Answer key: Earthquake Epicenter Activity

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Goal: Use S–P lag times from three seismograms to find how far away an earthquake was from each station, then locate its epicenter by triangulation.

Connects to NGSS MS-ESS3-2 (Analyze and interpret data on natural hazards to forecast future catastrophic events and inform technologies to mitigate their effects.)

Completed results table

Arrival times read to the nearest 0.1 s, as the finder’s snap places them. Readings within about 1 s are fine; each second of lag is 8.4 km.

Answers vary. With the distances above, the three circles meet within about 0.5 km of the true epicenter, which is 260 km east and 200 km south of the map’s north-west corner.

The seismograms, marked

Answers

1. Which station was closest to the earthquake? How can you tell from the seismograms alone, before doing any math?

   Cedar Ridge. Its S–P lag is the shortest (about 16.1 s), because the S wave had the least distance in which to fall behind the P wave. Bayview, with the longest lag (about 30.1 s), was farthest away.

2. Show your calculation of the distance from Bayview to the earthquake.

   S–P lag = 82.1 − 52.0 = 30.1 s, and 30.1 × 8.4 ≈ 253 km. (The exact distance in the model is 252.2 km, so the 8.4 rule gets very close.)

3. P waves travel at about 6.0 km/s and S waves at about 3.5 km/s. Explain why the S–P lag gets longer the farther a station is from the earthquake.

   Both waves leave the focus at the same moment, but the S wave is slower, so it falls further behind with every kilometer: about 0.119 s per km (1 ÷ 3.5 − 1 ÷ 6.0). Over 8.4 km it falls 1 second behind, which is where the “× 8.4” rule comes from.

4. With only one station, what do you know about where the earthquake happened? What about two stations? Why do we need three?

   One station gives only a distance, so the quake could be anywhere on a circle around it. Two circles usually cross at two points, so there are still two possible places. A third circle passes through only one of those points, which pins down the epicenter.

5. Your three circles may not meet at exactly one point. Give two reasons why.

   Reading the arrival times by eye adds small errors: even reading them to the nearest 0.1 s moves the best meeting point about 0.5 km from the true epicenter, and a pick that is 1 s off moves a circle by 8.4 km. Real waves also travel at different speeds through different rock and curve with depth, and a real focus lies kilometers below the surface, while this model uses constant speeds along the surface.

6. Challenge: Cedar Ridge recorded a largest S-wave amplitude of 15.5 mm. Estimate the magnitude with M = log₁₀(A) + 3 × log₁₀(8 × lag) − 2.92.

   M = log₁₀(15.5) + 3 × log₁₀(8 × 16.1) − 2.92 ≈ 1.19 + 6.33 − 2.92 ≈ 4.6. The finder's quake is magnitude 4.6: a light earthquake that people nearby would feel.