## PSN-L Email List Message

Subject: Re: Video of a experimental pivot
From: Brett Nordgren brett3nt@.............
Date: Sat, 25 Jul 2009 23:07:26 -0400

```Hi Chris,

First we need to distinguish between vertical force change due to a tilt
theta (DC tilt) and a dynamic tilt resulting from an oscillating earth
motion which rotates the instrument about its horizontal pivot axis such as
you would get from trees blowing in the wind; the same sort of motion as in
a Rayleigh wave.  Such motion produces a rotational acceleration about the
pivot generating an output signal which combines with the signal from any
vertical motion.  Two identical instruments oriented in opposite directions
will indeed cancel this kind of error if their outputs are added.

>Hi Brett,
>
>     That won't work!
>
>     The vertical force change due to a tilt theta is mgCos(theta) = 1 -
> theta^3 / !3 +

I think it is the force f which = mgCos(theta),  so the rate of force
change with respect to theta = df/d theta = -mgSin(theta).
As theta approaches zero, -mgSin(theta) approaches -mgSin(0) = zero.  The
rate of force change with respect to theta approaches zero.  Small DC tilts
produce even smaller force changes.

This seems to be confirmed in the literature:

"For small tilt angles, the contribution to the vertical component is
negligible" Forbriger "Low-frequency limit for H/V studies due to tilt"
October, 2006 Unpublished.
and
"While in a precisely vertical sensor the effect of tilt is of second order
and thus in most cases, negligible....."  Wielandt and Forbriger,
"Near-field seismic displacement......" Annali de Geofisica, June 1999

Of course with horizontal sensors it is a totally different story.

Brett

>     This is HIGHLY non linear with angle. Moreover, you get the same
> negative polarity force change for tilts in ANY orientation in the
> horizontal plane.
>
>     You might want cross check your assumptions about tilt rotation noise?
>>Obviously DC tilts don't necessarily cancel, but I wouldn't expect that
>>to be the primary problem.  Come to think of it, wouldn't you even be
>>slightly off-center in one direction and the opposing one the same amount
>>in the
>>opposite direction?
>     Not in general. If you set up two sensors with identical offsets in
> opposite directions, they will both still produce a tilt error if the
> tilt direction is at right angles to the line joining the centres of the
> two instruments.
>You need triaxial sensors to resolve this, but you still won't know if an
>effect is due to a tilt, or to a horizontal acceleration. You need a pure
>tiltmeter to resolve this hoary ancient problem - a liquid level meter
>WON'T do!

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