Why linear array are not appropriate for ambient vibrations

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Why linear array are not appropriate for ambient vibrations

Postby admin » Sat Oct 19, 2013 7:55 pm

Often, this question has been a topic of hard debates since the publication of REMI technique by J. Louie (2001).

Geopsy provides a tool for passive linear arrays but I would like to explain in this post why I do not recommend a general usage of this method. This is my own opinion but generally shared by geophysists interested in quality measurements.

With a line of sensors, you can measure only the apparent velocity. If the incoming waves are perpendicular to the line, the velocity is infinite. To get the true velocity, the waves must travel parallel to the line. Nature is rather well done and a cosine is still close to 1 in a certain range of angle. Hence, we still get proper results with an angle of +/-25 degrees around the line axis (max 10% error).

If the wavefield is sufficiently isotropic, i.e. waves are travelling in all directions, one can achieve good results with a single linear array. But we never know the wavefield structure prior an experiment. There are many cases where most of the energy comes from one particular direction (a motorway, a nearby town or industrial zones, oceanic waves,...). Additionally, this direction may not be constant over the frequency band of interest. The ONLY way to get a correct measure of the ambient vibration directions of propagation is to setup a 2D array with a sufficient number of stations (>=7-8).

Ambient vibrations are generally sold as non-expensive experiments. However, being forced to redo a site investigation because the orientations of arrays were not correct is far from being efficient and cost effective. Moreover, with the results of a linear array alone it is impossible to estimate the bias of a misoriented wavefield direction.

Ambient vibrations can propagate in any direction that no one can predict except in some well investigated sites. To measure true velocities and not apparent, one should use the correct array setup: a 2d distribution of stations with a rather circular shape. It does not mean that the stations must lay on a circle but the aperture of array must be approximately the same in all directions to provide a uniform resolution power in all directions.

valerio
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Joined: Mon Jan 14, 2008 1:56 pm

Re: Why linear array are not appropriate for ambient vibrati

Postby valerio » Mon Oct 21, 2013 8:41 am

Ciao Marc,
I do actually agree with you on all points.
Linear arrays can only be used under strong assumptions that are hardly verified in reality. The best approach would certainly be using a 2D configuration of standalone stations, to avoid bias on apparent velocity estimation.
On the other side, I can somehow understand the situation of practitioners (especially in Italy), who often have no money to buy a dedicated equipment. They are forced to deal with what they have in hand, with the risk of providing bad/wrong results. Ok, this is a further issue to be solved….
An intermediate (though still sub-optimal) approach would be to use a seismic line of geophones in a “L” configuration. For example, with a 24 channel digitizer, one can deploy 12 sensors in a given (preferred) direction and the remaining ones perpendicularly. Something like:

X
X
X
X
X X X X X

In this case, even though the array response is still far from being isotropic, the azimuthal coverage is better than just using the linear configuration. Would you agree?
Best,
Valerio


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