Applied Geophysics : Seismics

Applet    ( in separate window, ca. 470 x 410 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

for some historical instruments and actually used seismograph systems.

( Background : see Seismometer Documentaion
  und Seismometer-Galvanometer Dokumentation, in separate window )

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Dialogue Window :
( Screenshot )

SEISMOGRAPH SYSTEM : WIECHERT_Z...
alows to select one of the seismograph systems implemented :

WIECHERT_Z, WIECHERT_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, KIRNOS and DEMO_SP / LP

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 ),

the sensitivity values of seismometer and galvanometer are selected to meet the ampification maxima of the curves in fig. 1.1 of the manual.

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 von E. Wieland,

in New Manual of Observatory Practice.

RESP TO ...

selects the type of ground motion,

i.e. ground displacement,velocity or acceleration,

for the calculation of the transfer function ( frequency domain ) and the response in the time domain.

SIG^2 x 1.000 ... 0.001

refers to demo systems DEMO_SP / LP only, and

allows to reduce the value of the coefficient σ^2, here max = 1, preserving the other parameters of the system.

As in general σ^2 < 0.5, the arbitrary dimensioned demo system with σ_max = 1, are implemented to demonstrate the influence of the coefficient to the response curve.

( Details see : Seismometer-Galvanometer Documentation )

CLEAR TEXT ...

clears the text area of the applet

and lists i

the parameters of the actually selected system ( LIST SEIS ),

the coeficients of the frequency response and / or of the corresponding Z-transform ( LIST COEFF ),

ior

the frequency / time response ( FREQ / TIME RESP ).

The graphic display is controlled by the display dialogue ( background light blue ) :

XFR ( F ) / XFR ( Z ) / F  +  Z

shows the frequency response, the corresponding Z-transform or both

( AMPL = ampltude, PHAS = phase in separate windows )

for

OUTPUT = 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 ),

and

K_2 x HANNING ( = as above, with Hanning taper ).

( 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 ...

( = 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 2-pole Bessel low pass ( corner freq. = 0.25 × F-SAMP ) 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.

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Colors : magenta = OUTPUT, cyan = SEIS, orange = GALV.

XFR ( F ) :
Amplitude ( AMPL ) and Phase ( PHAS ) of the frequency responses

The amplitude response to ground displacement ( OUTPUT, 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 ).

XFR ( Z ) :
Amplitude ( AMPL ) of the Z-transforms
(F-SAMP 80 [Hz], +LOWPASS )

Response to UNIT STEP :
( XFR ( Z ) as above, red = input = ground displacement / input current to galvanometer )

Positioning the mouse cursor on the label FCT ( blue, upper left corner ) shows informations to the curves displayed ( type, scaling and color code, etc. ).

LIST SEIS :

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Class and html files for a local installation of the applet are available as a zip file and as a tar.gz file.

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