[rotation] More comments on rotation nomenclature paper

Charles Adam Langston (clangstn) clangstn at memphis.edu
Tue Jan 29 18:33:54 CET 2008


John, Alain, and the working group,

What an interesting discussion!  I see the point with the concern about
pseudo vectors.  I dusted off my venerable Morse and Feshbach to write a
short theoretical section on rotation.  Being a geologist, I was never
exposed to the term ³pseudo vector² in mathematical physics yet have
appreciated the differences between the vector treatment of rotations and
the usual treatment of ³polar² vectors of particle displacement, velocity,
and acceleration.  Personally I prefer ³axial vector² to describe rotation
since it has a precise definition in the math physics literature.  ³pseudo²
implies falsity.  The short write up gives the theoretical development of
rotation that should be unambiguous.

Concerning the ³dots² and ³primes² in derivatives.  ³primes² are usually
reserved for a derivative with respect to the entire argument of the
function.  It does not represent the spatial derivative.

The only point in bringing up the spatial derivatives of rotation was to
enforce the time derivatives in your statement.  I don¹t want to call the
spatial derivatives anything.

The discussion involving ³inferred² vs ³point² rotations is an observational
issue and partly an instrumental issue.  I¹m reminded of the problems that
the strain community has in understanding the effects of heterogeneity on
³observed² strain from Gladwin Tensor Strain Meters (GTSMs).  The ³observed²
strain is a sensitive function of how the instrument is grouted into the
hole and the heterogeneity of the near-hole environment. Attached is a
figure from a recent study that I performed on computing strain from Anza
network data and comparing it to the ³observed² GTSM strain.  The array
strain computed from a M8.1 earthquake was very stable across the 50 km of
the array.  However, observed GTSM strains are quite variable showing large
changes in wave amplitude and wave polarities.  Presumably, once the strain
meters are calibrated they will yield the correct strains for seismic waves.
Should the strains from a calibrated instrument be called ³inferred² or
³point² strains? Do we know enough about rotation observations and
instrumentation yet to understand the problems?

Chuck Langston
January 29, 2008

************************************************

Charles A. Langston
Center for Earthquake Research and Information
University of Memphis
3876 Central Ave., Suite 1
Memphis, TN 38152-3050

clangstn at memphis.edu
http://www.ceri.memphis.edu/~clangstn
(901) 678-4869
(901) 678-4734 (Fax)

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