Applied Geophysics : Seismics
Response Functions of Seismographs
Applet
( in separate window, ca. 480 x 530 Pixel )
- The applet shows
- amplitude and phase of the transferfunction with
respect to ground displacement, velocity and acceleraton,
- and
- the response in the time domain to some impulsive ground motions
and to a sweep signal
- for some historical instruments and actually used
seismograph systems.
( Background : see
Seismometer Documentaion,
Seismometer-Galvanometer Dokumentation and
Manual of Seismological Observatory Practice,
in separate window )
- NEW : Determination of Systemparameters
- for an evtl. simplified transferfunction, applying the
calculus of the program CALEX to the simulated recording of a
broadband acceleration signal ( sweep ).
- see :
Seismic Sensors and their Calibration
by E. Wielandt
und
free software by E. Wielandt,
( description of program and FORTRAN Source calex.f )
- Table of Content -
- HowTo
- Program Control
- Graphics Control
- Screenshots
- Frequency Domain
- Time Domain
- CALEX-Calibration
- Comments
- Program Control
- Results
- Download
- HowTo -
Dialogue Window :
( Screenshot )
SEISMOGRAPH SYSTEM : WIECHERT_Z...
alows to select one of the seismograph systems implemented :
- WIECHERT_Z / H and WOOD-ANDERSON
- are historical seismometers with "direct" recording,
- characterized by natural period, damping and a
static amplification
( = recorded amplitude / mass excursion ),
- where the feedback force of the mechanical recording system
( WIECHERT ) is neglected.
- ( Parameter values from : Elemente der Seismologie
und Seismometrie (1960), E.F.Sawarenski and D.P.Kirnos. )
- WWSSN_SP / LP, BENIOFF_LP, GALITZIN and
KIRNOS
- are seismometer - galvanometer systems, where
- a velocity transducer ( coil-magnet-assemly ) is connected
to a galvanometer coil via a resistive T element,
- i.e. two resistances in series with seismometer / galvanometer coil
and one shunt resistance.
- The response of the system is charakterized by the natural period
and the damping of both seismometer and galvanometer and
- a dimensionless "coupling coefficient" σ^2
( denoted α^2 in some publications, range 0...+1 ),
describing the reciprocal influence of the two electro-mechanical
devices.
- ( see
Seismometer-Galvanometer Documentation
and applet
Seismometer-Galvanometer Coupling )
- The frequency response corresponds to the product of a
2-pole high pass ( seismometer ) and a
2-pole low pass ( galvanometer )
- with an adittional quadratic term proportional to
σ^2 in the resulting denominator polynomial of
4th degree and a factor proportional to σ
( = sqrt(σ^2) ), determining the amplification
of the system.
- The parameter values for the systems implemented are based on
tables in
Manual of Seismological Observatory Practice
( 1979 Edition, Chap. Instruments, 1 Type of
Instrument ).
- These tables provide numerical values for natural period and
damping of seismometers and galvanometers and for the
"coupling coefficient" for various types of
seismograph systems.
- ( without details of the the instruments used and the coupling
network )
- For the systems simulated in the applet an amplification factor
of the frequency response is chosen to meat the
amplification curves shown in fig. 1.1 of the manual.
- For the seismometer S-13_1Hz ( Geotech )
- the output voltage of the moving coil transducer is
is observed on a recorder with unity gain in the relevant
frequency range of 0 to 1000 [Hz].
- The geophones SM4_10Hz and L4_2Hz
- are moving coil instruments connected to a digital
recording system StrataView, and
- the parameters used are taken from the data sheets of the manufacturers,
- i.e. I/O Sensor Nederland bv ( SM4 ), Mark Products
( L4 ) and Geometrics ( StrataView ).
- The seismometer STS_2
( Wielandt - Streckeisen )
- is a force-balance broadband seismometer, and
- its parameters are taken from the manual of the instrument and from
Seismic Sensors and their Calibration,
E. Wieland,
- in New Manual of Observatory Practice.
- RESP TO ...
- selects the type of ground motion, i.e.
- displacement,
- velocity
- or
- acceleration
- for the calculation
of the transfer function ( frequency domain ) and the response
in the time domain.
- SIG^2 = 0.980 ... 1.E-8
- refers to seismometer - galvanometer systems only, and
- allows to vary the value of the coefficient σ^2,
preserving the other parameters of the system, to demonstate the
influence of the coupling coefficient on the response curve.
- The default value of σ^2 ( from definition table )
is displayed on white background, user selected values on yellow
background.
- ( Details of seismometer-galvanometer coupling see :
Seismometer-Galvanometer Documentation )
- CLEAR TEXT ...
