Seismic Instruments

Seismic instruments 

Seismic Instruments 

The seismometer as a forced oscillator 

The seismometer equation 

Transfer function, resonance 

Broadband sensors, accelerometers 

Dynamic range and generator constant 

Rotation sensors 

Strainmeters 

Tiltmeters 

Global Positioning System (GPS) 

Ocean Bottom Seismometers (OBS) 

Data examples, measurement principles, interconnections, accuracy, 

domains of application


Spring-mass seismometer 

vertical motion 

Before Before we we look look more more carefully at at 

seismic instruments we we ask ask 

ourselves what what to to expect for for a 

typical typical spring spring based based seismic 

inertial sensor. This This will will highlight 

several fundamental issues issues we we 

have have to to deal deal with with concerning 

seismic data data analysis.


Seismometer – The basic principles 

x 0 

x r 

x 

x 

x m 

u 

x 0 

u g 

u m 

u 

x r 

mass 

x 0 

ground displacement 

displacement of seismometer 

mass equilibrium position



The motion of the seismometer mass as a 

function of the ground displacement is 

given through a differential equation 

resulting from the equilibrium of forces (in 

rest): 

x 0 

x r 

F spring 

+ F friction 

+ F gravity 

= 0 

x 

for example 

. 

F sprin 

=-k x, k spring constant 

.. 

F friction 

=-D x, D friction coefficient 

u g 

F gravity 

=-mu, m seismometer mass



using the notation introduced above the 

equation of motion for the mass is 

ẍ r 

t 2ε ẋ r 

t 

¿+ϖ 0 2 x r t =−ü g t 

x 0 

x 

x r 

From this we learn that: 

- for slow movements the acceleration 

and 

velocity becomes negligible, the 

seismometer records ground 

acceleration 

u g 

- for fast movements the acceleration of 

the 

mass dominates and the seismometer 

records ground displacement

A simple finite-difference solution of the seismometer equation 

Seismic instruments


Seismometer – examples 

x 0 

x 

x 

r 

u 

g


Varying damping constant 

x 0 

x 

x 

r 

u 

g


Seismometer – Calibration 

1. How can we determine the damping 

properties from the observed behaviour of 

the seismometer? 

x 0 

x 

x 

r 

2. How does the seismometer amplify the 

ground motion? Is this amplification 

frequency dependent? 

u 

g 

We need to answer these question in 

order to determine what we really want to 

know: 

The ground motion.

Seismometer – Release Test 

1. How can we determine the damping 

properties from the observed 

behaviour of the seismometer? 

x 0 

u 

x 

x 

r 

ẍ r (t )+hϖ 0 ẋ r (t )+ϖ 0 2 x r (t )=0 

g 

x r 

( 0)=x 0 

, ẋ r 

(0)=0 

We release the seismometer mass from a given initial 

position and let it swing. The behaviour depends on 

the relation between the frequency of the spring and 

the damping parameter. If the seismometers 

oscillates, we can determine the damping coefficient 

h. 




1 

F 0 = 1 H z , h = 0 

1 

F 0 = 1 H z , h = 0 .2 

D is p la c e m e n t 

0 .5 

0 

-0 .5 

0 .5 

0 

-0 .5 

x 0 

u 

g 

x 

x 

r 

-1 

0 1 2 3 4 5 

-1 

0 1 2 3 4 5 

1 

F 0 = 1 H z , h = 0 .7 

1 

F 0 = 1 H z , h = 2 .5 

D is p la c e m e n t 

0 .5 

0 

-0 .5 

0 .5 

0 

-0 .5 

-1 

0 1 2 3 4 5 

Tim e (s ) 

-1 

0 1 2 3 4 5 

Tim e (s )



a k 

a k+1 

The damping 

coefficients can be 

determined from the 

amplitudes of 

consecutive extrema a k 

and a k+1 

We need the logarithmic 

decrement L 

Λ=2ln 

( a k 

a k+1) 

x 0 

u 

g 

x 

x 

r 

The damping constant h can then be determined through: 

h= 

Λ 

√4π 2 +Λ 2


Seismometer – Frequency 

a k 

a k+1 

T 

x 0 

x 

x 

r 

u 

g 

The period T with which the seismometer 

mass oscillates depends on h and (for h


Seismometer – Response Function 

2. How does the seismometer amplify the ground 

motion? Is this amplification frequency dependent? 

