Earthquake Math: The Japan 7.7 Does Not Line Up

stock here: I have tried to push Earthquake prediction forward, by observing as much as possible, creating new models, and ignoring the mainstream so as not to pollute my observation and instinct. But on this last Japan Eq, my instinct told me….something is not right. The aftershocks of the “Trigger” were fairly low Mag, and spread out in too even of a pattern.

My first review of Eq Math, agrees with that instinct. It seems that the current aftershock pattern is less than 1% likely based on how Eqs normally follow a big quake.

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So the clean place to start is probably Omori’s law, because it is the basic math for how aftershock rate decays with time after a mainshock. Modern treatments usually use the modified Omori law:

$n(t)=\frac{K}{(c+t)^p}$n(t)=(c+t)pK​

Where:

• $n(t)$n(t) = aftershock rate at time $t$t after the mainshock
• $K$K = productivity constant, bigger means more aftershocks
• $c$c = small time offset so the rate does not blow up at $t=0$t=0
• $p$p = decay exponent, commonly near 1 in many sequences

What it means in plain English:

• right after the mainshock, aftershocks are dense
• then they thin out with time
• if $p=1$p=1, the decay is roughly inverse with time
• if $p>1$p>1, the sequence dies off faster
• if $p<1$p<1, it lingers longer

The other two major earthquake “math laws” that usually sit beside Omori are:

Gutenberg–Richter law for how many quakes exceed a given magnitude:$$\log_{10} N = a – bM$$log10​N=a−bM

That means each step up in magnitude gives you far fewer events; with $b \approx 1$b≈1, a magnitude-4-and-up population is about 10 times rarer than magnitude-3-and-up.

Båth’s law for the gap between a mainshock and its largest aftershock:$$\Delta M \approx 1.2$$ΔM≈1.2

Meaning the largest aftershock is, on average, about 1.2 magnitude units smaller than the mainshock.

So a compact “earthquake math starter pack” is:

1. Time decay: Omori / modified Omori
2. Magnitude-frequency: Gutenberg–Richter
3. Mainshock-largest aftershock gap: Båth’s law