- clears the text area of the applet
- and lists
- the parameters of the actually selected system
( LIST SEIS ),
- the coeficients of the frequency response and / or
of the corresponding Z-transform
( LIST COEFF ),
- or
- the frequency / time response
( FREQ / TIME RESP ).
- ( TIME RESP lists max. 500 samples starting from t = 0 [s],
CONT TIME lists subsequent blocks of 500 SMP each. )
The graphic display is controlled by the display dialogue
( background light blue ) :
- XFR (F) / XFR (Z) /
XF(BIL) / F + Z
- shows the frequency response, the corresponding Z-transform
or both
- ( AMPL = ampltude, PHAS = phase in separate windows )
- for
- SYS_OUT = system output,
- SEIS = seismometer output and
- GALV = transfer function of the galvanometer
- ( HP_1 = 1-pole high pass for StrataView with SM4_10Hz and
L4_2Hz ).
- HIDE RESP WIN ...
- hides / shows the above output signals in the
time domain for different ground motions :
- DELTA IMP ( = Dirac impulse ),
- UNIT STEP,
- KUEPPERS_2 ( = Kueppers signal, order 2 ),
- K_2 x HANNING ( = as above,
with Hanning taper ),
- or a sweep signal ( DOWN / UP SWEEP )
covering the the range of characteristc frequencies a system.
- ( 200 SMP... refers to Kueppers signal only and allows to select
the signal length and, together with F-SAMP, the predominant frequency of
the signal. )
- F-SAMP : 1 ... 800 [Hz] ( = sampling
frequency )
- refers to the Z-transform XFR ( Z ), used as a
recursive filter to calculate the response in the
time domain,
- and
- can be selected in a wide range of reasonable values, limited by
the charakteristic frequencies of the seismograph system.
- + LOWPASS
- includes a 4-pole Butterworth low pass
( corner freq. = F-SAMP / 8 ) in the
recursive filtering to reduce aliasing errors.
- INF and HLP refer to the graphic display windows, where
- informations to the actual cursor position ( INF )
- and / or
- hints to actually possible mouse actions ( HLP )
- are displayed.
HowTo
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- Screenshots -
SYSTEM : KIRNOS, RESP TO GROUND DISPLACEMENT
( param. see below : screenshot Text Area )
Colors : magenta = SYS_OUT, cyan = SEIS,
blue = GALV.
- Frequency Domain -
XFR ( F ) :
Amplitudes ( AMPL ) and Phases ( PHAS )
of the frequency responses
CENTER>
The amplitude response to ground displacement ( SYS_OUT,
magenta ) is "flat" for periods from approx.
20 to 0.08 [sec] as a result of the relatively
high galvanometer damping
( α = 8.0, see screenshot
Text Area ).
- Positioning the mouse cursor on the label FCT
( blue, upper left corner )
- shows informations to the curves displayed
( type, scaling and color code, etc. ).
XFR ( Z ) :
Amplitudes ( AMPL ) of the Z-transforms
(F-SAMP 80 [Hz], +LOWPASS )
- Time Domain -
Response to UNIT STEP :
( XFR ( Z ) as above,
red = input = ground
displacement [ m, mm, µm ]
SEIS and GALV : normalized, max = 1 )
Response to KUEPPERS_2 :
( param. as XFR ( Z ) above,
red = input signal,
100 [Smp] = 1.25 [sec] )
- For the input signals KUEPPERS_2 and SWEEP
- the corresponding frequency transform ( red,
normalized, max = 100 )
- can be included in the display of the frequency response AMPL :
- Text Area -
LIST SEIS :
( KIRNOS, RESP TO VEL, σ^2 = DEF = 0.05 )
The value of Afac(VEL) [s] corresponds to the
amplification factor A [s] in
Seismometer-Galvanometer Documentation.
Screenshots
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- CALEX-Calibration -
- Comments -
- The transfer function of the system to be examined ( filter,
seismometer and/or galvanometer )
is represented / approximated in the frequency domaine by a product
of 1-pol and 2-pol filters.
- Characteristic parameters of the product ( amplitude, corner
frequencies, damping constants ) are determined in an iteration :
- The response in the time domain of the model filter to an
arbitrary input signal is fitted to the response of the
system to the same input signal.
- ( topics : least sqare fit,
method of conjugate gradients )
- The frequency band of the input signal ( here : sweep )
should cover the the range of characteristic frequency constants of
the system / model filter, and
- the input signal and the sytem response should be recorded by the same
digital recorder to eliminate its influence.
