From: Randall Peters PETERS_RD@..........

Date: Thu, 19 Jul 2007 11:52:05 -0400

Because of the recent interest in FFT's, I have posted some files on my webpage at http://physics.mercer.edu/hpage/psn/psn.html The pdf's should help those of you who have been wondering how the Fourier transform works and why the Cooley-Tukey form (Fast version) is SO MUCH better than the discrete FT (for which there is much needless, repetitive calculations). The executable can be downloaded (I promise that it is safe to use) and some data files have been posted to the site so that you can run test cases. test and test 2 are pure sine signals, one with a period of 17 s and the other 1000 s. The 0704 file is a record of the Solomon Islands EQ recorded wtih Larry Cochrane's VolksMeter. Before you can use the files you must rename your saved version (*.txt) to *.dat. This suffix must be typed in along with the filename when you are prompted for the input file. I have included the basic file from which the executable was created by QuickBasic (dos version which I've used for about 15 years). For those who might want to create a 'streaming' executable that operates on binary data, I can give you a sample file to look at--from there you will be 'on your own'. The FFT code that I've used is based on the structure given in the very excellent "Numerical Recipes" book by Press et al, with which most scientists are familiar. I hope that many of you will want to also transition from the FFT to the power spectral density (PSD), since the former is instrument dependent, whereas the latter is not (transfer function of the instrument used to provide correction). With the PSD, individuals having different hardware designs could still do meaningful comparison of their data. Some of you may wonder how I ever learned how to do the things posted on this webpage. Answer--years ago I became interested in the Fourier Transform because of its enormous importance to physics in general. I actually coded some early personal computers (with abysmally small memory) to do the necessary calculations. When speed was also abysmally slow, I became interested in the incredible improvement to be realized with the 'fast' version. The vector graphics form that I've provided in the pdf descriptions enables one to appreciate why the Cooley-Tukey algorithm allow 'technology to fly'. I enjoy the discussions on the listserve even though I have not been a frequent contributor to them. Keep up the good work; you guys are great! Randall psn-l-digest-request@.............. wrote: > .------ ------ ------ ------ ------ ------ ------ ------ ------ ------. > | Message 1 | > '------ ------ ------ ------ ------ ------ ------ ------ ------ ------' > Subject: Springs again > From: "Paul Cianciolo"> Date: Tue, 17 Jul 2007 12:07:36 -0400 > > Hello Folks, > > I have been building a vertical sensor for the past few weeks, doing lots of > experiments. > > It seems that the longer the spring, the longer the period... As a rough > rule of thumb. > I also remember Chris explaining about a "Zero Length" spring. > > My vertical sensor is the type with a lever arm that is 26" long with a mass > at one end. > The other end of the lever arm has a pivot point about 2" from the end, and > a spring on the end to a base plate. > > This arrangement certainly not a new idea, is new to me., > This arrangement yields a 1.1 approx. sec period. > By careful adjustment of the pivot point and spring location, I can vary the > period and the mass needed to achieve balance. > > 2 questions. > > 1) What is the relationship between spring position, pivot location, and > mass weight. > As I would like to try to optimize this design , if indeed this is a valid > path to follow. > > 2) If a rule of thumb....the longer the spring, the greater the period, > within the obvious constraints applies. > Has or why not has a vertical sensor been tried with a watch spring, > mainspring, arrangement been tried. > > Sort of a torsion spring, but one with many turns and greater length. > Perhaps my assumption that the main spring arrangement equates to a longer > spring is faulty? > > Please comment > > Thank You > > PauLC > W1VLF > Station VLF in Connecticut. > > .