x 0 

x 

x 

r 

To answer this question we excite our 

seismometer with a monofrequent signal and 

record the response of the seismometer: 

u 

g 

ẍ r (t )+hϖ 0 ẋ r (t )+ϖ 0 2 x r (t )=ϖ 2 A 0 e i 

ϖt 

the amplitude response A r 

of the seismometer 

depends on the frequency of the seismometer w 0 

, 

the frequency of the excitation w and the damping 

constant h: 

∣ A r 

A 0 

∣= 

1 

√( T 2 )2 

2 

T −1 +4h 2 T 2 

2 

0 

T 0


Amplitude Response Function - Resonance

Phase Response 


Clearly, the amplitude and 

phase response of the 

seismometer mass leads to a 

severe distortion of the original 

input signal (i.e., ground 

motion). 

Before analysing seismic signals 

this distortion has to be revered: 

-> Instrument correction


Seismometer as a Filter 

Restitution -> Instrument correction


Seismometer as a Filter 

Restitution -> Instrument correction


Electromagnetic Seismograph 

Electromagnetic seismographs 

measure ground velocity


The STS-2 Seismometer 

www.kinemetrics.com


Accelerometer 

force-balance principle 

Feedback circuit of a force-balance accelerometer (FBA). The motion 

of the mass is controlled by the sum of two forces: the inertial force 

due to ground acceleration, and the negative feedback force. The 

electronic circuit adjusts the feedback force so that the two forces very 

nearly cancel. (Source Stuttgart University)


Seismic signal and noise 

The observation of seismic noise had a strong 

impact on the design of seismic instruments, 

the separation into short-period and long-period 

instruments and eventually to the development 

of broadband sensors.


Seismic noise


Seismometer Bandwidth 

Today most of the 

sensors of permanent 

and temporary seismic 

networks are broadband 

instruments such as the 

STS1+2. 

Short period instruments 

are used for local 

seismic events (e.g., the 

Bavarian seismic 

network).


(Relative) Dynamic range 

Dynamic Range DR: the ratio between largest measurable 

amplitude A max 

to the smallest measurable amplitude A min 

. 

DR = V max 

/V min 

Units Units … what what is is 1 Bell? Bell? 

… it it is is the the Base Base 10 10 Logarithm of of the the ratio ratio of of two two 

energies 

L= L= log log (P (P 1 

/P 

1 

/P 2 

) 

2 

) B = 10 10 log log (P (P 1 

/P 

1 

/P 2 

) 

2 

) dB dB 

Where Where B is is a 10th 10th of of B, B, and and in in terms terms of of amplitudes 

L = 10 10 log log (A (A 1 

/A 

1 

/A 2 

) 

2 

) 2 2 dB dB = 20 20 log log (A (A 1 

/A 

1 

/A 2 

) 

2 

)


(Relative) Dynamic range 

Nature: 

The Earth has motions varying 10 orders of magnitude 

from the strongest motion to the lowest noise level 

-> DR Earth 

= 20 log (10 10 )dB = 200 dB ! 

Instruments: e.g., e.g., 10 10 bit bit digitizer 

Dynamic range range = 20 20 log log 10 

(A 

10 

(A max 

/A 

max 

/A min 

) 

min 

) dB dB 

Example: with with 1024 1024 units units of of amplitude (A (A min 

=1, 

min 

=1, 

A max 

=1024) 

max 20 20 log log 10 

(1024/1) 

10 dB dB ~ 60 60 dB dB


Bits, counts, dynamic range


Dynamic range of a seismometer 

ADC (analog-digital-converter) 

A n-bit n-bit digitzer will will have have 2 n-1 n-1 intervals to to 

describe an an analog analog signal. signal. 

