From: stead@skadi.CSS.GOV (Richard Stead)
Newsgroups: ca.earthquakes
Subject: Re: Quake felt in Menlo Park 1pm Sunday
Date: 22 Dec 92 15:27:24 GMT

In article <1h5g6fINNj9b@agate.berkeley.edu>, greg@perry.berkeley.edu (Greg Anderson) writes:
> OK, here's the info from us here at UCB and from the USGS in Menlo Park.
> Location:  1 mile NNE of San Leandro (San Leandro Hills)
> Time:	1:05 pm PST 20 December
> Magnitude: Mw 3.6
> 	   ML 3.7

This must be the "Little Earthquake that Could" or something.  It made the
Washington Post!  Pretty famous for such an itty-bitty quake.

> 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...

Well, it gets a little messier than that.  There are actually quite a few
different waves that can arrive at local distances (the "local" range extends
to about 300 to 1000 km, depending on who you talk to).  There are several
types of P waves, but they all come in pretty close together, and usually
only one will be big enough to notice - the others are of interest only
to seismologists.  One the other hand, there are many S waves and surface
waves, most of which can be felt in a large quake, and are separated by
a lot of time.  Some S waves:
Sg  an old notation "S granite" from when it was thought that the crust was
    a layer of granite over a layer of basalt.  It travels through the middle
    of the crust.
Sn  This is a tiny S wave, but is the first beyond about 200 km.  It is a
    "head wave" that travels on top of the MOHO
Lg  The most common and often largest S wave in local and regional ranges.
    This is a very complex wave, part surface wave (the L stands for Love
    wave, one of the two types of surface waves) and multiple reflected
    waves, possibly even conversions to P waves and back again.  Despite
    its complexity, the onset of its peak amplitude has a velocity of about
    3.5 km/s that is relatively constant, and it has a very stable amplitude
    dependence on distance making it an excellent choice for magnitudes.  It
    carries the bulk of the quake energy that you feel.
SmS This is a reflection off the MOHO that is strong only in limited ranges,
    and is thought to be a principal contributor to the large amplitudes
    of S at San Francisco from the Loma Prieta quake.
Rg  This is the Rayleigh wave in the crust - Rayleigh waves are a very specific
    type of surface wave.  They have a unique particle motion - retrograde
    elliptical.  They are much longer period than the other waves mentioned
    and are often responsible for the damage of large structures in quakes
    (which have natural periods that long).  They are also responsible for that
    swaying motion you feel after a big quake.
There are even more for certain areas - S*, Sb, S-, etc., but that's more
complication than is necessary.
To be able to estimate range to a quake, it is important to identify the phases
felt correctly.  P is always a very sharp jolt, as much heard as felt - it
is heard as a sort of low boom, but more often as a quick and sudden rustle
of leaves or "whump" of a house.  It is hard to actually feel it because
it is rather short period, low amplitude and brief in duration.
The Sn can be mistaken for P, since it also may carry high frequency, is
low amplitude and short in duration.  It has different motion however -
Sn is mostly felt, not heard, and it has more of a side-to-side motion,
while P is more vertical.  Sn also is not important until you are at least
100 km from the quake.  At some distance (between 120 and 180 km, depending
on where you are), Sn crosses Sg and starts coming in first.  Closer than
that, Sg is first.
Lg is what most people think a quake feels like (and they're right, since
it carries the most energy usually).  It moves side-to-side and "shakes",
it also generally lasts a long time.  Rg is that swaying motion that sort
of makes you feel sea-sick (that's the principle way you feel it, since
it's a very smooth motion and isn't jerking you all around - sometimes,
you don't feel it at all, but see all the trees, cars, chandeliers, or whatever
slowly swaying).

> 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.

I think Caltech uses Mc for coda magnitudes, but I don't remember for certain.

> 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!).
...
> Now, we measure the ML (or Richter magnitude) by looking at a record from this

Well, nowadays, we actually just take a nice, modern seismometer and using
some signal processing, make a digital seismogram the equivalent of what
the W-A would have made.  Then the amplitude is measured off that.

> 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.

Yes - this is the "saturation" problem.  Basically, a W-A seismometer is best
around 1 Hz.  Trouble is, the energy spectrum of a quake is not the same for
different size quakes.  As quakes get bigger, the peak energy shifts to lower
frequencies, and eventually 1 Hz is past the "corner frequency".  At this point,
all quakes "look" the same size at 1 Hz.  They are bigger, however, and
therefore have more energy in longer periods, and longer durations of shaking.
This shift is also the reason why 1 unit of mgnitude, representing a factor
of 10 in amplitude, represents only a factor of 32 in energy.  If the spectrum
were constant, that unit of magnitude would be a factor of 10 in amplitude
and a factor of 100 in energy.  This is because a long period wave of the same
amplitude as a short-period wave carries less energy.  All magnitude scales
except Mw suffer from saturation at some point, so for the largest quakes
(we get on every 5 years or so that's above 8.3), only Mw gives an accurate
measure of the magnitude.

> 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

Oh, bunches more.  USGS at Denver (NEIC) reports mb and MS.  mb is a 1 second
body-wave magnitude, and can be calculated from a variety of waves.  MS
is the surface wave magnitude, usually computed from teleseismic 20 second
Love waves.  It can be calculated at longer periods, however, and corrected
to 20 seconds.  The nuclear monitoring community likes MLg, because of
its stability, but it's really a type of mb.  There is an intensity magnitude
measured from isoseismal contours that is valuable for measuring the
magnitudes of historic quakes that occurred before instrumental seismology.
There are dozens of others.  They are always calibrated against ML (directly
or indirectly) over some range of magnitudes in order to make all
magnitudes directly comparable.

> 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 

Mo is Moment (not a magnitude) and is related to displacement and area by

Mo = mu * A * d

where mu is the rigidity of the material containing the fault, A is the area
of fault surface that slipped, and d is the average displacement across the
fault.  Then the strain energy release is

W = Wo = ds * Mo / (2 * mu)

where ds is the stress drop in the material (stress before - stress after).

Having the energy, we can define Mw, using the energy-magnitude relation

log Wo = 1.5 Mw + 11.8

The little o on Mo and Wo indicates that the value is measured at DC (zero
frequency).  W = Wo only if the quake releases all the stress.  Since faults
have been determined to have very low "friction", quakes will usually
release most stress as waves, so that the assumption is approximately correct.
Wo can be estimated from ultra-long period seismograms, making Mw
essentially an infinite period magnitude.  As an example, 100 second MS
(often denoted M100) is related to Mo by

log Mo = 2.83 * M100 + 4.83

This works until the quake saturates 100 seconds, at which point an even
longer period would need to be measured.

Now I've told the group more than they ever wanted to know about Mw.

> 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.  

It may also have to do with propagation effects.  Most organizations try
to average these away by combining magnitude estimates from several individual
seismometers into one network magnitude, but Caltech's network may still give
a different result than Berkeley's for the same quake due to radiation pattern,
directivity, differences in the media that the waves propagate through,
focusing and defocusing by heterogeneities, constructive and destructive
interference, off-azimuth propagation, etc.  (Sorry for the slug of jargon
there, but I think I've explained most of these before, and this post is
already too long).


--
Richard Stead
Center for Seismic Studies
Arlington, VA
stead@seismo.css.gov