PSN-L Email List Message

Subject: Re: strain and tilt units
From: Mariotti Mauro mariottim@............
Date: Sat, 23 Sep 2000 10:13:28 +0200

thank you for your kindly reply.
It was very exaustive, as ever you do.
Thank you again, now all it's clear.

At 14.15 18/09/2000 -0500, you wrote:
>There is no such thing as a dumb question, and not responding could be
>dangerous, as my parents often found out when I asked such obvious childhood
>questions as how an alarm clock worked and they didn't respond, so I took 
>it apart to find out. (I really got into trouble with the tube radio).
>I assume that you know that 10^-7 means 0.000 000 01, or one part in
>1/10 th of a million.
>Strain and tilt are generally considered dimensionless, although the
>small angle approximation that sine(i) = i (in radians), means that
>tilt is represented in microradians (a radian is 360 degrees/ (2* pi));
>Strain is the change in length over a distance divided by that distance.
>So a change of 1 micron over 1 meter is a strain of 10^-6, or 1 microstrain.
>To measure it, some stable reference length, like quartz rods or laser
>interferometers, are used to determine the distance, and some sensitive
>transducer is used to compare the reference length with the actual length
>of the piece of earth in question. One of my earliest projects involved
>100 ft quartz tube strainmeters deep in a lead mine in Missouri. Some of
>the best laser/optical strainmeters are run by UCSD at LaJolla, where
>lasers in 750 meter vacuum tubes have resolutions of 10^-9 and annual
>stability of 10^-6. The new LIGO (Laser Interferometer Gravitational
>Wave Observatories) use multi-path laser interferometers 4 kilometers 
>per arm to try to detect gravitational waves from supernovas, colliding
>black holes, etc., that will strain the earth at 10^-18 to 10^-21.
>This megabucks NSF project has two LIGOs (Washington state and Louisiana),
>to sort out non-deep-space noise.
>Tilt has a similar definition of the change in elevation at one end
>of a reference length divided by that length. So if I balance a 30 cm
>ruler at the hole in the center, the length to the end is 150 mm. If I
>can measure any change in height at the free end to within 0.1 mm, this
>would be a tilt of 0.1/150 or 0.00067 radians, or 6.7 x 10^-4.
>The usual units of tilt are in microradians, or 10^-6. The geodetic 
>tiltmeters that I had installed as part of the USGS "prediction" effort
>in the '80s (in the Aleutians, at Parkfield, and almost at the Palmdale 
>bulge before Dave Jackson at UCLA found it to be a surveying artifact), have 
>resolutions of 10^-9, and annual stability if 10^-6, so the earth tides 
>at 10^-7 are a ready calibration signal for which we have accurate 
>computer models for comparison. The annual stability of 10^-6 was the
>best we could get three co-sited instruments to agree, and was much 
>larger than what models of tectonic deformation indicated for pre-earthquake
>deformation. The largest coherent signal was the annual rainfall hydrology.
>I have submitted an abstract to the AGU meeting regarding the new dynamic 
>broadband tiltmeter that senses pure tilt but is not sensitive to horizontal
>acceleration as a seismometer is, so it can be used to record and
>remove tilt noise from broadband horizontal seismic data. The current
>resolution is 8.3 picoradians (10^-12). It readily records such earth tilt
>noises as acoustic gravity waves (from storms) at 50 nanoradians (10^-9)
>amplitude. (I will post the abstract on m web site later in the week.)
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Larry Cochrane <cochrane@..............>