From: greg@perry.berkeley.edu (Greg Anderson)
Newsgroups: ca.earthquakes
Subject: Re: Quake felt in Menlo Park 1pm Sunday
Date: 21 Dec 92 22:24:15 GMT
Organization: UC Berkeley
NNTP-Posting-Host: perry.berkeley.edu

In article <1992Dec21.010651.2986@netcom.com> tweek@netcom.com (Michael D. Maxfield) writes:
>
>Yes, I felt it in Moraga too.  It felt like one single `drop' or shake.  
>According to the callers on the radio, a lot of them felt two quakes...
>the sudden jolt one and a shaker afterwards.  I wonder why I missed the 
>second one?  The epicenter was reported to have been in San Leandro and a
>first report placed it at 3.3 while latter reports said it was between 3.5
>and 4.0.  (Probably two different sources and the media decided to take
>the larger one for the SENSATIONALIZATION FACTOR.)
>


OK, here's the info from us here at UCB and from the USGS in Menlo Park.

UCB:

Location:  1 mile NNE of San Leandro (San Leandro Hills)
		37 degrees, 44.7 min North
		122 degrees, 08.6 min West
		depth = 2 miles

Time:	1:05 pm PST 20 December

Magnitude: Mw 3.6
	   ML 3.7


USGS-Menlo Park:
Magnitude: MD 3.4


Now, my guess as to why people reported feeling two quakes (a sharp jolt
and a slow shaker) was that people were actually feeling the arrival of two
distinct groups of seismic waves from the same event.  The first (sharp jolt)
would be the 'P', or compressional, wave.  The second (slow shaker) would be
the 'S', or shear, wave.  These two wave travel at different speeds (with
P always faster than S), and if you are more than about, oh, 10 kilometers
or so away from the earthquake, you will feel two distinct bursts of
motion from the earthquake.  As a general rule of thumb, in case you are
interested, for every second of time between the onset of the P and the onset
of the S, you are about 8 kilometers from the epicenter.  This is rough, of
course, but for distances of about 150 kilometers or less, it should work
fairly well...

Now, as to the differences in magnitudes described, here's the story.  You note
from the beginning of this note (hee! hee!) that there are three different mags 
listed for the earthquake.  These are an Mw of 3.6, and ML of 3.7, and an
MD of 3.4.  

The USGS in Menlo Park mainly calculates what are called "coda duration" 
magnitudes, which are abbreviated as MD (correct me if I'm wrong, Andy.
Had an interesting conversation with Barry yesterday about this...).  To explain
this, we should do a little elementary seismology.  If the world were nice
and homogeneous and unlayered, all seismograms for local earthquakes would 
have a single pulse of energy for the P and a single pulse of energy for the
S, and would look like this (forgive the ASCII graphics!):


	     P wave           S wave

		/\		/\
	       /  \            /  \
---------------    \    -------    \    -------
		    \  /            \  /
		     \/              \/


which would certainly make life boring for seismologists!  However, since the
world is not nice and homogeneous, we get stuff which looks like this:


	P wave         P coda      S wave      S coda

		                     /\
	       /\                   /  \       /\
              /  \    /\           /    \     /  \
--------------    \   | | /\-\/-/\-      \   /    \   /\-------
		   \/\/  \/               \-/      \ /  /
					            -   

The MD (duration magnitude) is calculated by measuring the duration of the little
P coda wiggles (those wiggles after the first P arrival) which have a certain
amplitude, and then adding in a distance factor.  The USGS in Menlo Park has 
calibrated their coda magnitudes against our Richter magnitudes.


Now, the more familiar magnitude is, of course, the Richter magnitude, which was
developed in 1935 and is called the ML.  This magnitude is based on recordings
from a wonderful, lovely, old photographic instrument called a Wood-Anderson
Torsion Seismometer (this last statement was heavily dripping with sarcasm, 
for those who haven't had the dubious pleasure of working with one of these 
things.  They are a pain in the ass!).  This is a machine with a fine gold wire
suspended vertically with a little mass at one point along its length.  The mass
has a mirror on it and this whole mechanism twists when an earthquake hits (hence 
the "Torsion" in the name).  A light beam reflects off the mirror and bounces back
onto photographic paper, causing the line we see when we develop the films.
Here's a picture (once again, no laughing at the drawing!):



      paper drum	light paths	     wire with mirror

		\				|
		 \				|
		  )				_
		  |			       [ ]
		  | <------------------------  | |  mirror assembly
		  |   			 ----> [ ]
		  )               --------      _
		 /        --------	        |
	        /     {}--                      |
			light source


	(this is a side view, by the way!)


Now, we measure the ML (or Richter magnitude) by looking at a record from this
system (see the fake-o seismograms above for an example), and measuring the
difference, in millimeters, between the peak amplitude of the deflected line
(usually the peak is in the S arrival or S coda) and the "zero" line (which in
my drawing is the ------ lines.)  We then take the log (base 10) of this
number and add a distance correction factor, and voila! you have your ML.

Here's the equations, for those who are interested:

	ML = log(A) - log(A0)  

		A = maximum zero-to-peak amplitude, in mm.
	        -log(A0) = distance correction factor

The equation is fixed so that a one (1) millimeter max amplitude on a record
recorded 100 km from the earthquake will have a ML=3.0.


Now, here is a good time to note a few problems with the Richter magnitude.
First, strictly speaking, it cannot be used beyond 300 kilometers (originally
600 kilometers) from the earthquake.  Also, Richter calibrated it only for
Southern California earthquakes.  And, it becomes really, really inaccurate
at magnitudes above about 7.0 or so, and really, really, really, really inaccurate
for the largest earthquakes known.

Also, it is not really an absolute measure of the size of the earthquake, but
rather a relative measure from quake to quake.  That's the real reason it was
invented, so that we could say, "Well, this one was a 3.5, and this one was
a 7.2"...


The final magnitude in use for local earthquakes (generally, there may be others.
Andy? Sue? Richard?) is called "moment magnitude" or Mw.  This magnitude is unique
in that it is actually derived from the physical area which ruptured in the 
earthquake, and as such it is actually a measure of how big the earthquake was! 
Also, because it depends on the physical area which breaks in the quake, it 
doesn't become inaccurate at large magnitudes.  There are a whole host of other
advantages.

So, when you hear different magnitudes from the same event, you can usually be
assured that it has to do with different methods of calculating magnitudes between
different organizations.  I mean, here at Berkeley, we alone calculate both Mw and
ML, so we usually get two very slightly different numbers.  

Which leads to one more minor point:  don't worry about small differences in magnitude
(i.e. +/- 0.2 magnitude units).  Differences that small are really meaningless.

Differences above that are more interesting, and have a whole host of explanations.
But that's for another post!

Whew!  So much for a short reply....


(Guess that's what I get for taking on the FAQ, Eugene!  8-0)


Greg Anderson
UCB Seismographic Stations
greg@perry.berkeley.edu
Newsgroups: ca.earthquakes