  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

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

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 )

Amplification ( always enabled ) :
VELOCITY
scaling factor, applied to the velocity output V
DISPLACEMENT
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 )

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

the GROUND_DISPLACEMENT w(t),
the GROUND_VELOCITY w'(t),
the GROUND_ACCELERATION w"(t)
( 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 )

- Related Applets -

Frequency Response of a Seismometer

Free Motion of a Seismometer

Calibration of a Short Period Seismometer