Geophysics Department TU Clausthal

Applied Geophysics : Seismics

Long Period Vertical Seismometer
Applet
( in separate window, ca. 820 x 610 Pixel )
 The applet simulates
 an astatic verticalseismometer / gravitymeter with
Lacoste suspension
 ( zerolength spring on the hypotenuse of a right triangle ).
 Dimensions and technical specifications correspond to
 a Sprengnether S5100V Seismometer.
 ( Sprengnether Instruments Inc., St. Louis, Mo. USA )
 The initial state of the applet represents
 an instrument completely assembled from factoryadjusted parts and
ready for installation and final adjustment.
 Table of Content 
 Seismometer
 Screenshot
 Specifications
 Comments
 Coordinate System
 LaCoste  Geometry
 "ZeroLength" Spring
 Equation of Motion
 Additional Parameters
 Simulation
 HowTo
 Opration
 Mechanical Adjustment
 Electrical Adjustment
 Position Marker
 Period Measurment
 Adjustment Procedures
 Initial Setup
 Period Adjustment
 Period Stability
 Download
 Seismometer 
Screenshot :
The mechanical system of the instrument is displayed in a simplified
vertical section ( scale approx. 1 [Pixel/mm] ).
 A pedulum ( beam + seismic mass, blue )
 is suspended by two hinges ( crossed flexures,
H, red ), forming a horizontal axes of
revolution.
 A spring with negative preload ( magenta ) is fixed
 to the pendulum ( B ) by a suspension wire of fixed length and
 to the frame of the instrument ( A ) by a wire of
adjustable length.
 The postion of the upper suspension point A is
factory adjusted,
 but can be moved along the center line of the spring, if necessary or for
experimantal purposes.
 The tilt of the instrument about the direction of the hinge line
is
 adjusted by a levelling screw ( orange,
lower right ) and observed at a bubble level
( orange ).
 The excursion of the pendulum, limited to ±11 [mm] by
two stops,
 can be observed as a moving blue mark at an enlarged scale,
and
 its value is displayed at the upper edge of the
graphic area.
 Electromechanical components are displayed as simplified
electric cicuits :
 the damping coil with adjustable external damping resistance
( orange ) and
 the calibration coil with adjustable DCcurrent
( green ).
 The output signals for
 displacement ( DSP OUT, blue ) and
 velocity ( VEL OUT, magenta )
 can be displayed on a "strip chart recorder" with
selectable amplitude and time scale.
 Program and recoder are contolled in a menue field
above the graphic area of the applet.
Specifications
( from ASSEMBLY AND OPERATING INSTRUCTIONS, Sprengnether Instruments, Inc. )
Moving Mass

10.92

[Kg]

Spring Constant

1030

[N/m]


Distance from Hinge line to :


Center of Oscillation

35.8

[cm]

Center of Mass

32.2

[cm]

Center line of Signal Coils

35.7

[cm]

Center line of Calibration Coil

24.2

[cm]

Point of Suspension

18.7

[cm]

Scale

43.2

[cm]


2 Signal / Damping Coils :


Coil Constant

89.0

[Vs/m]

Coil Resistance

500

[ohms]


Calibration Coil :


Coil Constant

5.0

[N/A]

Coil Resistance

68

[ohms]

Screenshot
Table of Content
Top of Page
 Comments 
Coordinate System
 X = direction of axes of revolution
( hingei line ), "horizontal
 Y = coordinate "along beam",
"horizontal", from hinge line to zero of scale
( in applet pos. to left )
 Z = "vertical", pos. upward
 "vertical" = Zaxes, evtl. tilted against
the local direction of gravity
 "horizontal" = XYplane
 mechanical system symmetrical to YZplane
LaCoste  Geometry
 Using

 leads to

 for the magnitude and the vector of the force
acting on suspension point B
 with an "effective spring constant"
κ_{eff}, in general a function of the actual
length L of the spring.
"ZeroLength" spring
 This results in a momentum of the spring acting on the beam

