## PSN-L Email List Message

Subject: Re: Verticals
From: ChrisAtUpw@.......
Date: Sun, 27 Dec 2009 11:34:06 EST

```In a message dated 27/12/2009, tchannel@............ writes:

have put in some numbers and see it calculates  very long periods under
certain conditions, periods of  >20.

Hi Ted,

The signal amplitude falls off as f^2 below the  resonant period of a
magnet + coil sensor, so you need quite a large short  period signal
amplitude to enable you to reconstruct long period signals. A 1 Hz  P signal would
need to be well over 400 counts to reconstruct the 20 second long  period
signal.
You CAN'T do sensible arithmetic on long  period counts of 0 or 1! The
digital technique is likely to be much more  valuable when you are using a
24 bit ADC and also have very low noise.

My question is can long periods like these really  be achieved? I have
build several models and some working sensors using this  approach, but I have
never gotten more than about 3x the springs natural  frequency. A spring of
..5 second, just hanging vertically, resulted in a  sensor of 1.5 seconds. I
guess the AS1 is another example. The design of  the AS1 is widely used and
am I correct that it is operating at about 1.5  seconds? In theory, is this
shape, capable >10  seconds?

I run an AS1 which has a natural period of 1.5  seconds, but the
special amplifier provided compensates this correctly out to  4.5 seconds. Thus I
only need an extra gain of x20 to display the 20 second  Rayleigh waves at
their true amplitude. Yes, digital period  extension can work very nicely, so
long as the amplifier gain and the  signals are large enough. But don't
expect to do this with small total  count signals.

I hope to use Bob's program to construct another  vertical, but I am
confused, about my results. I know there are methods for  extending the period,
but here I am just asking about the physical results of  using  a
spring-supported pendulum constrained to move  in a vertical plane.   Perhaps these
calculated long  periods would only be possible under the best of conditions,
where all factors  were perfect. I seem to get a period of around x3 that of
the spring  hanging vertical with a mass.

Try increasing the amplifier gain by x50?

This is why I have suggested using a period  extending amplifier,
rather than by trying to tackle the problem digitally. It  is quite easy to get a
x10 period extension.

Regards,

Chris Chapman

In a message dated 27/12/2009, tchannel@............ writes:

McClure's=20
great program SpringCalc.exe. I have put in some numbers and see it calc=
ulates=20
very long periods under certain conditions, periods of=20
>20.
Hi Ted,

The signal amplitude falls off as f^2 below=
the=20
resonant period of a magnet + coil sensor, so you need quite a large=
short=20
period signal amplitude to enable you to reconstruct long period signals.=
A 1 Hz=20
P signal would need to be well over 400 counts to reconstruct the 20 secon=
d long=20
period signal.
You CAN'T do sensible arithmetic on long=
=20
period counts of 0 or 1! The digital technique is likely to be much=
more=20
valuable when you are using a 24 bit ADC and also have very low noise.

My question is can long periods like th=
ese really=20
be achieved? I have build several models and some working sensors using=
this=20
approach, but I have never gotten more than about 3x the springs natural=
=20
frequency. A spring of .5 second, just hanging vertically, resulted=
in a=20
sensor of 1.5 seconds. I guess the AS1 is another example. The desi=
gn of=20
the AS1 is widely used and am I correct that it is operating at about 1.=
5=20
seconds? In theory, is this shape, capable >10=20
seconds?
I run an AS1 which has a natural period of 1.=
5=20
seconds, but the special amplifier provided compensates this correctly out=
to=20
4.5 seconds. Thus I only need an extra gain of x20 to display the 20 secon=
d=20
Rayleigh waves at their true amplitude. Yes, digital period=20
extension can work very nicely, so long as the amplifier gain and the=
=20
signals are large enough. But don't expect to do this with small=
total=20
count signals.

I hope to use Bob's program to construc=
t another=20
vertical, but I am confused, about my results. I know there are methods=
for=20
extending the period, but here I am just asking about the physical resul=
ts of=20
using  a spring-supported pendulum constrained to=
move=20
in a vertical plane.   Perhaps these calculated=
long=20
periods would only be possible under the best of conditions, where all=
factors=20
were perfect. I seem to get a period of around x3 that of the sprin=
g=20
hanging vertical with a mass.

Try increasing the amplifier gain by x50?

This is why I have suggested using a period=
=20
extending amplifier, rather than by trying to tackle the problem digitally=
.. It=20
is quite easy to get a x10 period extension.

Regards,

Chris Chapman
```