Japan Earthquake False Alarm: M9.9 vs M6.9 — How Much Bigger?

Step by step

1. Japan's phones: an M9.9 earthquake warning
   Japan's phones just warned of the biggest earthquake ever recorded: magnitude nine point nine.
2. 8 minutes later: withdrawn · real quake M6.9, off Kamchatka
   Eight minutes later, it was taken back. The real quake was a six point nine, off Russia's Kamchatka Peninsula.
3. M9.9 vs M6.9: only 3 apart. How much bigger?
   Nine point nine versus six point nine. Only three apart. How much bigger is that?
4. Number 1 · wave height: × 10 per step · 10 × 10 × 10
   There are two different numbers here. First, the wave height. On a seismograph, each step up makes the waves ten times taller. Three steps: ten, times ten, times ten...
5. Waves: 1,000 × taller
   a thousand times taller.
6. Number 2 · energy: taller waves + longer fault + longer shaking
   Second, the energy. A bigger quake doesn't just make taller waves. It breaks a longer fault and shakes for longer. So the energy grows faster than the wave height.
7. Every 2 steps = × 1,000 energy → 1 step = √1,000 ≈ 31.6
   Seismologists measured it: every two steps means exactly a thousand times the energy. So one step is the square root of a thousand: about thirty-one point six. Call it thirty-two.
8. 3 steps: 32 × 32 × 32 ≈ 32,000 × the energy
   Three steps: thirty-two, times thirty-two, times thirty-two... about thirty-two thousand times the energy.
9. M6.9 ≈ 23 Hiroshima bombs · M9.9 ≈ 700,000 (≈ 210 Tsar Bombas)
   How much energy is that? A six point nine releases about as much as twenty-three Hiroshima bombs. A nine point nine: about seven hundred thousand. That's more than two hundred Tsar Bombas, the biggest bomb ever tested.
10. What would a 9.9 do? Two real giants
    So what would a nine point nine actually do? It has never happened. But two real giants show what big ones do, far beyond one country.
11. 2011 Japan M9.1: Hawaii ~8 h · California ~10 h · Crescent City ~8 ft
    In twenty eleven, a nine point one hit Japan. Its tsunami crossed the whole Pacific: Hawaii in about eight hours, California in about ten. In Crescent City, the water rose about eight feet.
12. 1960 Chile M9.5: Hawaii 15 h (61 died) · Japan next day (~140 died)
    In nineteen sixty, Chile's nine point five, the biggest ever recorded, sent its tsunami to Hawaii in fifteen hours, where sixty-one people died. The next day it reached Japan, ten thousand miles away, and about one hundred forty died there.
13. M9.9 ≈ 4 × Chile 1960 · ≈ 16 × Japan 2011
    A nine point nine would release about four times the energy of Chile, and about sixteen times Japan's twenty eleven quake.
14. On a test: energy ratio = 10^(1.5 × difference)
    On a test: the energy formula is log E equals one point five M plus four point eight. Each step multiplies the energy by ten to the one point five. Three steps: ten to the four point five, about thirty-one thousand six hundred. Point four steps above Chile: ten to the point six, about four. Point eight steps above Japan twenty eleven: ten to the one point two, about sixteen.