 "ZeroLength" Spring
LaCoste  Geometry
Coordinate System
 Screenshot
Table of Content
Top of Page
Equation of Motion
 The equilibrum of all internal and external forces acting
on the pendulum leads to a differential equation of
2nd order

 for the varaiables ( time functions )

 and with constant parameters of the instrument

 adjustable quantities

 and the external disturbance

 contributing to the momentum of gravitational acceleration and
 neglected in the adjustment procedures performed in
a very quiet environment.
 Using the approximations for small angular excursions of the
contributions of the forces
 acting on the suspension point B of the spring

 and
 acting on the effective center of gravity

 and deviding the resulting differential equation by the moment
of inertia leads to
 the normalized equation of motion

 with commonly used abbreviations


Additional Parameters
 Some of the parameters used in the calculations,
 the additional mass m_{W} and its
distance s_{W} from the hinge line,
 the torsion constant τ and the angular
offset ϕ_{0} of the axes of revolution and
 the mechanical damping δ_{0} of the
instrument
 are not listed with the manufactorer's specifications.
 Their values have to be estimated / set arbitrary :
 In the applet the values
 for the additional mass m_{W} = 300 [g]
and for its distance reange s_{W} =
95 ± 80 [mm]
 are assumed to be somewhat greater than in the original instrument.
 The remaining parameters are derived from the static equilibrum

 with an adjustment

 leading to a natural frequency and a static
angular excursion of the beam

 For the calculation of the simulation
 the corresponding natural preriod is set to T_{0} =
100 [s], the angular offset to
ϕ_{0} ca. 0.2 [deg],
 and
 the dimensionless mechanical damping
α_{0}( T_{0} ) = 0.05
 is set to an extremely small value, to allow the observation of several
free oscilations at periods above 100 [s].
 ( realistic : max. 2 to 3 oscilations above 100 [s] )
 The assumption T_{0} = 100 [s]
leads to

Simulation
 The angular excursion ϕ(n∗δt) of
the pendulum is calculated recursively in constant time steps of
δt = 80 [ms],
 evaluating a difference equation derived from the equation of
motion
 with
 coefficients, derived from the values of the mechanical and
electrical specifications, the additional parameters and
the adjustable quantities.
 ! For L_{0} ≠ 0 the
"effective spring constant κ_{eff}
is a funktion of the actual beam position ϕ,
and therefore, the coefficients depending on
κ_{eff} are recalculated for every time
step !
 The output signals
 for displacement ( DSP OUT ) and velocity
( VEL OUT )
 are scaled to correspond
 to the motion observed at the scale
( distance to hinge line approx. 400 [mm] ).
 In order to simplify the parameter adjustment,
 presumably resulting approximate values of the natural
period T_PER, the damping
α (T_PER) and
the static beam excursion S_SCL (T_PER)
 can be estimated from the coefficients of the equation of
motion and listed to the display / JAVAconsole.
 Screenshot :
 ( adjustment s. screenshot applet )

 Additional Parameters
Equation of Motion
Coordinate System
 Screenshot
Table of Content
Top of Page
 HowTo 
Operation
Dialogue area :
( Screenshot )
 HALT / RUN / RES
 Stops and starts continuous calculations and graphic display
 and
 resets mechanical adjustments to initial values
( after assembly of the instrument ).
 STEP
 Initiates calculation and graphic display for one time
step ( 80 [ms] ).
 POS / NEG
 Selects the polarity of the calibration dccurrent,
raising / lowering the pedulum from its actual zero position.
 ON / OFF
 Swiches the calibration current on / off.
 T_REAL = ... Allows to adjust the real time behavior :
 T_CAL displays the result of calculation of one time step
( 80 [ms] ) in real time,
 T x 2, T x 4 reduces,
 T / 2, T / 4, T / 10 increases the apparent speed by factors
of 2, 4, 10,
 and
 AUTO selects the highest speed, compatible with given computing
power.
 DISPLAY / RECORDER Selects the the display mode of the
output signals :
 DISPLAY simulates an analog voltage meter,
 RECORDER simulates a strip chart recorder,
 both calibrated in [mm] and [mm/s] referred to scale, according to the
selected respective full scale value F.S. for DISPLACEMENT and
VELOCITY.
 40 [sec] ... 800 [sec]
 is enabled in RECORDER mode only and selects the display length
( => resolution ) in time.
 HELP displays
 hints to possible mouse button actions,
 INFO
 some internal parameter values, not visible to the operator of
a real instrument, and greatly simplifies the adjustment procedures.
 Parameter values displayed :
 Effective spring length,
 "horizontal" component of gravity and
 "horizontal" distance of upper suspension point from hinge line.
 ( "horizontal" = hinge line > scale zero,
here = parallel to base plate )
 HELP + INFO lists
 the actual "counters" of the boxes
+++ ... and
 the resulting estimated values for the zero position
S_SCL, the natural period T_PER and the damping
α
 at the screen / the JAVAconsole.
Mechanical Adjustments
Boxes  + + +  + + +           :
 Left mouse button increments / decrements
 by 1 (  +    ),
 by 100 (  + +     ),
 by 10000 (  + + +  =    )
 and middle or right mouse button
 by 10 (  +    ),
 by 1000 (  + +     ),
 by 100000 (  + + +  =    )
 The value 1000 corresponds
 to approx. 0.1 [mm] for the displacement of the additional
mass,
 to approx. 1.0 [mm] for the leveling screw,
 to approx. 1.4 [mm] for the displacement of the
upper suspension point A and

