Esci 411, Advanced Exploration Geophysics (Micro)seismicity

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 • How do we measure ground motion using an instrument that is itself attached to the ground, and moving? • How do we make reliable measurements of motion occurring over a very wide range of frequencies and amplitudes?

4. spring constant, k (t) mass, m A mass on a spring • Force on mass due to spring • F = –k • Newton’s 2nd law • F = ma  –k = m • Natural frequency • 02  k/m • Overall equation •  = –02  .. ..

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

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

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

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

9. The seismometer equation Undamped oscillation term Pendulum acceleration Viscous damping term Ground 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 Amin and Amax are the minimum and maximum recordable amplitudes, then • dynamic range (dB) = 20 log10(Amax/Amin)

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, 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

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 • Highbandwidth • Highdynamic range

22. .. .. Input .. u – x u .. –x Inertial sensor Coil Output Force transducer 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

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 • Original data • Low-pass filtered • High-pass filtered • 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”