------ ------ ------ ------ ------ ------ ------ ------ ------ ------. > | Message 2 | > '------ ------ ------ ------ ------ ------ ------ ------ ------ ------' > Subject: Re: Springs again > From: ChrisAtUpw@....... > Date: Tue, 17 Jul 2007 22:26:18 EDT > > --part1_c43.15acd5bc.33ced44a_boundary > Content-Type: text/plain; charset="US-ASCII" > Content-Transfer-Encoding: 7bit > > In a message dated 2007/07/17, Paulc@........ writes: > > > My vertical sensor is the type with a lever arm that is 26" long with a > > mass > > at one end. > > The other end of the lever arm has a pivot point about 2" from the end, and > > a spring on the end to a base plate. > > Hi Paul, > > This is a bit difficult to visualise. Can you make a rough drawing > using text characters? > > > This arrangement certainly not a new idea, is new to me., > > This arrangement yields a 1.1 approx. sec period. > > By careful adjustment of the pivot point and spring location, I can vary the > > period and the mass needed to achieve balance. > > You can get out to 4 or 5 seconds, but beyond this you need NiSpanC > springs to keep the system stable with ambient temperature variations. However, > you can extend this period either electronically or using software up to ~x10. > See the Roberts circuit for geophones in psn references and on John Lahr's > website. It may be easier to make a system for 2.5 seconds and then extend this > to 25 seconds. > The spring attachment point needs to be maybe 1/2" to 1" above the > horizontal arm. > > > 2 questions. > > > > 1) What is the relationship between spring position, pivot location, and > > mass weight. > > As I would like to try to optimize this design , if indeed this is a valid > > path to follow. > > How good is your applied maths? This is a fairly simple triangle of > forces problem. You usually start with a coil spring and adjust the arm, mass > etc to suit. > > See the spring calculator at > http://jclahr.com/science/psn/mcclure/springcalc/index.html and also > http://jclahr.com/science/psn/mcclure/vert1/vert2.html > > Is your seismometer design anything like > http://jclahr.com/science/psn/hill/index.html ? I would strongly advise you to use electromagnetic damping > as opposed to oil. > > Have a look at http://quake.eas.gatech.edu/Instruments/LPVERT0.htm > > > 2) If a rule of thumb....the longer the spring, the greater the period, > > within the obvious constraints applies. > > Has or why not has a vertical sensor been tried with a watch spring, > > mainspring, arrangement been tried. > > This is just how long period verticals are designed, but using long > triangular shaped leaf springs. Clock type coil springs have too many vibration > modes. 'Mouse trap' type torsion coil springs have been used. > > For a simple spring, the extension E = g x T^2 / (2 x Pi)^2, where T > is the period. Thus to get a period of say 10 sec, you need an extension of > ~25 metres.... > > > Sort of a torsion spring, but one with many turns and greater length. > > Perhaps my assumption that the main spring arrangement equates to a longer > > spring is faulty? > > No, but this cannot be extended very far, or you start to see the > spring vibration modes. > > You can also make a very good horizontal seismometer using a U tube > water manometer. > > Regards, > > Chris Chapman > > --part1_c43.15acd5bc.33ced44a_boundary > Content-Type: text/html; charset="US-ASCII" > Content-Transfer-Encoding: quoted-printable > > In a me= > ssage dated 2007/07/17, Paulc@........ writes:

