multicomponent signal processing for rayleigh wave ellipticity …€¦ · spsc – signal...
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SPSC – Signal Processing & Speech Communication Lab
Professor Horst Cerjak, 19.12.20051
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Multicomponent Signal Processing for Rayleigh wave Ellipticity Estimation
Ebner Thomas Helmberger Michael
SPSC – Signal Processing & Speech Communication Lab
Professor Horst Cerjak, 19.12.20052
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Overview1. Introduction2. Seismic Waves3. Soil structure estimation
1. Dispersion Curves2. Rayleigh Ellipticity
4. Epllipticity meaurement using a single seismic sensor1. H/V Ratio2. HVTFA3. RAYDEC
5. Epllipticity meaurement using array sensors1. The Method of Poggz and Fäh2. MUSIQUE
6. Comparison of the different methods
SPSC – Signal Processing & Speech Communication Lab
Professor Horst Cerjak, 19.12.20053
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Introduction
- Local soil structure estimation
- Estimation of the seismic hazard at a given site
- Soil structure can be determined:- Drilling boreholes- Using (surface) waves
SPSC – Signal Processing & Speech Communication Lab
Professor Horst Cerjak, 19.12.20054
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Seismic Signals4 types of seismic waves:
Bodywaves:• Pressure (P)• Shear (S)
Surfave waves:• Love• Rayleigh
SPSC – Signal Processing & Speech Communication Lab
Professor Horst Cerjak, 19.12.20055
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
P Wave
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
S Wave
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Love Wave
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Rayleigh Wave
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Professor Horst Cerjak, 19.12.20059
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Soil Structure Estimation
• S-waves have different velocities in different media
• Surface wave velocities approximates S-wave velocities
Velocity of surface waves is directly linked to local underground structure
1. Dispersion Curves
2. Rayleigh ellipticity curves
SPSC – Signal Processing & Speech Communication Lab
Professor Horst Cerjak, 19.12.200510
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Dispersion Curves
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Professor Horst Cerjak, 19.12.200511
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Dispersion Curves
S-wave velocity
Dispersion Curve
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Dispersion Curves - Properties
• Dispersion Curves have been used successfully in the past
• To get good resolution for deep layers a large number of sensors is needed
• Active sources do not penetrate the soil very deeply
De
pth
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Rayleigh wave ellipticity
- Rayleigh wave ellipticity correlates with underground structure
- complementary information to dispersion curves- Can be measured with a single sensor- Seismic ambient vibrations
De
pth
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Horizontal/Vertical Ratio
• very simple• widespread techinque • Ratio of horizontal and vertical Fourier spectra of
ambient seismic vibration recordings
XX... Eastern component
XY... Northern component
XZ... Vertical component
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
H/V Ratio - Experiment
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Professor Horst Cerjak, 19.12.200516
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
H/V Ratio - Experiment
SPSC – Signal Processing & Speech Communication Lab
Professor Horst Cerjak, 19.12.200517
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
H/V Ratio - Experiment
SPSC – Signal Processing & Speech Communication Lab
Professor Horst Cerjak, 19.12.200518
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
H/V Ratio - Summary
•Exact theory behind the H/V ratio not yet completely understood
•Misestimation of the amplitude of the ellipticity curve
•If only Rayleigh waves present, true ellipticity curve
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H/V using time-frequency analysis,HVTFA
- Improvement of H/V – Ratio- Limitation to the most energetic Rayleigh wave
arrivals
- Continuous Wavelet Transform CWT
Motherwavelet: modified Morlet wavelet
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
HVTFA - Principle
• Time-frequency representations of both horizontal components are merged:
• Scan vertical CWT (|CWTV|) for maxima to detect Rayleigh wave arrivals
• Save ratio between vertical and horizontal components
• Repeat for all frequencies
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
HVTFA
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HVTFA
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RAYDEC
• Based on the random decrement technique commonly used to characterize dynamic parameters of buildings
• Uses statistical means to suppress all wave types except Rayleigh waves
• Rayleigh wave ellipticity to be recovered over a wide frequency range by using ambient noise recordings
First Step: filter signals in a narrow range of bandwidth
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
RAYDEC
Z
X
Y
∆
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Professor Horst Cerjak, 19.12.200525
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
RAYDEC
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Professor Horst Cerjak, 19.12.200526
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
RAYDEC
SPSC – Signal Processing & Speech Communication Lab
Professor Horst Cerjak, 19.12.200527
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
RAYDEC
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Professor Horst Cerjak, 19.12.200528
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
RAYDEC
Repeat algorithm over whole frequency range
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
RAYDEC - Summary
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Professor Horst Cerjak, 19.12.200530
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
References
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Ellipticity measurement using sensor arrays
Overview
● Motivation
● 2 methods to estimate ellipticity
● Comparison of different methods
● Conclusions
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Professor Horst Cerjak, 19.12.200532
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Ellipticity measurement using sensor arrays
Motivation
● In contrast to single-station: estimation of the wave velocity
● Extraction of wave polarization
● Reduction of noise
● Averaging over an area
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Professor Horst Cerjak, 19.12.200533
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Method of Poggi and Fäh
● Advanced Version of High-Resolution Frequency-Wavenumber (HRFK) method
● HRFK is based on Frequency Wavenumber (FK) method
● Provides an estimation of the dispersion curve and the ellipticity over frequency.
