## PSN-L Email List Message

Subject: Re: Modulated Seismic
From: Geoffrey gmvoeth@...........
Date: Sat, 23 Apr 2011 03:16:46 +0000

```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,
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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