Seismic Instruments - uni-muenchen.de€¦ · Modern Seismology – Data processing and inversion 2 Seismic instruments Spring-mass seismometer vertical motion Before we look more

Modern Seismology – Data processing and inversion1

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


Seismic instruments

Spring-mass seismometer vertical motion

Before

we

look

more

carefully

at seismic

instruments

we

ask

ourselves

what

to expect

for

a typical

spring based

seismic

inertial

sensor. This

will highlight

several fundamental issues

we

have

to deal

with

concerning

seismic

data analysis.

Before

we

look

more

carefully

at seismic

instruments

we

ask

ourselves

what

to expect

for

a typical

spring based

seismic

inertial

sensor. This

will highlight

several fundamental issues

we

have

to deal

with

concerning

seismic

data analysis.


Seismic instruments

Seismometer – The basic principles

u

x x0

ug

um

xm

x

x0 xr

u ground displacement

xr

displacement of seismometer massx0

mass equilibrium position


Seismic instruments

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):

Fspring

+ Ffriction

+ Fgravity

= 0

for example

Fsprin

=-k x, k spring constant

Ffriction

=-D x, D friction coefficient

Fgravity

=-mu, m seismometer mass


ug

x

x0 xr

.

..


Seismic instruments


ug

x

x0 xr

using the notation introduced above the equation of motion for the mass is

mkh

mD

tutxtxtx grrr

===

−=++

200

20

,2

)()()(2)(

ϖϖε

ϖε &&&&&

From this we learn that:

- for slow movements the acceleration and velocity becomes negligible, the seismometer records ground acceleration

- for fast movements the acceleration of the mass dominates and the seismometer records ground displacement


Seismic instruments

A simple finite-difference solution of the seismometer equation


Seismic instruments

Seismometer – examples

ug

x

x0 xr


Seismic instruments

Varying damping constant

ug

x

x0 xr


Seismic instruments

Seismometer – CalibrationSeismometer – Calibration

ug

x

x0 xr

1. How can we determine the damping properties from the observed behaviour of the seismometer?

2. How does the seismometer amplify the ground motion? Is this amplification frequency dependent?

We need to answer these question in order to determine what we really want to know:The ground motion.


Seismic instruments

Seismometer – Release TestSeismometer – Release Test

ug

x

x0 xr1.

How can we determine the damping properties from the observed behaviour of the seismometer?

0)0(,)0(0)()()(

0

200

===++

rr

rrr

xxxtxtxhtx

&

&&& ϖϖ

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.


Seismic instruments


ug

x

x0 xr

0 1 2 3 4 5-1

-0.5

0

0.5

1F0=1Hz, h=0

Dis

plac

emen

t

0 1 2 3 4 5-1

-0.5

0

0.5

1F0=1Hz, h=0.2

0 1 2 3 4 5-1

-0.5

0

0.5

1F0=1Hz, h=0.7

Time (s)

Dis

plac

emen

t

0 1 2 3 4 5-1

-0.5

0

0.5

1F0=1Hz, h=2.5

Time (s)


Seismic instruments


ug

x

x0 xrThe damping coefficients

can be determined from the amplitudes of consecutive extrema

ak

and ak+1We need the logarithmic decrement Λ

ak

ak+1

⎟⎟⎠

⎞⎜⎜⎝

⎛=Λ

+1

ln2k

k

aa

The damping constant h can then be determined through:

224 Λ+

Λ=

πh


Seismic instruments

Seismometer – FrequencySeismometer – Frequency

ug

x

x0 xr

The period T with which the seismometer mass oscillates depends on h and (for h<1) is always larger than the period of the spring T0

: 20

1 hTT−

=

ak

ak+1

T


Seismic instruments

Seismometer – Response FunctionSeismometer – Response Function

ug

x

x0 xr

tirrr eAtxtxhtx ϖϖϖϖ 0

2200 )()()( =++ &&&

2. How does the seismometer amplify the ground motion? Is this amplification frequency dependent?

To answer this question we excite our seismometer with a monofrequent

signal and record the response of

the seismometer:

the amplitude response

Ar

of the seismometer depends on the frequency of the seismometer w0

, the frequency of the excitation w and the damping constant h:

20

22

2

20

2041

1

TTh

TTA

Ar

+⎟⎟⎠

⎞⎜⎜⎝

⎛−

=


Seismic instruments

Amplitude Response Function - Resonance


Seismic instruments

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


Seismic instruments

Seismometer as a Filter Restitution -> Instrument correction


Seismic instruments

Electromagnetic Seismograph

Electromagnetic seismographs measure ground velocity


Seismic instruments

Seismic signal and noiseThe 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 instruments

Seismic noise


Seismic instruments

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).


Seismic instruments

The STS-2 Seismometer

www.kinemetrics.com


Seismic instruments

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 instruments

Accelerometer

www.kinemetrics.com


Seismic instruments

(Relative) Dynamic rangeWhat

is

the

precision

of the

sampling

of our

physical

signal

in amplitude?

Dynamic

range: the

ratio

between

largest

measurable amplitude

Amax

to the

smallest

measurable

amplitude

Amin

.

The

unit

is

Decibel

(dB) and is

defined

as the

ratio

of two power values

(and power is

proportional to amplitude

square)

What

is

the

precision

of the

sampling

of our

physical

signal in amplitude?

Dynamic

range: the

ratio

between

largest

measurable amplitude

Amax

to the

smallest

measurable

amplitude

Amin

.