- Here :
- The applet calculates both time series and feeds them as floating point
numbers to a slightly modified JAVA version of the CALEX program
( originally FORTRAN code ), thus avoiding distortions and
scaling problems of a recording device.
- Exceptions :
- The geophone parameters of SM4_10Hz and L4_2Hz are determined from
highpass filtered input and output signals, to simulate a StrataView
recording.
- Corresponding to the original program, input and output are lowpass
filtered, to reduce aliasing errors.
- The control parameters of the CALEX program, i.e.
- corner frequency and slope of the antialiasing lowpass,
- number, type and order of the partial filters,
- initial values for the parameter iteration ( amplitude, corner
frequencies and damping constants )
- are set automatically by the applet, depending on the
seismograph system selelected, and
- are described in detail in the
documentation
of the FORTRAN prorgram calex.f of E. Wielandt.
- The applet lists in its textfield
- the control parameters and initial values of the iteration,
- the iterative modification of the parameter values and
- the final result of the parameter fit
- in a format comparable to the original program.
- The time series
- input signal "stimulus"
( STIM ORG / +LP ),
- system response ( SYST ORG&nbs;/ +LP ),
- model response ( SYNTH ) and
- difference ( ERROR = SYST+LP - SYNTH )
- are displayed in a separate graphic window,
updated for every iteration step.
Comments
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- Program Control -
The CALEX program is controlled by the menue items on yellow
background&nb :
- The button CALEX ( SWEEP ) activates the CALEX mode
of the applet :
- The selection of a seismograph system is disabled ( here
previously selected : BENIOFF_LP ),
- the system response is swiched to
RESP TO GROUND ACCELERATION and the input function
to SWEEP ( def. = DOWN SWEEP, UP SWEEP
selectable ).
- The frequency range of the sweep signal
- depends on the parameters of the system selected and
- determines the lower limit for the selection of the
sampling rate ( F-SAMP ).
Screenshot sweep signal and system response :
( Syst. = BENIOFF_LP, RESP. TO ACC.,
F-SAMP = 20 [Hz] )
- By activating the INIT button
- the options and parameters, and
- resulting control parameters and initial values
- are transferred to the CALEX program, listed in text area of the applet,
and
- their modification is disabled :
Screenshot text area parameters ( after INIT ) :
- TRACE PLOT
- displays the actual state of the iteration in a separate graphic window
- ( see below : screenshot graphic protocol )
- RUN / HALT
- starts / stops the iteration,
- STEP
- initiates a sigle iteration step.
- ( After HALT or STEP : RUN => continue )
- RESET
- quits the CALEX mode and restores the previous state of the applet.
Screenshot text area iteration protocol :
- The lines below CALEX INIT
- list the initial values and ( preceded +- )
the "radii of variation" of the iteration and
- the corresponding amplifications ( GAIN ).
- Below CALEX START
- the actual state of the iteration process is displayed, i.e.
- the values of factors applied to the "radii" are listed.
- RMS_nrm is the RMS value of the error signal
- ERROR = SYST +LP - SYNTH,
- normalized to the RMS value of the system response
SYST +LP.
Screenshot graphic protocol :
Program Control
Comments
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- Results -
- If the approximation converges or after max. 100
iterations
- the program stops,
- lists the actual results ( true parameter values and
dimensions ), and
- displays amplitude and phase of the resulting frequency respons in the
corresponding graphic displays of the seismograph system
( see screenshot AMP / PHS ).
- ( RUN continues the iteration for up to 100 steps )
Screenshot text area results :
- The warning between lines 78 and 79 ( UPD SYSTEM ... )
refers to the fact that in step 79 of the iteraton at least once the value 1
for the damping of the galvanometer ( lp2 ) occurred
( not implemented in the the iteration calculus an replaced by
1.0002 ).
- In the applet the amplitude ( [m/s^2] ) of the
input signal is known, and
- the amplification of the system for
- acceleration ( ACC GAIN ),
- velocity ( VEL GAIN ), and
- displacement ( DSP GAIN )
- can be calculated from the factor amp.
Screenshots AMPL / PHAS :
( red : normalised spectral amplitude of sweep signal,
green : amplitude / phase of frequency response of the
system, calculated from the results of CALEX-program,
and hiding the frequency response from original parameter values )
Results
Program Control
Comments
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- Download -
Class and html files for a local installation of the applet are available as
a
zip file and as
a
tar.gz file.
More applets at :
Geophysics Department TU Clausthal
Rev. 12-nov-2012
Comments to
Fritz Keller
( ned gschempfd isch globd gnueg )
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CALEX Calibration