## PSN-L Email List Message

Subject: Re: Modulated Seismic
From: Geoffrey gmvoeth@...........
Date: Sun, 24 Apr 2011 15:50:54 +0000

```This is similar to what I'm looking for,
There must be some famous person of the past who
developed a formula which anyone may use,
I need it described in high school terms
beneath the level of calculus which, here
in the USA, generally is taught only in Universities
or Colleges. So much math on the internet fails to condense
into the final summary and tends to loose me within all
the derivations,Using symbology (is this a word?) I have no background to understand.

thanks,
geoff

-----Original Message-----
From: Mike Price
Sent: Saturday, April 23, 2011 10:05 AM
To: psnlist@..............
Subject: Re: Modulated Seismic

One technique if the Goertzel Filter. Conceptually, it is a single bin
DFT. It's easy to code and very efficient. One common use is DTMF tone
detection, since it can be implemented on simple processors.

A summary of the algorithm and some code can be found at:
http://www.mstarlabs.com/dsp/goertzel/goertzel.html

Mike

On 4/22/2011 8:16 PM, Geoffrey wrote:
> Is there some way to pick a frequency
> like 0.123 Hz then process the sampled
> seismic signal to see if any energy of only
> that frequency is present ?
>
> Can you point me to a complete subroutine
> [complete meaning does not use a library of functions]
> to obtain such an answer ?
>
> It would be like an FFT but you give the data,
> sample rate, and what SINGLE freq to look for ?
>
>
> -----Original Message----- From: Chuck / Judy Burch Sent: Sunday, April
> 17, 2011 3:44 PM To: psnlist@.............. Subject: Modulated Seismic
>
> All,
>
> Thanks to Randal for raising this interesting topic. The Teager-Kaiser
> Algorithm and Randal's rectification scheme are efforts to find the
> instantaneous amplitude (or envelop) of a seismic record. Think of a
> short enough piece of a seismic record -- it can be modeled by a
> waveform of a given frequency, phase and amplitude. Throw away the
> frequency and phase information and you are left with just the amplitude
> as a function of time. So you can think of a record (very approximately)
> as a collection of unit-amplitude waveforms from an appropriate
> frequency range that has been AM modulated by the envelop.
>
> The FFT of the envelop, then, can be thought of as the Fourier Transform
> of the "modulating" function.
>
> There are different ways of approximating the envelop. Many texts on
> signal processing discuss the "analytic trace" or "analytic signal"
> method, which is mathematically rigorous. If the original record is X,
> then the quadrature (90 degree advanced) record, Y, is the Hilbert
> Transform of X. The envelop of X is SQRT ( X2 + Y2 ).
>
> In the (remote) chance that anyone wants to pursue this, contact me and
> I'll show you an easy way to calculate the Hilbert Transform.
>
>
> Chuck Burch
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