Classification of ground motion
What is ground motion? How to measure and characterize it? Why to worry at all
about ground motion?
Earthquakes, certainly, represent an extreme case of ground motion.
Luckily, they are seldom though the displacements of ground during
an earthquakes can be quite large.
When we are talking about a particle accelerator, or about
a collider which smash submicron clouds of charged particles
hoping to produce some new, yet unknown particles,
or when we are talking about other sensitive and delicate
equipment, for example about large telescopes or
gravitational wave detectors, then we not as much (or not only)
worry about earthquakes, but rather about "normal"
ground motion, the one that occurs always.
Fast seismic motion
For the reason that will become clear a little bit later in the text,
SLAC people used to call ground motion above 0.1 Hz as "fast motion"
(perhaps, this terminology is not very common).
The sources that contribute to the "fast" motion are diverse.
The previous picture, for example, shows clear day night variations
for frequencies greater than 1 Hz. One can even distinguish two
weekends after five working days. It is then clear that this
contribution come from human activity and is also called
"cultural noise".
Other, more natural, sources of fast ground motion include
atmospheric activity (wind), motion of ocean water,
seismic activity (earthquakes), etc. For example, on the last picture,
the sharp peaks on the low frequency motion curves supposedly
correspond to remote earthquakes.
We need to discuss now one more important distinction about
ground motion. One can distinguish absolute and
relative ground motion.
The absolute motion is the motion relative to an
inertial frame, or "relative to stars".
The power spectrum shown above corresponds
to absolute motion since it was measured by
a single seismometer which measures
the motion with respect to an inertial frame.
We all know that the Earth itself moves
on a curved trajectory around Sun,
or rotates around its axis, so from this
point of view it performs "absolute" motion.
We however almost do not care about this motion
not only because it is slow, but also because it
does not produce noticable deformation of the
ground over a reasonably short distance, i.e. the
Earth moves as a whole body.
The relative motion of two locations is what
we usually worry about. Imagine what would happen
if the Earth rotation would cause ground to move
by half a meter over 100 meter distance?
We need, however, some additional information
to characterize the relative motion.
For example, from the above given picture
we have seen that the rms amplitude of the absolute ground motion
in the band 0.07-0.3 Hz is about 1 micrometer.
Can we tell, using this plots, what would be the
relative motion of two points separated by 10 meters?
What is expected rms relative motion for a time interval
1 second of two points separated by 1000 meters?
Obviously, we cannot answer these questions without
additional information on how the relative motion
occure. So, we need to know spatial
properties of ground motion. Such properties can be
studied in different ways, the most, perhaps, common
is to study ground motion with two or more seismometers
separated by some distance where you would
simultaneously measure the absolute and the relative
motion. These studies are called "correlation" measurements.
Studies in various places have shown that the fast motion
(in quiet conditions) can be represented by elastic waves which
travel with velocity determined by sound phase velocity in
the ground. The relative motion of two points would therefore
depend on the wavelength of the wave, its amplitude
and separation of this two points in space.
Slow motion (Diffusive ATL, systematic)
Slow motion, however, cannot be already clearly or understood
via the concept of elastic waves. The physical principles which
can produce slow (minutes to years and more time scale) are different
for slow motion than for the fast one.
Major sources of slow motion are temperature variations,
underground water and variation of its pressure, ground settlement
processes, slow changes of atmospheric pressure, dissipation
of fast elastic motion, etc.
The first model that attempted to describe slow motion
quantitatively is so called "ATL law", see
[Baklakov91],
[Shiltsev95]
for description of the model and underlying measurements.
This model suggests that the variance of relative misalignment of
two points dX**2 would be proportional to their separation in space L
and to the elapced time T with a coefficient A, so that
averaged dX**2 = A*T*L. As you see, this dependences suggest
"diffusive" of the motion.
Another model for slow motion, based mainly on observed LEP and SLAC
year to year motion, is so called "systematic" slow motion
[Pitthan95],
[Pitthan99].
In this case the time dependence of motion is mostly linear or very
smooth, so that the variance dX**2 would be proportional to T**2.
In
[ASTR2000]
it was suggested that the systematic motion can be described
by a "ATTL law" so that dX**2 = As*T**2 *L with another coefficient As.
The reasons for slow diffusive or systematic motion,
their dependence on geology or other factors, are not yet quite
understood. Certainly, the nature can be more complex than
this two simplified models, so that in reality
slow ground motion may consist of these two plus many other
types of motion.
Cultural noise
Cultural noise is ground motion produced by human via its activity.
It can significantly increase amplitudes of the fast ground motion.
It is especially dangerous if the noises are produced in close
vicinity from the place where we would want the ground motion to be
small. In the latter case, since the noise level can sharply depend
on location (due to geometrical and dissipative attenuation),
the concepts of the correlation based on elastic waves probably
would not be applicable for evaluation of the ground motion effect.
People know and worry about ground motions for many centuries.
Obviously, earthquakes and disasters that they bring have been
the reason.
The Chinese have been monitoring earthquakes for almost 2000 years.
In AD 132, Zhang Heng invented the first seismometer.
It consisted of a jar with ornamental dragons on its exterior.
The dragons held a small ball in their mouth that would roll
out if the jar was shaken in the direction parallel to the mouth
opening. The jar was surrounded by frogs with their mouths open.
The frogs would catch any released ball
and thereby record the direction of ground shaking.
However, this instrument could not measure how large
the shaking was.
How does ground motion look like if one measured by a modern
seismometer? Well, it depends on the frequency band of
seismometer. Here is an example measured by a seismometer with
0.1-100Hz frequency band
[VJ95].
As you can see, the displacement shown on this plot exhibits mostly low
frequency motion. That is because the
power spectrum of ground motion
drops very fast with frequency, approximately as 1/f^4 which can be seen from
this picture
[BB91],
[VJ95],
[VJ94],
[ZDR96],
[VS95].
Power spectra similar to what is shown above
allows to quantify the rms amplitude of motion in different frequency
bands. For example the following picture shows change in time
of the rms amplitude in several frequency bands
[VJ95].
One can see that while the rms amplitude is about 1 micron at 0.1 Hz,
it is only about 1 nanometer at 1 Hz.(Note, however, that this particular measurement
was taken in a very quiet location).
A famous example of atmosphere driven ground motion
is the so called "7-second hum" -- the peak in the
power spectrum at about 0.14 Hz. This peak is seen
almost everywhere around the Globe. In some cases it is
even possible to find the direction where this motion come
from, as shown in the picture taken from
[FM]
where it was shown that interaction of the ocean waves
with the coastline of Norway produce 2 Hz horizontal
motion seen in Germany.
