Transcript Seismology

Seismology
Part IX:
Seismometery
Examples of early attempts to record
ground motion.
Definitions:
Seismometer: Transducer from
ground motion to something else
(usually voltage). Also called
geophone.
Seismograph: The recording
device. Also called Data Logger.
Seismogram: The record of
ground motion.
Seismoscope: (obsolete) Record
of ground motion with no time
signal (e.g., pendulum in sand)
"Classic" devices date back to the
late 1800's. Modern (digital)
devices have been evolving for the
past several decades. A currently
used seismometer (CMG-3T) is
shown to the right.
The goal of any device is to
provide a high fidelity record of
ground motion, to the extent that
an investigator and recreate the
actual motion from the record.
The Mass on a Spring (Inertial Pendulum)
The simplest kind of transducer is a mass suspended from a casing by
a spring. The casing will move with the ground, and the spring
provides some kind of decoupling. To understand what happens, we
consider Hooke's law:
F = -ky(t)
where y(t) is the displacement of the mass from its equilibrium
position. Thus
my  ky
describes the unforced (homogeneous) and undamped oscillations of
the mass. We recognize this immediately as a simple wave equation
with the solution:
y  e i o t
where
o  k / m
Generally, we will concern ourselves with an oscillator driven by a
ground motion U(t), and with a damping force proportional to the
 and modify the above to be:
velocity of the mass,
my  U   ky  Dy
or
D
y   y  y  y  2y  o2 y  U
m
2
o
where
D

2m
If we amplify the ground motion by a factor G, then
x  2x  o2 x  GU
We consider, without loss of generality, the response to a sinusoidal
input:
U  eit
and consider a solution of the form X()e-it to get


2
2
2
 X()   i2  o  G
X( ) 

G 2
 2   o2  i2
  tan1


G 2

2
2
 2   o2

2
o
  4 
2
2
e i
2
Note that the response is a maximum
when  = o (it blows up with no
damping). This is called the resonance
or characteristic frequency of the
system.
If  << 1, the seismometer will "ring"
about o. If  > 1, the response x(t) will
not oscillate at all but gradually return to
zero. If  = 1, the oscillations are
critically damped.
Note that if  << o, then
X( ) 

G 2
 
2 2
o
2
 2
o
2 
  tan  2  tan10  0
 0 
1
which means that acceleration is transduced with no phase shift.
Thus, accelerometers
are designed with very high resonant

frequencies.
If  >> o, then
X( ) 
G 2
 
2
2
 const.
2 
  tan   
 
1

and so the sensor is directly proportional to ground displacement
(the  phase shift means that the mass motion is in the opposite
direction of U).

The instrument thus responds best to motion with periods near the
natural period, and the width of the response will depend on the
damping.
Electromagnetic Instruments
Electromagnetic transducers operate by
the relative motion of a magnet and a coil,
which produces a current in the coil.
The effect is generally to modify the
above equations with an additional 
term, because the signal generated will be
proportional to the velocity of the mass.
Examples:
WWSSN: Sensor, galvanometer, photo
paper
Geoscope/GSN: Force feedback sensors;
digital
IDA:Force feedback gravity meter; digital
NORSAR
US National Seismic Network
USArray
..\Pix\USArray6.mov