[rotation] nomenclature -- Your comments that rotations can be derived from translations

William H. K. Lee lee at usgs.gov
Wed Jan 30 16:33:09 CET 2008

Dear Alberto:

I enjoyed reading your excellent note that rotations can be derived from 
translations.  This is true if we assume the medium is homogeneous and 
isotropic with no "scale", and the classical elasticity theory applies. 
This approach has been extremely successful in seismology for the far-field 

Attached please find Twiss et al. paper published in 1993 in the Journal of 
Geophysical Research (vol. 98, p. 645-674).  These authors clearly 
demonstrated that the classical approach failed for the near-field, and 
Microplar (or Cosserat) elasticity theory is more appropriate.   They took 
into account two separate scales of motion: a large-scale average motion of 
the material (macro-motion), and a local motion (micro-motion).  Therefore, 
6 degrees of freedom (3 translational and 3 rotational) are necessary, and 
rotations can not be derived from translations in micro-motion.

My Taiwan colleagues and I are now conducting an experiment in an attempt 
to clarify this situation.  We are measuring rotation motions by two 
independent methods: (1) using accelerometer array(s), and (2) co-located 
three-component rotational sensor(s).  The initial deployment and some 
preliminary results were released in a relatively large report on Jan. 15, 
and a shorter version is attached here and was presented on Jan. 24.  We 
are deploying instruments in both free-field and in a building.  Also, 
velocity sensors are also deployed.  We plan to add at least 3 more 
rotational sensors in the near future: one more in the free-field and two 
in the building.

Your comments and suggestions will be greatly appreciated.

Best regards,

c.c.: Alain Cochard <alain at geophysik.uni-muenchen.de>, 
<rotation at geophysik.uni-muenchen.de>, "Charles Adam Langston (clangstn)" 
<clangstn at memphis.edu>, John R Evans <jrevans at usgs.gov>, 
<rotation-request at geophysik.uni-muenchen.de>, Mehmet Celebi 
<celebi at usgs.gov>, Heiner Igel <igel at geophysik.uni-muenchen.de>, Maria 
Todorovska <mtodorov at usc.edu>, Mihailo Trifunac <trifunac at usc.edu>, 
Vincent  Lee <vlee at usc.edu>, Zbigniew ZEMBATY <z.zembaty at po.opole.pl>, 
Robert Nigbor <nigbor at ucla.edu>

At 03:51 AM 1/29/2008, you wrote:
>Dear collegues, let me send a short remark about the topic. My best 
>regards, Alberto Castellani. --
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