SME
Grade 12 Science · Problem type
Comparing earthquakes by magnitude
Use this for “A magnitude 6 quake and a magnitude 4 quake: how much more shaking, and how much more energy?”
Diagram
M₂ − M₁ = 6 − 4 = 2.
The ground moves 10² = 100 times as far, and the quake releases 10³ = 1,000 times the energy.
This is an example. Type your own values to start a new problem.
A
=
10
−
ΔM
Difference in magnitude
worked out (not typed)
E
Energy, second quake ÷ first
worked out (not typed)
Formulas
ΔM
=
M₂
−
M₁
2 = 6 − 4
A
=
10ΔM
100
=
10
2
E
=
10
1.5 × ΔM
1,000
=
10
1.5 × 2
Assumptions
•
Magnitude is read from the largest swing of a seismogram, corrected for the station’s distance.
•
Each step of 1 in magnitude is 10 times the ground motion and about 32 times the energy.
•
Both quakes are measured on the same magnitude scale.
Step-by-step
WE KNOW
M₁ = 4, M₂ = 6
FIND
difference in magnitude (ΔM), shaking, second quake ÷ first (A), energy, second quake ÷ first (E)
Step 1 · Find difference in magnitude (ΔM)
Use ΔM = M₂ − M₁
How many steps of magnitude apart the two quakes are.
ΔM = 6 − 4
ΔM = 2
Step 2 · Find shaking, second quake ÷ first (A)
Use A = 10ΔM
Each step of magnitude is 10 times the ground motion.
A
=
10
2
A
=
100
Step 3 · Find energy, second quake ÷ first (E)
Use E = 101.5 × ΔM
Each
step
of
magnitude
is
about
32
times
the
energy:
10
1.5
.
E
=
10
1.5 × 2
E
=
10
3
E
=
1,000
Check
Put the numbers back in. Both sides should match.
2 = 6 − 4 ✓
100
=
10
2
✓
1,000
=
10
1.5 × 2
✓
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