[Phys-L] Re: earthquake

[jsd at AV8N.COM (John Denker)]

Anthony Lapinski wrote:
> I read a Yahoo news article from yesterday (Sunday) from the Asian
> Associated Press. In it the head of Italy's National Geophysics Institute
> said that "all the planet is vibrating" from the quake, and that the quake
> even disturbed the Earth's rotation. Nothing more specific regarding this
> phenomena was mentioned.
>
> Can any internal force disrupt the Earth's rotation?

As a theoretical physics question, as a matter of principle, yes.

Think of the proverbial ice skater pulling in her legs and arms.
There is a strict local conservation law for angular momentum,
but not for angular _rate_.

>  And if the quake
> really changed the Earth's movement, is it large enough to detect?

That's the right question.  Let's put in some rough numbers.

Approximate the earth as a cube 10,000 km on a side, so it has a
volume of 10^12 cubic km.

Take a wild guess that the earthquake moved a chunk of plate 200 km wide
x 200 km long x 2 km thick, so it has a volume of 10^5 cubic km.
So we are talking about a mass fraction m/M = 10^-7.

Guess that the chunk moved about 0.020 km vertically.  That gives us a
distance fraction r/R = 2x10^-6.

So to a rough approximation, the change in moment of inertia should be
a few parts in 10^-13.

The atomic clocks at NIST have an uncertainty of a few nanoseconds.  So
a day can be resolved to a few parts in 10^13.

Comparing these two numbers, it looks like a big earthquake is right at
the edge of current timekeeping technology, if you want to see the
effect within a day or two of the even.

A more serious limitation comes from astrometry.  How accurately can you
measure the rotation of the earth?  A really good transit instrument can
resolve a few dozen milli-arc-seconds, i.e. a few parts in 10^8.  That's
not nearly good enough.  So unless the interviewee has techniques I don't
know about, he's talking through his hat.

===

Also keep in mind that there's a difference between frequency modulation
(as discussed above) and phase modulation.  I can imagine that during
the hour or so that the tsunami is in motion, the solid earth will
rotate at a different rate, because some momentum has been temporarily
transferred to the water.  The effect on the rate is only temporary,
but there will be a lasting offset in the phase.