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How do seismic waves let us locate an earthquake and see inside Earth?

Explain how P-waves and S-waves behave and use the Reference Tables earthquake travel-time graph to find the distance to an epicenter, the origin time and the number of stations needed to locate it.

A Regents answer on earthquakes and seismic waves: P-waves and S-waves and how they differ, the Reference Tables P-wave and S-wave travel-time graph, finding the distance to an epicenter from the S-minus-P time, finding the origin time, why three stations are needed, and how the S-wave shadow zone reveals a liquid outer core, with worked exam questions.

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  1. What this topic is asking
  2. P-waves and S-waves
  3. Finding the distance to the epicenter
  4. Finding the origin time
  5. Why three stations are needed
  6. Seismic waves and Earth's interior
  7. Try this

What this topic is asking

The Regents wants you to compare P-waves and S-waves and to use the Reference Tables Earthquake P-wave and S-wave Travel Time graph to find the distance to an epicenter, the origin time, and to explain why three stations are needed. This is one of the most reliable Part B and Part C calculations in the lithosphere unit.

P-waves and S-waves

A few definitions the Regents tests:

  • Focus: the point underground where the earthquake originates.
  • Epicenter: the point on the surface directly above the focus.
  • Seismograph/seismometer: the instrument that records the wave arrivals as a seismogram.

Finding the distance to the epicenter

Because the P-wave outruns the S-wave, the S-minus-P time difference grows with distance. The Reference Tables travel-time graph plots travel time against distance for both waves. To find the distance:

  1. Measure the S-minus-P time from the seismogram.
  2. On the graph, find where the vertical gap between the S and P curves equals that time (mark the gap on a paper edge and slide it between the curves until it fits).
  3. Read straight down to the distance axis.

Finding the origin time

Once you know the distance, read the P-wave travel time for that distance off the graph, then:

origin time=P-wave arrival timeP-wave travel time\text{origin time} = \text{P-wave arrival time} - \text{P-wave travel time}

Why three stations are needed

A single station's distance defines a circle of possible epicenters around it. Two circles cross at two points, so two stations are not enough. Three stations give three circles that intersect at one point, the epicenter. This is triangulation.

Seismic waves and Earth's interior

Seismic waves also reveal the interior. S-waves cannot travel through liquid, so they are blocked by the liquid outer core, creating an S-wave shadow zone on the far side of Earth. P-waves slow and bend (refract) at layer boundaries. Together these effects let scientists infer the depths and states of the crust, mantle, outer core and inner core shown on the Inferred Properties page.

Try this

Q1. State two differences between P-waves and S-waves. [2 points]

  • Cue. P-waves are faster and travel through solids and liquids (compressional); S-waves are slower and travel through solids only (shear).

Q2. Explain why the time difference between the P-wave and S-wave arrivals increases with distance from the epicenter. [2 points]

  • Cue. P-waves travel faster than S-waves, so over a longer distance the faster P-wave pulls progressively further ahead, widening the arrival gap.

Exam-style practice questions

Practice questions written in the style of NYSED exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

Regents (style)2 marksPart B-2. At a seismic station, the P-wave arrives 4 minutes and 40 seconds before the S-wave. Using the Earthquake P-wave and S-wave Travel Time graph, determine the distance from the station to the epicenter. Explain how you used the graph.
Show worked answer →

A 2-point graph-reading question.

1 point for the method, 1 point for an answer in the correct range.

Method: 4 minutes 40 seconds is the S-minus-P time difference. On the travel-time graph, find the place where the vertical gap between the S-wave curve and the P-wave curve equals 4 min 40 s (you can mark this gap on the edge of a paper strip and slide it between the curves). Read straight down to the distance axis.
Answer: about 3,200 km (accept the range printed by NYSED, roughly 3,000 to 3,400 km).

Markers reward using the S-P gap (not a single curve) and a distance in the accepted range. A common error is reading off only the P-wave curve.

Regents (style)3 marksPart C. An earthquake is recorded at a station 4,000 km away. The P-wave arrives at 10:00:00. (a) Using the travel-time graph, find how long the P-wave took to travel 4,000 km. (b) Determine the origin time of the earthquake. (c) State the minimum number of seismic stations needed to locate the epicenter and explain why.
Show worked answer →

A 3-point extended-response question.

(a) 1 point: from the graph, a P-wave takes about 7 minutes to travel 4,000 km (accept the NYSED range).
(b) 1 point: origin time = arrival time minus travel time = 10:00:00 minus 7 minutes = about 9:53:00.
(c) 1 point: three stations are needed; each station's distance gives a circle of possible locations, and three circles intersect at one point, the epicenter (two circles cross at two points, so two are not enough).

Markers reward the graph-read travel time, subtracting it from the arrival time for the origin time, and the three-station triangulation reasoning.

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