Question

What is the fewest number of seismograph stations that are needed to locate the epicenter of an earthquake? A) two C) four B) three D) five

Short answer

Three seismograph stations are needed.

Step-by-step solution

Understanding the Problem

To locate the epicenter of an earthquake using seismograph stations, we need to interpret signals recorded from multiple locations. Each station can determine its distance to the epicenter but not the exact direction.

Concept of Triangulation

By using at least three seismograph stations, each measuring the distance to the epicenter, we can plot three circles on a map - each centered on a station with a radius equal to the distance calculated. The point where all three circles intersect is the location of the epicenter.

Choice Evaluation

Having fewer than three stations is insufficient because two circles will intersect at two points, leading to ambiguity in determining the precise location. Therefore, three stations are necessary to resolve this ambiguity and pinpoint the exact intersection.

Conclusion

Given these steps, the minimum number of seismograph stations needed to accurately locate the epicenter of an earthquake through triangulation is three.

Key concepts

Seismograph Stations

Seismograph stations are critical tools in helping us understand earthquakes. These stations are equipped with seismographs, which detect and record the vibrations of seismic waves traveling through the Earth. Each station provides important data on the seismic activity by measuring the time it takes for seismic waves to reach them. This information is essential in figuring out the distance between the station and the earthquake's epicenter, though it cannot point out the exact direction from the station to the epicenter.

Seismograph data are useful for determining the magnitude and location of an earthquake. The data collected from multiple seismograph stations allow scientists to determine where an earthquake originated. However, to precisely locate the epicenter, data from three or more seismograph stations are required. More stations usually yield more accurate results, but three is the minimum necessary for basic functionality.

Triangulation

Triangulation is a method used to pinpoint the location of an earthquake epicenter using data from seismograph stations. This technique involves measuring the distance from at least three different seismograph stations to the epicenter and using these distances to draw circles around each station. Each circle's radius represents the calculated distance from the station to the epicenter.

Where all three circles intersect is the epicenter of the earthquake. The reason three stations are essential is that just two circles will intersect at two points, creating ambiguity and uncertainty as it won't provide a single clear location. Adding a third circle resolves the ambiguity by giving a single point of intersection.

Triangulation is widely used due to its effectiveness in accurately locating seismic activity. The term "triangulation" comes from the idea of forming triangles out of the intersecting points, which become obvious when the circles representing the calculated distances are drawn on a map.

Seismic Waves

Seismic waves are the energy waves generated by the sudden breaking of rocks within the Earth or by the explosion of nuclear devices. These waves propagate outward from the source in all directions. There are different types of seismic waves, but the ones crucial in locating earthquake epicenters are P-waves and S-waves.

P-waves, or primary waves, are the fastest seismic waves and are the first to be detected by seismograph stations. They travel in a push-pull motion, compressing and expanding the ground as they move. S-waves, or secondary waves, follow P-waves and move in a side-to-side motion. They are slower than P-waves and hence arrive later.

The difference in arrival times between these waves is vital for calculating the distance from the seismograph station to the earthquake's epicenter. By measuring these time differences accurately, seismologists can calculate how far away an earthquake occurred from each station, which is the first step in using triangulation to determine the epicenter.