times (4 minutes) compared to the Paris station (6 minutes). Despite this information, we cannot pinpoint the location of the epicenter, as we would need additional data from more seismic stations and apply a technique called "triangulation" using at least three stations to determine the exact location.

Step-by-step solution

Seismograms record the waves generated by earthquakes. There are two primary types of seismic waves: P-waves (also called primary waves) and S-waves (also called secondary waves). P-waves travel faster than S-waves, and they arrive at seismic stations before S-waves. The difference in arrival times between P-waves and S-waves can be used to determine how far a seismic station is from the epicenter of an earthquake. #Step 2: Analyzing the time difference between P-wave and S-wave arrivals#

At the Paris seismic station, the time difference between the arrival of the P-wave and S-wave is 6 minutes. At the Mumbai seismic station, this time difference is 4 minutes. Since P-waves travel faster than S-waves, a smaller difference in arrival times at a station indicates that the station is closer to the epicenter. #Step 3: Determining which station is closer to the epicenter#

Comparing the time differences, we find that the Mumbai station (4 minutes) has a smaller difference in P-wave and S-wave arrival times than the Paris station (6 minutes). Therefore, the Mumbai station is closer to the epicenter of the earthquake. #Step 4: Discussing the possibility of pinpointing the epicenter location#

While we have determined which station is closer to the epicenter, we still do not have enough information to pinpoint the exact location of the epicenter. By knowing the time differences in P-wave and S-wave arrivals, we can only estimate the distance to the epicenter, not the specific location. To determine the exact location of the epicenter, we would need additional data from more seismic stations. A technique called "triangulation" is often used to determine the epicenter location by analyzing the data from at least three seismic stations.

Key concepts

P-wave and S-wave

Seismologists study earthquakes by analyzing the waves they produce. The two primary types of seismic waves are P-waves (primary waves) and S-waves (secondary waves).
P-waves travel through the Earth at high speeds and are the first to arrive at a seismograph station. They can move through both liquid and solid layers, which explains their fast travel.

• P-waves: Faster, arrive first, travel through liquids and solids.
• S-waves: Slower, arrive second, only move through solids.

S-waves are slower and follow P-waves. They only move through solids, which is why they lag behind P-waves. The time difference between their arrivals provides crucial data. Seismographs capture this data, which helps to calculate the distance to an earthquake's epicenter.
By observing that in Paris, S-waves arrived six minutes after P-waves, while in Mumbai, this difference was only four minutes, it's clear that waves took less time to reach Mumbai. This is an indication that Mumbai is closer to the earthquake's epicenter.

Epicenter Location

The epicenter of an earthquake is the point on the Earth's surface directly above where the earthquake originates underground.
The key to locating the epicenter lies in understanding the difference in arrival times of P-waves and S-waves at various seismic stations. The greater the time difference, the farther the station is from the epicenter.

• Paris station: 6 minutes difference.
• Mumbai station: 4 minutes difference.

In this scenario, the Mumbai station, with its shorter time difference, is closer to the epicenter than the Paris station.
However, knowing which station is closer helps only in estimating the distance, not the exact geographic coordinates. Additional methods are required for a precise location.

Triangulation Method

Triangulation is a technique used in seismology to accurately pin down the location of an earthquake's epicenter.
It requires data from at least three different seismic stations. Here's how it works:

• Each station determines its distance from the epicenter using the P-wave and S-wave time differences.
• A circle is drawn around each station with a radius equal to the calculated distance.
• The epicenter is located where these circles intersect.

The intersection point of the circles represents the earthquake's epicenter. Triangulation allows seismologists to utilize distance data from various points to zero in on the exact location, assisting in efficient and accurate earthquake response.
Without triangulation, we can only know how far the epicenter is from a station, not its precise location. This method highlights the interconnected nature of seismological data analysis.