1. Esci 411, Advanced Exploration Geophysics (Micro)seismicity John Townend EQC Fellow in Seismic Studies john.townend@vuw.ac.nz

2. 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

3. 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?

4. A mass on a spring Force on mass due to spring F = –k  Newton’s 2 nd law F = ma  –k  = m  Natural frequency  0 2  k/m Overall equation  = –  0 2   (t) spring constant, k mass, m..

5. Free resonance The mass oscillates at the natural frequency,  o

6. A simple harmonic oscillator natural frequency  (t) spring constant, k mass, m

7. A damped harmonic oscillator  (t) spring constant, k mass, m damping coefficient, c damping parameter

8. Damping Underdamping –Exponential decay in signal amplitude Critical damping –Non-oscillatory motion

9. The seismometer equation Pendulum accelerationViscous damping termUndamped oscillation termGround acceleration

10. 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

11. End-member responses High-frequency oscillations (  >>  o ): –Seismometer records displacement Low-frequency oscillations (  <<  o ): –Seismometer records acceleration

12. Frequency response How does the seismograph react to shaking at different frequencies? These curves are drawn in terms of the damping factor, h=  /  o

13. 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

14. 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

15. 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

16. Frequency response comparison Different response functions are required for different purposes Each seismometer’s response function is determined during calibration

17. 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 A min and A max are the minimum and maximum recordable amplitudes, then dynamic range (dB) = 20 log 10 (A max /A min )

18. 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

19. Seismometer calibration Natural period, T o =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

20. Digital seismometry Even electromechanical seismometers have limitations (especially dynamic range); with appropriate filtering, digital systems can overcome many of these

21. 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

22. 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 sensorCoil Force transducer Output –x–x.. u – x.. u

23. 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!

24. Broadband seismometers STS-2 broadband data in Pennsylvania from a July 1995 earthquake in Tonga 1.Original data 2.Low-pass filtered 3.High-pass filtered 4.Zoomed high-pass filtered

25. 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

27. US reference array US transportable array (as of today) US transportable array (plan as of 12/2010) Global seismic network (as of 06/2012)

28. 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”