## PSN-L Email List Message

Subject: Lehman tilt sensitivity
From: S-T Morrissey sean@...........
Date: Sun, 2 Jan 2000 20:00:25 -0600 (CST)

```Marchal,

Regarding estimating the sensitivity of a horizontal seismometer:

The question you ask is somewhat ambiguous since many unknowns
are involved. It is very hard to guess what a seis will do as
you walk up to it, the main variable being the strength of the
local support: floor, pier, isolated pier, rock outcrop, etc.
And the orientation of the sensor with respect to the supporting
medium and the induced disturbance is very important. For example,
if the horizontal seis is located on a concrete flooring slab
near a basement wall or foundation, the wall/foundation will
provide more support than the open area and act as a hinge to
the resulting tilting. So if the boom of the horizontal seis is
parallel to the wall, the offset will be much more than if the
boom is at a right angle to the wall or foundation. Tilting a
horizontal seis along the axis of the boom  only changes the mechanical
period, while tilting across the boom axis can cause large displacements
of the mass depending on the boom length and the operating period.
Of course, since a horizontal seis is generally longer than it
is wide, it is tempting to set up the seis with the boom axis
parallel to the wall rather than sticking out into the room. And,
also of course, all this depends on where you park your car.

I showed and explained the applicable equations a few days ago.
The most important point is that the tilt sensitivity is a function
of the square of the period, like a 20-second seis is 4 times as
sensitive as a 10-second sensor. The formulas also showed how the
displacement sensitivity of eith a horizontal or vertical can be
calibrated by tilting the base.

A general method of estimating the sensitivity of any long-period
seismometer (as is the Lehman design) is to look for the background
6-second microseisms. While these vary in amplitude by x 10 to x 100
depending on the seasons, locations in the world, hurricanes, typhoons,
and storms in the North Sea, they are always present. The period
ranges form 3 to 12 seconds, 6 being dominant, so a 10-second seis
will be particularly sensitive if it under damped. (The flat velocity
response of a VBB broadband system makes them obvious, but a 1-second
seis will only show them at high (100k) magnifications.

Today at St. Louis the microseisms started out at about 2 microns, but
have decreased to about 0.4 microns as the storm causing them moved away
from the New England coast. With my sensitivity of 5.29 mv/u/sec
1 micron at 6 seconds (since omega = 2*pi/T = 1 if T = 2*pi). With
my simple 12-bit digitizer, 5 mv is 50 counts out of 2048, or about
2.5%. If I had a 16-bit digitizer, I would want the microseisms to
be about 5%, or 1600 counts, which would provide nanometer resolution
at 1 second.

You mention that your system shows 3500 counts of tilt as you walk
up to it. A 16-bit system maximum is about 32000 counts, so your
tilt noise is about 9%. Unless you have a very competent site, I
would expect a much larger tilt. I would look for the microseisms
to be at least 1000 counts. Maybe someone who is operating the Lehman
design can let us know what their microseism levels are, or even what
their experience is with induced tilting.

Regards,
Sean-Thomas

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