WP 33 Geophysikalische Datenanalyse
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1 WP 33 Geophysikalische Datenanalyse Goals: Get a feel for information contained in seismograms Understand the concept of the spectral domain (frequency domain) See how the frequency representation can be used to your advantage Learn about limitations of digital signals
2 Seismogram interpretation What does seismic data look like? What kind of information can we extract from a seismogram?
3 Seismogram interpretation What does seismic data look like? What kind of information can we extract from a seismogram?
4 Seismogram interpretation What does seismic data look like? What kind of information can we extract from a seismogram? Wave speeds along path Scattering, absorption Site effect? Noise level Source: magnitude, mechanism, distance, depth Instrument?
5 Seismogram interpretation Seismic wave types
6 Seismogram interpretation Seismic wave types
7 Seismogram interpretation
8 Lokale Erdbeben (Δ < km) Kulhanek (1990/1997) Anatomy of Seismograms
9 Lokale Erdbeben (Δ < km) Kulhanek (1990/1997) Anatomy of Seismograms
10 Lokale Erdbeben (Δ < km) Kulhanek (1990/1997) Anatomy of Seismograms
11 Lokale Erdbeben (Δ < km) Kulhanek (1990/1997) Anatomy of Seismograms
12 Lokale Erdbeben (Δ < km) Entfernung: km Quelle: NMSOP (2013) P. Bormann (Editor)
13 Lokale Erdbeben (Δ < km)
14 Lokale Erdbeben (Δ < km) Dahm et al., 2007 Tiefenphasen können bei der Bestimmung der Tiefe eines Ereignisses sehr hilfreich sein
15 Lokale Erdbeben (Δ < km)
16 Teleseismische Erdbeben (Δ > km) Station Moxa (MOX), Deutschland Entfernung: 112.5
17 Teleseismische Erdbeben (Δ > km)
18 Teleseismische Erdbeben (Δ > km) Die Tiefe von Erdbeben hat großen Einfluß auf die Form der Seismogramme
19 Teleseismische Erdbeben (Δ > km)
20 Exercise Phasen? Entfernung? Magnitude? Zeitlänge (S-P)? Max. Amplitude?
21 Exercise Phasen: P, PP, S, SS, Love, Rayleigh Zeitlänge (S-P): 611 s Entfernung: km Max. Amplitude: 7.9e-4 m/s 0.8 mm/s Magnitude: Mw 8.1 Tiefe?
22 1 day seismic record
23 1 day seismic record
24 Frequency representation Wavelength (in space) Period (in time) Number of periods in 1 second = frequency
25 Frequency representation contributions to frequency ω Add all for each time 1 iωt F ω = f t e dt 2π f t = F ω e Add all iωt dω for each frequency contributions to time t Forward transform (analysis) Inverse transform (synthesis)
26 Frequency representation
27 Frequency representation
28 Frequency representation
29 Exercise 1) Can you think of examples of signals where you only consider specific frequencies or frequency ranges? 2) Play with the Fourier tool. Can you make a spike by adding sinusoids? What about a box?
30 1 day seismic record
31 Dispersion
32 Frequency representation
33 Filtering Often a recorded signal contains a lot of information that we are not interested in (noise). To get rid of this noise we can apply a filter in the frequency domain. The most important filters are: High pass: cuts out low frequencies Low pass: cuts out high frequencies Band pass: cuts out both high and low frequencies and leaves a band of frequencies Band reject: cuts out certain frequency band and leaves all other frequencies
34 Filtering Unfiltered
35 Filtering Unfiltered Band pass
36 Filtering Unfiltered Band pass Low pass
37 Filtering Unfiltered Band pass Low pass High pass
38 Filtering Unfiltered Band pass Low pass High pass Notch/band stop
39 Digital signals The Nyquist frequency (or Nyquist limit), is the highest frequency that can be coded at a given sampling frequency in order to be able to fully reconstruct the signal fny= 1/2 fs
40 Digital signals The Nyquist frequency (or Nyquist limit), is the highest frequency that can be coded at a given sampling frequency in order to be able to fully reconstruct the signal fny= 1/2 fs OR: A signal must be sampled with a frequency (fs) at least twice the highest frequency contained in the signal (fmax)
41 Exercise 1) Nyquist: how would you make sure your signal won't contain freqs > fny? 2) You have 10 seismometers at your disposal. You are interested in recording seismic waves with a wavelength between 5 and 10 km. At what distance from each other would you place your seismometers?
42 Exercise Now let's look at some earthquake signals! Open the notebook Earthquake signal. In there, you will be able to load signals from one event, recorded at three different stations in Germany. Try to find out where the event was!
43 Summary Signals can be represented in the time or in the frequency domain Sometimes different information can be extracted in each Filters can be used to zoom in to certain portions of the frequency domain (Almost) all our signals are digital. In the digitization step, we lose information. One must be aware of the limits imposed by the sampling frequency.
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Multirate Digital Signal Processing
Multirate Digital Signal Processing Basic Sampling Rate Alteration Devices Up-sampler - Used to increase the sampling rate by an integer factor Down-sampler - Used to increase the sampling rate by an integer
PART I: The questions in Part I refer to the aliasing portion of the procedure as outlined in the lab manual.
Lab. #1 Signal Processing & Spectral Analysis Name: Date: Section / Group: NOTE: To help you correctly answer many of the following questions, it may be useful to actually run the cases outlined in the