>

>: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">My vertical sensor is the type=20= > with a lever arm that is 26" long with a mass

> at one end.

> The other end of the lever arm has a pivot point about 2" from the end, and<= > BR> > a spring on the end to a base plate. #ffffff" style=3D"BACKGROUND-COLOR: #ffffff" SIZE=3D2 PTSIZE=3D10 FAMILY=3D"= > SANSSERIF" FACE=3D"Arial" LANG=3D"0">

>

> #ffffff" SIZE=3D2 PTSIZE=3D10 FAMILY=3D"SANSSERIF" FACE=3D"Arial" LANG=3D"0"= > >Hi Paul,

>

> This is a bit difficult to visualise. C= > an you make a rough drawing using text characters? 0000" BACK=3D"#ffffff" style=3D"BACKGROUND-COLOR: #ffffff" SIZE=3D2 PTSIZE= > =3D10 FAMILY=3D"SANSSERIF" FACE=3D"Arial" LANG=3D"0">

> #ffffff" SIZE=3D2 PTSIZE=3D10 FAMILY=3D"SANSSERIF" FACE=3D"Arial" LANG=3D"0"= > >

>: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">This arrangement certainly not=20= > a new idea, is new to me.,

> This arrangement yields a 1.1 approx. sec period.

> By careful adjustment of the pivot point and spring location, I can vary the= >

> period and the mass needed to achieve balance. " BACK=3D"#ffffff" style=3D"BACKGROUND-COLOR: #ffffff" SIZE=3D2 PTSIZE=3D10=20= > FAMILY=3D"SANSSERIF" FACE=3D"Arial" LANG=3D"0">

>

> #ffffff" SIZE=3D2 PTSIZE=3D10 FAMILY=3D"SANSSERIF" FACE=3D"Arial" LANG=3D"0"= > > You can get out to 4 or 5 seconds, but= > beyond this you need NiSpanC springs to keep the system stable with ambient= > temperature variations. However, you can extend this period either electron= > ically or using software up to ~x10. See the Roberts circuit for geophones i= > n psn references and on John Lahr's website. It may be easier to make a syst= > em for 2.5 seconds and then extend this to 25 seconds.

> The spring attachment point needs to be= > maybe 1/2" to 1" above the horizontal arm. ACK=3D"#ffffff" style=3D"BACKGROUND-COLOR: #ffffff" SIZE=3D2 PTSIZE=3D10 FAM= > ILY=3D"SANSSERIF" FACE=3D"Arial" LANG=3D"0">

> #ffffff" SIZE=3D2 PTSIZE=3D10 FAMILY=3D"SANSSERIF" FACE=3D"Arial" LANG=3D"0"= > >

>: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">2 questions.

>

> 1) What is the relationship between spring position, pivot location, and

> mass weight.

> As I would like to try to optimize this design , if indeed this is a validR> > path to follow.KGROUND-COLOR: #ffffff" SIZE=3D2 PTSIZE=3D10 FAMILY=3D"SANSSERIF" FACE=3D"Ar= > ial" LANG=3D"0">

> #ffffff" SIZE=3D2 PTSIZE=3D10 FAMILY=3D"SANSSERIF" FACE=3D"Arial" LANG=3D"0"= > >

> How good is your applied maths? This is= > a fairly simple triangle of forces problem. You usually start with a coil s= > pring and adjust the arm, mass etc to suit.

>

> See the spring calculator at http://jcl= > ahr.com/science/psn/mcclure/springcalc/index.html and also http://jclahr.com= > /science/psn/mcclure/vert1/vert2.html

>

> Is your seismometer design anything lik= > e http://jclahr.com/science/psn/hill/index.html ? I would strongly advise yo= > u to use electromagnetic damping as opposed to oil.

>

> Have a look at http://quake.eas.gatech.= > edu/Instruments/LPVERT0.htm style=3D"BACKGROUND-COLOR: #ffffff" SIZE=3D2 PTSIZE=3D10 FAMILY=3D"SANSSERIF= > " FACE=3D"Arial" LANG=3D"0">

> #ffffff" SIZE=3D2 PTSIZE=3D10 FAMILY=3D"SANSSERIF" FACE=3D"Arial" LANG=3D"0"= > >

>: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">2) If a rule of thumb....the lo= > nger the spring, the greater the period,

> within the obvious constraints applies.

> Has or why not has a vertical sensor been tried with a watch spring,

> mainspring, arrangement been tried. K=3D"#ffffff" style=3D"BACKGROUND-COLOR: #ffffff" SIZE=3D2 PTSIZE=3D10 FAMIL= > Y=3D"SANSSERIF" FACE=3D"Arial" LANG=3D"0">

>

> #ffffff" SIZE=3D2 PTSIZE=3D10 FAMILY=3D"SANSSERIF" FACE=3D"Arial" LANG=3D"0"= > > This is just how long period verticals= > are designed, but using long triangular shaped leaf springs. Clock type coi= > l springs have too many vibration modes. 'Mouse trap' type torsion coil spri= > ngs have been used. =3D"BACKGROUND-COLOR: #ffffff" SIZE=3D2 PTSIZE=3D10 FAMILY=3D"SANSSERIF" FAC= > E=3D"Arial" LANG=3D"0">

> #ffffff" SIZE=3D2 PTSIZE=3D10 FAMILY=3D"SANSSERIF" FACE=3D"Arial" LANG=3D"0"= > >

> For a simple spring, the extensio= > n E =3D g x T^2 / (2 x Pi)^2, where T is the period. Thus to get a period of= > say 10 sec, you need an extension of ~25 metres....