for the
adjusment of the spring length L_{0}.
 The levelling screw ( bottom right, orange )
 tilts the whole instrument about an axes parallel to the hinge
line, thus varying the "horizontal" component of gravity.
 ( Tilt is not reflected by the graphics display, but may be observed
at the bubble level. )
 The upper spring suspension point ( upper right, red and
orange )
 is "factory preadjusted", and should remain
unchanged during initial setup and adjustment procedures.
 ( Evtl. adjustments necessary for extreme long natural periods should
be performed very carefully because of possible instability of the
instrument. )
 The spring length adjustment ( upper right, magenta )
shortens / lengthens the upper suspension wire :
 During initial setup
 the pendulum is raised / lowered util it oscilates between
its limit stops ( ±11 [mm] at Scale ),
 during period stability adjustments
 postion changes are compesated by by moving the additional mass ( see
below ) and the the spring assembly is adjusted to react as a so
called zero length spring.
 Zero length spring :
 Force F prop. total length L of spring assembly, i.e.
F = 0 for L = 0.
 Technical realization :
 Fixedlength lower suspension wire + negative preloaded
spring ( = negative length ) + adjustablelength
upper suspension wire => effective spring
length = 0.
 The additional Mass ( movable along the
beam, orange )
 allows to adjust the zero postion of the pedulum by
shifting the effective center of gravity to and from the hinge line.
Electrical Adjustments
 R_EXT ( external damping resistance, orange ) and
 I_CAL ( calibration current, green ) :
 Left mouse button increments ( + ) and
decrements (  ) the respective column,
 middle or right mouse button sets the respective
parameter value to max / min
 ( R_EXT > 9999.999 / 0000.000 [kOhm], I_CAL > 9.9999 /
0.0000 [mA] ).
Postion Marker
 The actual position of the beam can be observed as a
blue marker
 moving between the limit stops ±11 [mm] of an enlarged
scale left of the instrument.
 Its value is displayed above the instrument ( S_SCL [mm],
blue ).
 Whenever the pedulum has come to rest
 ( observable at VELOCITY OUTPUT in DISPLAY / RECORDER mode at high
resulution, i.e. F.S. < 100 [µm/s] ),
 this postion can be marked as actual zero position
( red marker ) with the left mouse button
 ( middle or right mouse button removes the red
marker ).
 Its value is displayed above the instrument ( S_REF [mm],
red ).
 Pendulum excursions from the actual zero postion,
normally caused by switching on a calibration current,
 are displayed above the instrument ( S_AMP [mm],
green ).
Period Measurement
 Setting the zero position marker starts the period measurement :
 Postion adjustment and raising / lowering the
pendulum by a calibration current
 should be performed at relatively high damping values
 ( R_EXT = 0.5 ... 10 [kOhm], depending on the actual
free period ).
 Switching off the calibration current with R_EXT
≥ 1 [MOhm]
 should cause very weakly damped oscillations about the actual zero
postion.
 The time difference between two adjacent zero crossings in
the same direction ( passings of the red marker )
 is displayed above the intrument ( T_PER [sec],
red ).
 This value represents the period of the weakly damped
pendulum.
 To facilitate the calculation of the actual damping value and the natural
period of undamped system, the period values and the pendulum
velocities at zero crossings ( => extrema of velocity ) are
printed to the screen / Java Console.
 Position Marker
Electrical Adjustments
Mechanical Adjustments
Operation
 Comments
Screenshot
Table of Content
Top of Page
Adjustment Procedures
( taken from ASSEMBLY AND OPERATING INSTRUCTIONS, Sprengnether
Instruments, Inc. )
 The final result of the adjustment should be a seismometer with
