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Tsunami propagation

Subject: Tsunami propagation
From: Marty Michener <>
Date: Tue, 04 Jan 2005 10:03:04 -0500
HI:

In 1975 I taught a course in Oceanography, so this is from memory. Walt is 
right, but tsunami arrivals can be quite complex. Some of this may already 
been gone over, if so, my apologies - I have not read every word of every 
post recently.

Usually starting in deep water, they travel as what are called square-root 
of GD waves - Rayleigh waves whose speed is controlled strictly by the 
depth of the ocean at each point. Specifically, the square root of the 
depth times gravity.  So in the mks system, for ocean depth of 1000 meters, 
say G=10 m/sec2, GD equals 10,000 and the square root is 100 meters per 
second, roughly 220 miles per hour -- fast, but far less than the speed of 
sound in air.

So, given a 3-D bathymetric map of an ocean floor, the location of the 
bottom shift that causes it, and a bank of computers, it is easy to predict 
exactly WHEN the wave will arrive at each shoreline.  WHEN, but not HOW 
BIG, which is the weak point of the famous Pacific Basin alarm system - 
nobody has any idea of the magnitude of these waves, unless one has very 
accurate, timely surface level measurements.  With these in place, and an 
elaborate real-time monitoring system, one can do much better.  That is 
why, pretty much, the Hawaiian Islands are so safe to surf.

One earthquake may shift laterally along a fault line, like the numerous 
cracks that make up the San Andreas Fault, or the shift of the bottom floor 
may be a more vertical thrust fault, starting a huge hump of water moving 
at high speed.  Unnoticed by boats over deep water, the main wave energy is 
so slow to shift and so long of a period, that sailors have no idea it is 
happening.  I had friends from Hollis in Turkey four years ago during their 
horrendous earthquake - but my friends were onboard a boat in the Bosporus 
(sp?) and had no idea until they arrive in port anything was wrong.  They 
didn't feel a thing - not an exact analogy, but in a boat the slow gets 
ignored for the quick.

Boaters nearer shore in several hundred feet of water are often lost, 
because by that time the wave is slowing down, as "its feet hit the shallow 
water", and the energy builds up a much higher magnitude wave form.  If I 
remember correctly, Rayleigh waves begin to break when the medium depth 
reaches approximately 1/2 to 1/4 of their wavelength.  In our initial 
example, let us say the periodicity (crest to trough and back to crest) is 
about an hour.  In that time, in 1 km deep water, the wave has gone 220 
miles for this example's sake.  The wavelength (lambda) is then 220 miles, 
or 350 km.  This means water less than 55 miles deep will start to break 
the wave - build the height and shorten the length as it slows down: i.e. 
anywhere it goes, it becomes higher.  Of course, for any given situation, 
the time period is not apriori predictable, but could be computed from the 
water level sensors - if any had been installed in the Indian Ocean.

As you may know, the synch function describes an impulse gone through a 
modest low-pass filter. This often describes the arriving tsunami wave, as 
in Walt's fascinating narration of his Oregon experiences - the bell begins 
to ring more gradually than you might expect, reaches a peak magnitude 
after a few cycles then dies off again slowly.  This may be because the 
ocean bottom is uneven, similar to a distant shot heard in a forest, or a 
hand-clap at the other end of a cylindrical culvert pipe - some of the 
echoes actually can beat the main impulse to your ears -- in the tsumani 
case propagation can be wavelength-dependent. Uneven ocean floor would tend 
to cancel the higher frequencies initially present in the ocean bottom 
fault shift, the same as a forest branches and leaves dampen audio tones 
about 2 khz, roughly speaking.

This case is a happy instance for the victims, because (and I thought 
EVERYBODY ALREADY KNEW) the water level begins oscillating BEFORE the main 
wave hits, and so if you ever see the water leave the bay - RUN for 
it!  Evidently a lot of children went out into the tide pools to catch the 
flopping fish, instead of seeking higher ground.  This is the most 
appalling fact I have yet heard about the current tragedy - so preventable, 
yet again I also wonder how many American school kids living on a coast 
know this simple rule?  BTW does everyone know why a tsunami is physically 
impossible on the Atlantic coast?  The news guy yesterday didn't!  It is 
protected by the relatively shallow banks, upon which 99% of the energy 
would be spent.

Generally speaking, matter is not created or lost, so the volume of water 
in the huge wave has to come from somewhere -- it has to drain out (like 
the surf undertow) before it can come crashing back in --- and local alarms 
are quite feasible - if the water level drops over 15 minutes - everybody 
gets loudly notified.

Well, thanks for reading my ramble.  I do hope we, as a society, can rise 
to this horrific occasion.  Like all such events, it has its "blessing 
aspects" as well.


--  best regards,  Marty Michener
MIST Software Assoc. Inc.,  P. O. Box 269, Hollis, NH 03049
http://www.enjoybirds.com/

Don't blame me, I vote in New Hampshire!

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