>

>: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">Sort of a torsion spring, but o= > ne with many turns and greater length.

> Perhaps my assumption that the main spring arrangement equates to a longerR> > spring is faulty?

>

> No, but this cannot be extended very fa= > r, or you start to see the spring vibration modes.

>

> You can also make a very good horizonta= > l seismometer using a U tube water manometer.

>

> Regards,

>

> Chris Chapman > > --part1_c43.15acd5bc.33ced44a_boundary-- > > .------ ------ ------ ------ ------ ------ ------ ------ ------ ------. > | Message 3 | > '------ ------ ------ ------ ------ ------ ------ ------ ------ ------' > Subject: Re: FFT Code > From: Barry Lotz> Date: Tue, 17 Jul 2007 21:22:37 -0700 (PDT) > > --0-1895494773-1184732557=:22985 > Content-Type: text/plain; charset=iso-8859-1 > Content-Transfer-Encoding: 8bit > > Hi Bob > this thread reminds me - > > I had a Fortran fft program that I picked up years ago. I converted it to Quick Basic with success. I tried to convert it to assembly language to run faster but I had problems with the rounding off of numbers. I wrote a triggering program with the fft routine to do short term /long term averaging with frequency rather than amplitude. You could choose the frequency zones for monitoring (avoiding known noisy frequencies). It also worked well . (written in Quick basic) I wanted the program to be able to learn the difference between a near and teleseismic event but never got there. When the recording of the "fft amplitude/area under the curve" fell below the running long term average the recording of the event stopped. I could look at my computer screen after coming home from work an could instantly see blips on the screen from possible events. I fell in to the easy mode now by recording continuously and then looking on the internet every couple of days for events that I > think may have been recorded by my sensors. I am thinking of "blowing the dust off and starting again with the investigation. > regards > Barry > PS back when computers were slow the was a frequency transform called a Walsh transform which used square waves rather than sine waves. It ran quite fast but I guess became useless when processors stepped up. > > --0-1895494773-1184732557=:22985 > Content-Type: text/html; charset=iso-8859-1 > Content-Transfer-Encoding: 8bit > > Hi Bobthis thread reminds me -I had a Fortran fft program that I picked up years ago. I converted it to Quick Basic with success. I tried to convert it to assembly language to run faster but I had problems with the rounding off of numbers. I wrote a triggering program with the fft routine to do short term /long term averaging with frequency rather than amplitude. You could choose the frequency zones for monitoring (avoiding known noisy frequencies). It also worked well . (written in Quick basic) I wanted the program to be able to learn the difference between a near and teleseismic event but never got there. When the recording of the "fft amplitude/area under the curve" fell below the running long term average the recording of the event stopped. I could look at my computer screen after coming home from work an could instantly see blips on the screen from possible events. I fell in to the easy mode > now by recording continuously and then looking on the internet every couple of days for events that I think may have been recorded by my sensors. I am thinking of "blowing the dust off and starting again with the investigation.regardsBarryPS back when computers were slow the was a frequency transform called a Walsh transform which used square waves rather than sine waves. It ran quite fast but I guess became useless when processors stepped up.> --0-1895494773-1184732557=:22985-- > > __________________________________________________________ > > Public Seismic Network Mailing List (PSN-L) > > To leave this list email PSN-L-DIGEST-REQUEST@.............. with > the body of the message (first line only): unsubscribe > See http://www.seismicnet.com/maillist.html for more information.