 a stable natural period ≥ 20 [sec],
 uniform ( ±3 % ) over the whole range
between the limit stops.
Initial Setup
 1. Adjust the spring length
 ( upper suspension wire,
 + +  +      ,
magenta, ! not upper suspension point ! )
 until the pedulum will oscillate in the range of its limit stops.
 2. Move the small additional mass
 for fine adjustments of the pendulum position.
 If the pendulum is unstable, that is, it tends to move to one of the
stops,
 tilt the insrument by raising its hinge
end with the leveleling screw and
 Repeat steps 1 and 2.
Period Adjustment
 The natural period is adjusted by tilting the intrument :
 Raising the hinge end
 increases the "horizontal"
component of gravity ( pointing from hinge to scale ) and thus
decreases the natural period,
 lowering the hinge end
 decreases the "horizontal" component of gravity and thus
increases the period.
Period Stability
 1. Move the additional mass away from the hinge until
 the pedulum oscillates about a point near the lower limit
stop ( see above, S_REF [mm] approx. 6 ... 8 )
and measure the period.
 2. Move the additional mass toward the hinge until
 the pedulum oscillates about a point near the center point
( see above, S_REF [mm] approx. 1 ... +1 ) and
measure the period.
 3. Move the additional mass toward the hinge until
 the pedulum oscillates about a point near the upper limit
stop ( see above, S_REF [mm] approx. +6 ... +9 )
and measure the period.
 If the period is not uniform within ±3 %, especially
if the periods measured near the limit stops are not shorter than measured
near the center by approx. the same amount,
 the spring assemly is not "zero length"
( see above )
 and
 the spring length needs adjustment.
 Period longer at the upper position ( = spring assembly
is "negative length" ) :
 Increase spring length
(  + +  + , magenta )
 and
 compensate by moving the additional mass towards hinge
until the pedulum again oscillates in the range of its limit stops.
 Period shorter at the Upper Position ( = spring assembly is
"positive length" ) :
 Decrease spring length
(       magenta )
 and
 compensate by moving the additional mass away from hinge
until the pedulum again oscillates in the range of its limit stops.
 Repeat steps 1. to 3.
 Period Adjustment
Initial Setup
 HowTo
Comments
Screenshot
Table of Content
Top of Page
Note
This is a simulation ( fairly realistic, as I hope ),
but there is no ground noise and for instance the period stability
adjustment loop in reality implies some steps not implemented
here :
 Remove the instrument cover.
 Lock the pendulum, to avoid excessive bumps to the limit stops.
 Unclamp the upper suspension wire.
 Adjust the spring length.
 Retighten carefully the upper suspension wire clamp, to avoid
variations of the effective spring length if bending the wire upward /
downward during oscillations of the pendulum.
 Unlock the pedulum and gently guide it to the limit stop, it tends to
travel to.
 Reinstall the istrument cover ( if possible, without exciting weakly
damped fre oscilations of the spring ).
( The leveling screw is mounted on the base plate outside the
instrument cover and the additional mass on the beam is motor driven.
Electrical adjustments and observing / recording of output signals are
of course performed outside the cover and at some distance from the
instrument to avoid ground noise caused by the operator. )
 Download 
Class and html files for a local installation of the applets Long Period
Vertical and Horizontal Seismometer are available as
a
zip file and as
a
tar.gz file.
More applets at :
the author's
Homepage
Rev. 07nov2007
Comments to
Fritz Keller
( ned gschempfd isch globd gnueg )
Adjustment Procedures
HowTo
Comments
Screenshot
Table of Content
Top of Page
Back to the
Applet Index ( Geophysics Dept.,
TU Clausthal )