Geophysics Department TU Clausthal

deutsch english Applied Geophysics : Seismics

Seismometer Demonstration

Applet ( in separate window )    ca. 650 x 490 Pixel    ca. 800 x 430 Pixel

The applet simulates a seismometer's reaction to an adjustable ground motion w(t). The displacement x(t) of the movable mass relative to the case is calculated recursively from the case (=ground) displacement w(t), based on the second order differential equation :

( See Seismometer Documentation for physical / mathematical background )

The basic parameters, determining the seismometer's behaviour ( transfer function ), i.e. the natural frequency and damping of the mechanical system are selectable from a wide range of values, as well as the type and time scale of the ground motion.

The resulting relative and absulute motion of the mass, and the driving ground motion are dispayed proceeding with time :

-x'(t) = relative mass velocity ( output V )
w(t)+x(t) = total ( = absolute ) mass displacement
-x(t) = relative mass displacement ( output D )
w(t) = ground ( = case ) displacement
w_res(t) = Seidl's Restitution of ground displacement

- Index -

Control Buttons : START/NEW, CONT/HALT and STEP
Ground Motion : FUNC, MODE, AMPL and FREQ
Seismometer : FREQ and DAMP
Amplification : FACT(VEL) and FACT(DISP)
Seidl's Restitution : RESTITUDE W
Response Curves : RESP/HIDE

Related Applets


Screenshot Applet :

The animation is controlled by the buttons START/NEW, CONT/HALT and STEP :

initiates the run mode, based on the GROUND and SEISMOMETER parameters, actually selected, and disables the parameter selection,
stops the actual run, to select new parameters ( restart = START ).
continues / interrupts the actual run,
switches to a single step mode, advancing one time increment per click,

Parameter selection is enabled by activating NEW and
disabled in the run mode ( activating START ).

It allows to specify

the parameters of the ground displacement w(t) :

different functions of time
( including "man made earthquakes" : FUNC MOUSE )
continuous signals or single pulses of selectable polarity
the amplitude of the ground displacement
the "frequency" ( time scale ) of the ground motion

the parameters determinig the seismometer response :

the natural frquency of the seismometer
the dimensionless damping ( 1 = critical )

Amplification ( always enabled ) :
scaling factor, applied to the velocity output V
scaling factor, applied to the displacement output D
Restitution of "true" Ground Displacement :
The signal w_res(t) is calculated recursively from the the output signal x(t) of the displacement transducer D. Based on the calculus of the Z-Transform ( Bilinear-Transform ), a filter is derived, that converts the output signal x(t) to the output w_res(t) of a seismometer of significantly lower natural frequency ( here : 1/100 and damping 0.707 ). Thus w_res(t) represents the ground displacement in the frequency range above this corner frequency ( = 1/100 of the natural frequency of the actual seismometer ).
( Dr. Dieter Seidl, Seismological Central Observatory ( SZGRF ), Erlangen )

All numerical parameters are selectable in 1 - 2 - 5 steps, where frequency values are in a arbitrary scale ( ofcourse identical for ground motion and seismometer ).
The time scale of the animation strongly depends on the power and actual load of the computer running the applet
( FREQ = 1.0 corresponds to about 0.2 [Hz] on a 100 Mhz / 486 cpu, running Netscape under Linux, 1 user ).

( See Seismometer Documentation for physical / mathematical background )

Top of Page    Index

Screenshot Frequency Response :

The button RESP/HIDE shows / hides the the normalized amplitude and phase response of the seismometer, relating the displacement and velocity output ( red / magenta ) to

( selectable in the response display ).
Frequency and amplitude are plotted in a logarithmic scale, the frequency is normalized to the natural frequency F_SEIS of the seismometer.
Green : Actually selected "frequency" of ground motion ( GROUND : FREQ, normalized to F_SEIS )
Cyan : Amplitude, phase and corner frequency of restitution filter.
RESP interrupts, HIDE continues a current animation and
if displayed during the parameter select mode ( = NEW ), the response curves imediatly reflect the actual setting of the seismometer damping.

( See Seismometer Documentation for physical / mathematical background )

Top of Page    Index

- Related Applets -

Frequency Response of a Seismometer

Free Motion of a Seismometer

Calibration of a Short Period Seismometer

- Download -

Class and html files for a local installation of the seismometer applets ( DEMO + CALIB ) are available as a zip file and as a tar.gz file.

More applets at : the author's Homepage

Rev. 06-apr-2007

Comments to Fritz Keller
( ned gschempfd isch globd gnueg )

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