Esci 411, Advanced Exploration Geophysics

(Micro)seismicity

John Townend

EQC Fellow in Seismic Studies

john.townend@vuw.ac.nz

Outline

• A history of seismometry

• Simple and damped harmonic motion

• The seismometer equation– Forced oscillation of a damped pendulum

• Response characteristics– Frequency response, bandwidth, dynamic range

NB: Several figures from Stein & Wysession (2003) are gratefully acknowledged

Fundamental challenges

1. How do we measure ground motion using an instrument that is itself attached to the ground, and moving?

2. How do we make reliable measurements of motion occurring over a very wide range of frequencies and amplitudes?

A mass on a spring

• Force on mass due to spring F = –k

• Newton’s 2nd law F = ma –k = m

• Natural frequency 0

2 k/m

• Overall equation = –0

2 (t)spring constant, k

mass, m

..

..

Free resonance

The mass oscillates at the natural frequency, o

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5 6

Time

Dis

pla

ce

me

nt

original mass, original springlarger mass, original springoriginal mass, stiffer spring

A simple harmonic oscillator

mkss ,02

natural frequency

(t)spring constant, k

mass, m

A damped harmonic oscillator

(t)spring constant, k

mass, m

damping coefficient, c

mco 202 2 ,

damping parameter

Damping

• Underdamping– Exponential decay in signal amplitude

• Critical damping– Non-oscillatory motion

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Time

Dis

pla

cem

ent

no dampingunderdampedcritically damped

The seismometer equation

uo 22

Pen

dulu

m a

ccel

erat

ion

Vis

cous

dam

ping

ter

m

Und

ampe

d os

cilla

tion

term

Gro

und

acce

lera

tion

Harmonic shaking, no damping

• How does an undamped seismometer react to sinusoidal shaking, u(t) = A sin pt ?

• We’ll look at the signal amplification only:

• So, if the forcing frequency p is equal to the seismometer’s natural frequency o, we get resonance and destroy the seismometer

222 ppu o

End-member responses

• High-frequency oscillations (>>o):

– Seismometer records displacement

• Low-frequency oscillations (<<o):

– Seismometer records acceleration

uo 22

uo 22

Frequency response

• How does the seismograph react to shaking at different frequencies?

• These curves are drawn in terms of the damping factor, h=/o

Summary

• In recording seismic waves, we face three principal complications– Our recording instrument is not stationary– The waves contain energy at many frequencies– The waves have a broad range of amplitudes

• In the next series of slides, we’ll look at how to overcome these issues using specific instruments

Electromechanical seismometers

Instead of measuring the mass’s motion by a

mechanical device, we can measure the voltage

induced in a moving coil

voltage sensor velocity

This increases damping

Schematic system response

• Amplitude responses– Pendulum 2 (<s)

– Velocity sensor – Galvanometer –2 (<g)

• Overall response– Governed by the particular

characteristics of these three principal components

Frequency response comparison

• Different response functions are required for different purposes

• Each seismometer’s response function is determined during calibration

Magnification and dynamic range

• Two factors control the signal magnification– Dynamic magnification (instrument response)– Static magnification (recording amplification)

• The overall magnification controls the instrument’s dynamic range:– If Amin and Amax are the minimum and maximum

recordable amplitudes, then

dynamic range (dB) = 20 log10(Amax/Amin)

Earth noise

• Tides, atmospheric pressure variations, anthropogenic sources, ocean waves, rain,…

• Mostly 5–10 s periods (0.1–0.2 Hz)

• Can be largely filtered out of broadband data

Seismometer calibration

• Natural period, To=2/o

– Time a number of undamped oscillations

• Damping, h– Measure the amplitude ratio () for a

number of successive oscillations

• Magnification, V()– Measure the ratio between the output and

input amplitudes

Digital seismometry

Even electromechanical seismometers have limitations (especially dynamic range); with appropriate filtering, digital

systems can overcome many of these

Some practical issues

• Signal frequencies– Seismic waves contain frequencies of mHz–kHz

• Signal amplitudes– Displacements can be as little as 10 µm–10 cm

• The ideal seismometer requires– High bandwidth– High dynamic range

Force-balance instruments (1)

• The compensating force is proportional to ground acceleration• The instrument behaves as if the sensor mass is much larger,

and the instrument’s natural frequency is therefore much lower

Input

Inertial sensor Coil

Force

transducer

Output

–x..

u – x....

u..

Force-balance instruments (2)

• Rationale– Negative feedback reduces the relative motion of

the sensor, and reduces nonlinear instabilities

• Advantages– Removes dependence on mechanical systems– Increases sensitivity, linearity and dynamic range– Can overcome the need for a large sensor mass

in inhospital/cramped circumstances– Reduces seismometer size!

Broadband seismometers

STS-2 broadband data in Pennsylvania from a July 1995 earthquake in Tonga

1. Original data2. Low-pass filtered3. High-pass filtered4. Zoomed high-pass filtered

Summary

• Using electromagnetic sensors and force-feedback systems, we can improve the bandwidth and dynamic range of seismometers

• This enables us to “tune” (design) instruments for specific purposes

• Array and network geometries are likewise designed for specific targets

US reference array

US transportable array (as of today)

US transportable array (plan as of 12/2010)

Global seismic network (as of 06/2012)

Suggested reading material• Stein & Wysession (2003)

– Section 6.6 (most accessible reference)

• Havskov & Alguacil (2006)– “Instrumentation in earthquake seismology”

• Udias (1999)– Chapter 21

• Aki & Richards (2002)– Section 12.1

• Scherbaum (2007)– “Fundamentals of digital seismology”