SME
Grade 12 Science · Earth & Space Science
Earthquakes, seismic waves and Earth's interior
Use this for “The S wave arrives 100 s after the P wave. How far away was the earthquake?”
Diagram
P arrives after 840 ÷ 6 = 140 s; S after 840 ÷ 3.5 = 240 s.
The farther the station, the longer the lag.
This is an example. Type your own values to start a new problem.
L (s)
=
d (km)
÷
vₛ (km/s)
−
d (km)
÷
vₚ (km/s)
tₚ
P travel time
worked out (not typed)
tₛ
S travel time
worked out (not typed)
Formulas
tₚ
=
d
vₚ
140
=
840
6
tₛ
=
d
vₛ
240
=
840
3.5
L
=
d
vₛ
−
d
vₚ
100
=
840
3.5
−
840
6
Assumptions
•
S waves are slower than P waves, so the lag between them grows with distance.
•
Average speeds of 6 and 3.5 km/s are for the crust; real travel-time curves bend because deeper rock is faster.
•
One station gives a distance, not a direction.
•
Past about 10,000 km (104°) no S waves arrive: the liquid outer core stops them.
Step-by-step
WE KNOW
L = 100 s, vₚ = 6 km/s, vₛ = 3.5 km/s
FIND
distance to the focus (d), P travel time (tₚ), S travel time (tₛ)
Step 1 · Find distance to the focus (d)
Use L = d ÷ vₛ − d ÷ vₚ
Each
km
adds
1
vₛ
−
1
vₚ
seconds
of
lag:
divide
the
lag
by
that.
d
=
L
1 ÷ vₛ − 1 ÷ vₚ
d
=
100
1 ÷ 3.5 − 1 ÷ 6
d
=
100
0.28571 − 0.16667
d
=
100
0.11904
d
=
840
km
Step 2 · Find P travel time (tₚ)
Use tₚ = d ÷ vₚ
Travel time is the distance over the P wave’s speed.
tₚ
=
840
6
tₚ = 140 s
Step 3 · Find S travel time (tₛ)
Use tₛ = d ÷ vₛ
Travel time is the distance over the S wave’s speed.
tₛ
=
840
3.5
tₛ = 240 s
Check
Put the numbers back in. Both sides should match.
140
=
840
6
✓
240
=
840
3.5
✓
100
=
840
3.5
−
840
6
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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