Applied Geophysics : Seismics |
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
Screenshot Applet :
The animation is controlled by the buttons START/NEW, CONT/HALT and STEP :
- START
- initiates the run mode, based on the GROUND and SEISMOMETER parameters, actually selected, and disables the parameter selection,
- NEW
- stops the actual run, to select new parameters ( restart = START ).
- CONT/HALT
- continues / interrupts the actual run,
- STEP
- 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
Amplification ( always enabled ) :
- GROUND
- the parameters of the ground displacement w(t) :
- FUNC
- different functions of time
( including "man made earthquakes" : FUNC MOUSE )- MODE
- continuous signals or single pulses of selectable polarity
- AMPL
- the amplitude of the ground displacement
- FREQ
- the "frequency" ( time scale ) of the ground motion
- SEISMOMETER
- the parameters determinig the seismometer response :
- FREQ
- the natural frquency of the seismometer
- DAMP
- the dimensionless damping ( 1 = critical )
Restitution of "true" Ground Displacement :
- VELOCITY
- scaling factor, applied to the velocity output V
- DISPLACEMENT
- scaling factor, applied to the displacement output D
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 )
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
Frequency and amplitude are plotted in a logarithmic scale, the frequency is normalized to the natural frequency F_SEIS of the seismometer.
- the GROUND_DISPLACEMENT w(t),
- the GROUND_VELOCITY w'(t),
- the GROUND_ACCELERATION w"(t)
- ( selectable in the response display ).
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 )
Frequency Response of a Seismometer
Free Motion of a Seismometer
Calibration of a Short Period Seismometer
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 : Geophysics Department TU Clausthal
Rev. 06-apr-2007
Comments to
Fritz Keller
( ned gschempfd isch globd gnueg )