[time-nuts] Q/noise of Earth as an oscillator

Tom Van Baak tvb at LeapSecond.com
Sun Jul 31 20:13:50 EDT 2016

Ron Ott wrote:
> There might be two Qs: one relating to the axil rotation and another concerning the volume behavior

Hi Ron, Chris, and now also Bill,

I was thinking this tangent wouldn't come up, but yes, in the fields of Seismology or Earth Science, you will also see "quality factor" and the letter Q used. In their case it refers to the attenuation of seismic waves traversing through the earth and bouncing back. It's a clever way to explore the composition of the earth, from the inner core outwards. It's an ironic (in the Fe sense) way to make large earthquakes a wonderful tool of science in addition to a dreadful threat to property and life.

Here's a few links that mention this type of Earth Q:

"Deep Earth Structure – Q of the Earth from Crust to Core"
in Treatise on Geophysics, Seismology and structure of the Earth, 2008

"Anisotropy of Earth’s inner core intrinsic attenuation from seismic normal mode models"
in Earth and Planetary Science Letters, 2014

"Wide-band coupling of Earth’s normal modes due to anisotropic inner core structure"
in Geophysical Journal International, 2008

"Tidal dissipation compared to seismic dissipation: in small bodies, in earths, and in superearths"
in The Astrophysical Journal, 2012

Any you're right. The "vibrating planet jello" Q is unrelated to the "rotating planet timekeeping" Q that I mentioned. The jello Q is a couple of hundred. The rotation/clock Q is a couple of trillion. That's why we define the second from the rotation of the earth and not the sound of the earth.

Just in case readers think there can't ever be more than one Q, I refer you to pendulum clocks. The main Q, the one that is related to timekeeping, is derived from the periodic decay of the swing of the pendulum. Especially for precision pendulum clocks, there are other Q's as well: the rod/bob combination lends itself to many unwanted modes of physical vibration, up/down, front/back, left/right, twist, "violin modes", etc. Each of these modes have amplitude, period, and decay. They all interact with each other and with the main swinging of the pendulum in nasty ways. And yes, they all have their own Q.


----- Original Message ----- 
From: "Ron Ott" <ronott at sbcglobal.net>
To: <chris at chriscaudle.org>; "Discussion of precise time and frequency measurement" <time-nuts at febo.com>
Sent: Wednesday, July 27, 2016 9:57 AM
Subject: Re: [time-nuts] Q/noise of Earth as an oscillator

There might be two Qs: one relating to the axil rotation and another concerning the volume behavior of the earth as a giant bowl of Jello. But you'd have to figure out how to really slam the planet to excite the entire volume. Earthquakes are probably too wimpy.

      From: Chris Caudle <chris at chriscaudle.org>
 To: time-nuts at febo.com 
 Sent: Wednesday, July 27, 2016 8:50 AM
 Subject: Re: [time-nuts] Q/noise of Earth as an oscillator
On Wed, July 27, 2016 10:33 am, Chris Caudle wrote:
> Does that imply that this value is not constant:
>>> And if you take the classic definition
>>> Q = 2 pi * total energy /energy lost per cycle
>>> then it would seem earth has a Q factor.

After re-reading "The Story of Q" I agree that Q of a rotating body could
be non-constant, but also consistent with the original definition of Q as
the ratio of reactance to resistance of an inductor, which of course would
vary almost completely linearly over a wide frequency range where the
resistive dissipation was not frequency dependent (i.e. where skin effect
was negligible).

Perhaps a more useful question is whether that is still a useful
definition compared to how the term is more typically used now to refer to
resonance bandwidth.

Chris Caudle

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