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Université de Liège
Faculté des Sciences Appliquées
Array recordings of ambient vibrations:
surface-wave inversion
A thesis submitted for the degree of
Doctor of Applied Sciences
presented by Marc Wathelet
February, 2005, revised March 2007
Contents
List of Figures
List of Tables
Résumé
Abstract
Introduction
Objectives
Thesis outline
Measuring wave velocity
Ambient vibrations
Frequency-wavenumber method
Principles
Theoretical array response
Implementation
High resolution method
Principles
Implementation
Spatial auto-correlation method
Principles
Implementation
Artificial sources
refracted waves
refracted waves
Surface wave inversion
Implementation
Conclusions
The inversion algorithm
Definition
Available methods
Gridding method
Iterative methods
Neural Networks
Monte Carlo methods
The neighbourhood algorithm
Conditional parameter spaces
Conclusions
Forward computation
Dispersion Curves
Propagator-matrix method
Displacements, Stresses, and strains
Eigenvalue problem for Love waves
Theory
Eigenfunctions
Implementation
Eigenvalue problem for Rayleigh waves
Theory
Eigenfunctions
Implementation
A quick root search
Physical search interval
Bracketing the root candidates
Refining the brackets
Mode jumping control
Non-monotonous shape
End-point check
Misfit
Sensitivity of the dispersion against layer parameters
Two-layer model
Three-layer model
Conclusion
Ellipticity
Computation
Sensitivity
Misfit
Spatial auto-correlation
Computation
Misfit
Sensitivity
Conclusion
Parameterization of a ground model
Theoretical model used in parameterization tests
Thickness,
, and
Two layers
Three layers
Broad band dispersion curve
Narrow band dispersion curve
Low frequency dispersion curve
Prior information on depth
Prior information on
Stack of N layers
Arbitrary profile
inversion without LVZ
Non-uniform layers
Linear variation
Power law variation
Conclusions
Enhanced inversions
Multimodal curves
Rayleigh higher modes
First higher mode alone
Fundamental mode alone
Fundamental and first higher modes
Conclusions
Love and Rayleigh
Higher mode identification
Spatial auto-correlation
Uniqueness of auto-correlation curves
Synthetic model
Validation of auto-correlations
Inversion
Ellipticity inversion
Test cases
Synthetic ambient vibrations
Model description
Single source wavefield
Frequency-wavenumber method
High resolution method
Spatial auto-correlation method
Discussion and Conclusions
Liège site
The test site
Refraction
Rayleigh wave processing
refraction
Ambient vibrations recording
Frequency-wavenumber method
High resolution method
Spatial auto-correlation method
Conclusions
Conclusions
Sub-determinants of
Generating increasing velocity profiles
Selection method
Sorting method
Velocity-jump method
Interpolation method
Interpolation method with random start
Bissection method
Diagonal method
Including Poisson's ratio
Conclusions
Bibliography
About this document ...
2007-03-15
, and 
![\includegraphics[scale=0.85]{logo_geomac.eps}](img15.png)
![\includegraphics[scale=0.65]{logo_ulg.eps}](img16.png)
refracted waves
refracted waves