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Professor Horst Cerjak, 19.12.200534
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Frequency Wavenumber (FK)
● Applied to a single component of seismic array
● Beamforming in frequency domain
[1]
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Frequency Wavenumber (FK)
Blackboard...
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
[2]
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
High Resolution Frequency Wavenumber
● Weight Power output with 'adaptive filter' vector w(k)
● Minimization problem:
● Grid search stays the same
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Professor Horst Cerjak, 19.12.200538
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
[2]
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
High Resolution Frequency Wavenumber
● Better Resolution
● Solution contains matrix inversion
● If noise is too small or zero, matrix is singular (or close to singularity)
● Introduce artificial noise
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Professor Horst Cerjak, 19.12.200540
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Method of Poggi and Fäh
● Extension of HRFK to 3 components
● Seperation of Love and Rayleigh waves
● Eastern and Northern components are projected into their radial and transverse parts.
SPSC – Signal Processing & Speech Communication Lab
Professor Horst Cerjak, 19.12.200541
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
[1]
SPSC – Signal Processing & Speech Communication Lab
Professor Horst Cerjak, 19.12.200542
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Rayleigh ellipticity evaluation
● Finding the parts of the spectrum containing rayleigh waves
● Calculating the ellipticity with the following formula
● Now we have obtained ellipticity and dispersion curves
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Professor Horst Cerjak, 19.12.200543
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
MUSIQUE
● Allows to estimate the sense of rotation of the Rayleigh wave particle motion
● Distinguishes between prograde and retrograde particle motion
● Useful to separate the fundamental and higher Rayleigh modes
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
MUSIQUE algorithm
● First step: using the classical “MUSIC” algorithm(Multiple Emitter Location and Signal Parameter Estimation)
● Model:
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
MUSIQUE algorithm
Separation of signal and noise subspace:
● Calculate covariance matrices from the vertical, northern and eastern component.
● Add covariance matrices to get a single matrix.
● EV of largest eigenvalues -> span signal subspace● EV of smalles eigenvalues -> span noise subpsace
● Decide number of signals D
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MUSIQUE algorithm
● Put “noise Eigenvectors” into matrix EN
● “noise Eigenvectors” are most orthogonal to mode vectors ● Product of 2 orthogonal vectors is 0
● Therefore, search for D Peaks in this function.
a (Θ )
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
MUSIQUE algorithm
● No we identified the direction of arrival and slowness of the arriving signals
● Use Quaternion-MUSIC for estimation of polarization
● We obtain both phase difference and a amplitude of the arriving signals.
● Classify between retrograde and prograde particle motion using phase difference
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
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Ebner, Helmberger 7.1.2012 Signal Processing Seminar
[1]
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Conclusions
● There is no perfect method
● Therefore, use multiple methods and compare results
● Also combine single sensor and array methods
● Still an active research area
SPSC – Signal Processing & Speech Communication Lab
Professor Horst Cerjak, 19.12.200551
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
References
[1] Manuel Hobiger et. al. Multicomponent Signal Processing for Rayleigh Wave Ellipticity Estimation
[2] V. Poggi and D. Fäh, “Estimating Rayleigh wave particle motion from threecomponent
array analysis of ambient vibrations,” Geophys. J. Int., vol. 180, no. 1, pp.
251–267, 2010
[3] J. Capon, “High -resolution frequency–wavenumber spectrum analysis,” Proc.
IEEE, vol. 57, no. 8, pp. 1408–1418, 1969.
[4] R. O. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE
Trans. Antennas Propagat., vol. 34, no. 3, pp. 276–280, 1986.
[5] S. Miron, N. Le Bihan, and J. Mars, “Quaternion-MUSIC for vector-sensor array
processing,” IEEE Trans. Signal Processing, vol. 54, no. 4, pp. 1218–1229, 2006.
SPSC – Signal Processing & Speech Communication Lab
Professor Horst Cerjak, 19.12.200552
Ebner, Helmberger 7.1.2012 Signal Processing Seminar
Questions?