Multicomponent Signal Processing for Rayleigh wave Ellipticity …€¦ · SPSC – Signal Processing & Speech Communication Lab Professor Horst Cerjak, 19.12.2005 45 Ebner, Helmberger

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




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




Introduction

- Local soil structure estimation

- Estimation of the seismic hazard at a given site

- Soil structure can be determined:- Drilling boreholes- Using (surface) waves




Seismic Signals4 types of seismic waves:

Bodywaves:• Pressure (P)• Shear (S)

Surfave waves:• Love• Rayleigh




P Wave




S Wave




Love Wave




Rayleigh Wave




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




Dispersion Curves




Dispersion Curves

S-wave velocity

Dispersion Curve




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




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




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




H/V Ratio - Experiment












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




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




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




HVTFA




HVTFA




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




RAYDEC

Z

X

Y

∆




RAYDEC




RAYDEC




RAYDEC




RAYDEC

Repeat algorithm over whole frequency range




RAYDEC - Summary




References




Ellipticity measurement using sensor arrays

Overview

● Motivation

● 2 methods to estimate ellipticity

● Comparison of different methods

● Conclusions




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




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.




Frequency Wavenumber (FK)

● Applied to a single component of seismic array

● Beamforming in frequency domain

[1]




Frequency Wavenumber (FK)

Blackboard...




[2]




High Resolution Frequency Wavenumber

● Weight Power output with 'adaptive filter' vector w(k)

● Minimization problem:

● Grid search stays the same




[2]




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




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.




[1]




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




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




MUSIQUE algorithm

● First step: using the classical “MUSIC” algorithm(Multiple Emitter Location and Signal Parameter Estimation)

● Model:




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




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 )




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




[5]




[1]




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




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.




Questions?

Multicomponent Signal Processing for Rayleigh wave Ellipticity …€¦ · SPSC – Signal Processing & Speech Communication Lab Professor Horst Cerjak, 19.12.2005 45 Ebner, Helmberger

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