The Missing S-Waves at 4,200 Kilometers
Students in an Earth science lab examine records from a school seismograph 4,200 km from an M6.8 earthquake. The P wave arrives at 7 min 10 s; the S wave is not visible above background noise. A station 1,100 km from the same event clearly shows both P and S. The textbook says S waves cannot travel through liquid, and one student concludes, 'The outer core must be liquid under us,' while another says, 'The quake was too shallow to make S waves.' The teacher knows the S-wave shadow zone begins at about 103° from the epicenter. The school's instrument is a single vertical-component sensor with adjustable gain; the gain was left at a low setting after a nearby construction project. Students have a travel-time curve showing S arrival near 13 minutes at 38°. The class must decide whether the missing S wave is evidence about Earth's interior or about the measurement.
1. Calculate the angular distance and use the travel-time curve to evaluate both student claims.
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Distance: 4,200 km ÷ about 111 km per degree ≈ 38° from the epicenter.
Travel-time check: At 38°, the curve places the S arrival near 13 minutes. The observed P arrival at 7 min 10 s is broadly consistent with that distance, so the station is not in an unusual far-field geometry.
Claim 1-liquid outer core: The outer core is liquid, but that fact cannot explain this record. An S wave at 38° travels through the mantle and does not pass through the core. The S-wave shadow zone begins near 103°, well beyond this station. The missing S wave is therefore not evidence that the outer core is liquid beneath the school.
Claim 2-shallow quake: A shallow earthquake still generates S waves; shear faulting produces them directly. Shallow focus does not suppress S at regional distances. That claim is also unsupported.
Better interpretation: The most likely explanation is instrumental or environmental. A single vertical-component sensor is less sensitive to horizontal S motion, the gain is low after construction, and background noise may hide the arrival. The students should treat the absence as a measurement problem to test, not as a mantle or core observation. The claim that fits all the evidence is that the S arrival is probably present but not resolved on this record.
2. What checks and additional data would distinguish an instrument or noise problem from a real absence of S waves?
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Students should first check the recording system:
- Gain and clipping: raise the gain and compare a quiet nighttime record with the daytime construction period.
- Noise floor: measure background amplitude before the P arrival and compare it with the expected S amplitude.
- Component orientation: a vertical sensor records P well but is less sensitive to horizontal S motion. A three-component station should show S more clearly.
- Calibration: verify the time base and sensor response so the predicted S window is not misplaced.
- P coda: look for a later arrival or converted phase in the P coda that may indicate S energy.
Then compare with independent data:
- A nearby station at a similar distance should record S if the event truly produced it.
- The regional catalog may report S readings or a focal mechanism consistent with shear faulting.
- The predicted S-minus-P time should match the travel-time curve for the event depth.
If a nearby station at the same distance records S, the absence is local to the school instrument. If no station at that distance records S, then the event or path needs reexamination. The key is to test the measurement before drawing a conclusion about Earth's interior.
3. Explain how the teacher should use this episode to teach the S-wave shadow zone without reinforcing the misconception that the outer core is liquid directly under the school.
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The teacher should make the geometry explicit. Use a globe or a circle diagram and place stations at about 80°, 110°, and 140° from the epicenter. Have students draw straight-ray paths through a layered Earth. At 80°, S waves travel through the mantle and arrive. At 110° and beyond, the S path would have to pass through the liquid outer core, so S is absent. The P-wave shadow zone from about 103° to 142° should be shown on the same diagram.
Students should then write a claim-evidence-reasoning statement: 'S waves disappear beyond about 103° because they cannot pass through the liquid outer core; this station at 38° is not in that zone.' That statement separates the global observation from the local record. The teacher can also contrast a phase diagram with an eclipse diagram: Earth's shadow does not cause phases, and the core's shadow does not explain a local missing S wave.
Finally, have students critique the original claim. The outer core is liquid, but the evidence for it comes from stations in the shadow zone, not from a low-gain vertical record at 38°. This preserves the correct science while modeling how to match evidence to scale.