The

unit

is

Decibel

(dB) and is

defined

as the

ratio

of two power values

(and power is

proportional to amplitude

square)

In terms

of amplitudes

Dynamic

range

= 20 log10

(Amax

/Amin

) dB

Example: with

1024 units

of amplitude

(Amin

=1, Amax

=1024)

20 log10

(1024/1) dB ~

60 dB

In terms

of amplitudes

Dynamic

range

= 20 log10

(Amax

/Amin

) dB

Example: with

1024 units

of amplitude

(Amin

=1, Amax

=1024)

20 log10

(1024/1) dB ~

60 dB


Seismic instruments

Dynamic range of a seismometer ADC (analog-digital-converter)

A n-bit

digitzer

will have

2n-1

intervals

to describe

an analog signal.

Example:

A 24-bit digitizer

has 5V maximum

output signal

(full-scale-voltage)

The

least significant

bit

(lsb) is

then

lsb

= 5V / 2n-1 = 0.6 microV

Generator constant

STS-2: 750 Vs/m

What

does

this

imply

for

the

peak

ground velocity

at 5V?

A n-bit

digitzer

will have

2n-1

intervals

to describe

an analog signal.

Example:

A 24-bit digitizer

has 5V maximum

output signal

(full-scale-voltage)

The

least significant

bit

(lsb) is

then

lsb

= 5V / 2n-1 = 0.6 microV

Generator constant

STS-2: 750 Vs/m

What

does

this

imply

for

the

peak

ground velocity

at 5V?

Seismogram data in counts

Seismogram data in counts


Seismic instruments

Rotation the curl of the wavefield

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

∂−∂∂−∂∂−∂

=×∇=⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

xyyx

zxxz

yzzy

z

y

x

vvvvvv

21

21 v

ωωω

vz

vy

vx

ωz

ωy

ωx

Ground velocity Seismometer

Rotation rateRotation sensor


Seismic instruments

The ring laser at Wettzell

ring laserData accessible

at www.rotational-seismology.org


Seismic instruments

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


Seismic instruments

Ring laser – the principle

PfSagnac λ

AΩ ⋅=Δ

4

A

surface

of the

ring laser

(vector)Ω

imposed

rotation rate (Earth‘s rotation +

earthquake

+...) λ

laser

wavelength

(e.g. 633 nm)

P

perimeter

(e.g. 4-16m)Δf

Sagnac

frequency

(e.g. 348,6 Hz sampled

at

1000Hz)

A

surface

of the

ring laser

(vector)Ω

imposed

rotation rate (Earth‘s rotation +

earthquake

+...)λ

laser

wavelength

(e.g. 633 nm)

P

perimeter

(e.g. 4-16m)Δf

Sagnac

frequency

(e.g. 348,6 Hz sampled

at

1000Hz)


Seismic instruments

The Sagnac Frequency (schematically)

Tiny

changes

in the Sagnac

frequencies

are extracted

to

obtain

the

time series

with

rotation rate Δf -> Θ

Tiny

changes

in the Sagnac

frequencies

are extracted

to

obtain

the

time series

with

rotation rateΔf -> Θ

Sagnac

frequency

sampled

with

1000HzSagnac

frequency

sampled

with

1000Hz

Rotation rate sampled

with

20Hz


Seismic instruments

The PFO sensor


Seismic instruments

PFO


Seismic instruments

PFO


Seismic instruments

PFO


Seismic instruments

Expected amplitudes teleseismic events

From Igel et al., 2007


Seismic instruments

The PFO sensor – mode hops

72.60

72.80

73.00

73.20

73.40

0 200 400 600 800 1000

Rot

atio

n R

ate

[µra

d/s]

Epoch [s]


Seismic instruments

4C recordings – raw dataMw = 8.3 Tokachi-oki earthquake25.09.2003 19:50:38.2 GMTLat= 42.21 Lon= 143.84


Seismic instruments

Mw = 8.3 Tokachi-oki 25.09.2003 transverse acceleration – rotation rate

From

Igel et al., GRL, 2005


Seismic instruments

Rotation from seismic arrays? ... by finite differencing ...

xyyxz vv ∂−∂≈ω

vyvx

ωz

vyvx

vyvx

vyvx

Rotational motion estimated from

seismometer recordings

seismometers


Seismic instruments

Synthetics

Uniformity of rotation rate across array

Real data


Seismic instruments

Array vs. direct measurements

Wassermann et al., 2009, BSSA


Seismic instruments

A look to the future seismic tomography with rotations

From Bernauer et al., Geophysics, 2009


Seismic instruments

Strain sensors Network in EarthScope


Seismic instruments

Pinon Flat Observatory, CA


Seismic instruments

Strain meter principle


Seismic instruments

Interferometer


Seismic instruments

Strain - Observations


Seismic instruments

Strain vs. translations (velocity v, acceleration a)


Seismic instruments

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


Seismic instruments

Tilt vs. horizontal acceleration Earthquake recorded at Wettzell, Germany


Seismic instruments

GPS Sensor Networks


Seismic instruments

San Francisco GPS NetworkCo-seismic displacement measured in California during an earthquake.

(Source: UC Berkeley


Seismic instruments

Other sensors and curiosities

• Gravimeters• Ground water level• Electromagnetic measurements

(ionosphere)• Infrasound measurements


Seismic instruments

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)

Documents

Seismic Instruments - uni-muenchen.de€¦ · Modern Seismology – Data processing and inversion 2 Seismic instruments Spring-mass seismometer vertical motion Before we look more