Introduction to the problems

Classification of ground motion

What is ground motion? How to measure and characterize it? Why to worry at all about ground motion?

First seismometer 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.

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.

Sample of seismometer record 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].

Example of measured PSD 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].

rms vs bend 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).

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.

direction to the coastline 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.

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.

This page created on 07/12/00 & updated on October 02, 2002 by A.Seryi.
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