Seismogram 

data in counts 

Example: 

A 24-bit 24-bit digitizer has has 5V 5V maximum output output 

signal signal (full-scale-voltage) 

The The least least significant bit bit (lsb) (lsb) is is then then 

lsb lsb = 5V 5V // 2 n-1 n-1 = 0.6 0.6 microV microV 

Generator constant STS-2: STS-2: 750 750 Vs/m Vs/m 

What What does does this this imply imply for for the the peak peak ground ground 

velocity at at 5V? 5V?


Rotation: the curl of the wavefield 

(ω x 

ω y 

ω z 

)= 1 2 ∇×v= 1 2 

(∂ y 

v z 

−∂ z 

v y 

∂ z v x −∂ x v 

x) 

z 

∂ x 

v y 

−∂ y 

v 

v z 

ω y 

ω x 

v y 

v x 

ω z 

Ground velocity 

Rotation rate 

Rotation sensor 

Seismometer


How can we observe rotations? 

-> ring laser 

Ring laser technology developed by the 

groups at the Technical University 

Munich and the University of 

Christchurch, NZ


Ring laser – the principle 

Δf Sagnac = 4Ω⋅A 

λP 

A 

surface of of the the ring ring laser (vector) 

Ω imposed rotation rate rate (Earth‘s rotation + 

earthquake +...) +...) 

λ 

laser wavelength (e.g. (e.g. 633 633 nm) nm) 

Pperimeter (e.g. (e.g. 4-16m) 

∆f ∆f Sagnac frequency (e.g. (e.g. 348,6 Hz Hz sampled at at 

1000Hz)


The Sagnac Frequency 

(schematically) 

Sagnac frequency sampled with 1000Hz 

Tiny changes in in the the 

Sagnac 

frequencies are are 

extracted to to 

obtain the the time 

series with 

rotation rate rate 

Rotation rate sampled with 20Hz 

Df Df -> -> Q

The ring laser at Wettzell 


ring laser 

Data accessible at www.rotational-seismology.org


The Pinon Flat Observatory sensor


PFO


Rotation from seismic arrays? 

... by finite differencing ... 

ω z 

≈∂ x 

v y 

−∂ y 

v x 

seismometers 

ω z 

v y 

v x 

v y 

v x 

v y 

v x 

v y 

v x 

Rotational motion 

estimated from 

seismometer recordings


Direct vs. array-derived rotation

Array vs. direct measurements 

Wassermann et al., 2009, BSSA 



Strain sensors 

Network in EarthScope


Pinon Flat Observatory, CA


Strain meter principle


Strain - Observations


Tiltmeters 

• Tiltmeters are designed to 

measure changes in the angle 

of the surface normal 

• These changes are particularly 

important near volcanoes, or in 

structural engineering 

• In the seismic frequency band 

tiltmeters are sensitive to 

transverse acceleration 

Source: USGS


Tilt vs. horizontal acceleration 

Earthquake recorded at Wettzell, Germany


GPS Sensor Networks


San Francisco GPS Network 

Co-seismic displacement 

measured in California 

during an earthquake. 

(Source: UC Berkeley


Ocean Bottom Seismometers 

The OB Unit is equipped with a 

broadband Güralp seismometer 

and a Differential Pressure Gauge 

(from Scripps Institution of 

Oceanography). Additionally, it 

measures the absolute pressure 

with a Paroscientific Intelligent 

Depth sensor, manufactured by 

DIGIQUARZ. 

Source: GFZ Potsdam 

Source: USGS


Ocean Bottom Seismometers 

RHUM-RUM 

Investigating La Réunion 

mantle plume 

www.rhum-rum.net 

Source: USGS


Other sensors and curiosities 

• Gravimeters 

• Ground water level 

• Electromagnetic measurements 

(ionosphere) 

• Infrasound measurements


Summary 

• Seismometers are forced oscillators, recorded 

seismograms have to be corrected for the instrument 

response 

• Strains and rotations are usually measured with optical 

interferometry, the accuracy is lower than for standard 

seismometers 

• The goal in seismology is to measure with one 

instrument a broad frequency and amplitude range 

(broadband instruments) 

• Cross-axis sensitivity is an important current issue 

(translation – rotation – tilt)

Seismic Instruments

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