List of Figures

1. Theoretical array responses for 25 sensors
2. Theoretical array responses for 10 sensors
3. Reference model for refraction synthetic traveltime-distance plot
4. Inversion of synthetic traveltime-distance plot
5. Theoretical array responses for a line of sensors
6. Example of a f-k analysis for triggered surface waves
7. Definition of an inversion problem
8. Voronoi cells for a two-dimensional parameter space
9. Comparison of variable transformation and selection methods
10. High level condition intersection with Voronoi cells
11. Schematic one-dimensional model
12. Values taken by $l_{21}(z_0)$
13. Values taken by $R_{1212}(z_0)$
14. Velocity limits of Love and Rayleigh dispersion curves
15. Method for bracketing roots.
16. Method for refining roots
17. Dispersion curve of a model with a LVZ.
18. Two layers: influence of $V_{s0}$ with a constant $V_p$ profile
19. Two layers: influence of $V_{s0}$ with a constant Poisson's ratio
20. Two layers: influence of $V_{p0}$
21. Two layers: influence of $z_1$
22. Two layers: influence of $z_1$ for $V_s$ profile
23. Two layers: influence of $z_1$ for $V_p$ profile
24. Two layers: influence of $\rho _0$
25. Two layers: influence of $V_{s1}$ with a constant $V_p$ profile
26. Two layers: influence of $V_{p1}$
27. Two layers: influence of $\rho _1$
28. Three layers: influence of $V_{s1}$ with a constant Poisson's ratio
29. Three layers: equivalent two-layer model at high frequency
30. Three layers: influence of $V_{p1}$
31. Ellipticity 2 layers: influence of $V_{s0}$ with a constant $V_p$ profile
32. Ellipticity 2 layers: influence of $V_{s0}$ with a constant Poisson's ratio
33. Ellipticity 3 layers: influence of $V_{s1}$ with a constant Poisson's ratio
34. Auto-correlation, azimuth-inter-distance plot example
35. Auto-correlation: influence of $V_{s0}$ with a constant Poisson's ratio
36. Theoretical case for testing parameterizations
37. Inversion of the full dispersion curve with a two-layer model
38. Inversion with a two-layer model: variation of the minimum misfit
39. Inversion with a two-layer model: parameter space
40. Inversion with a two-layer model: velocity profiles
41. Inversion with a three-layer model over a broad frequency range
42. Inversion with a three-layer model over a restricted frequency range
43. Inversion with a three-layer model over a low frequency range
44. Inversion with a three-layer model with prior depth
45. Inversion with a three-layer model at high frequency with prior depth
46. Inversion with a three-layer model with prior $V_p$
47. Inversion with a three-layer model at high frequency with prior $V_p$
48. Inversion with a N-layer model accepting LVZ ($V_s$ only)
49. Inversion with a N-layer model accepting LVZ ($V_p$ and $V_s$ )
50. Inversion with a N-layer model rejecting LVZ by the diagonal method
51. Comparison of a three-layer and N-layer inversions
52. Inversion with a three-layer model with heterogeneous layers
53. Inversion with a three-layer model with heterogeneous layers
54. Comparison of three type of parameterizations
55. Inversion of first higher mode alone: no prior information
56. Inversion of first higher mode alone: depth between 1 and 20 m/s
57. Inversion of the fundamental mode alone
58. Inversion of the fundamental and the first higher mode
59. Inversion of the fundamental and the first higher mode: narrow band
60. Joint inversion of the Love and Rayleigh fundamental modes
61. Composite dispersion curve
62. Inversion of the composite curve assuming fundamental mode
63. Inversion of the composite curve with mode identification(a)
64. Inversion of the composite curve with mode identification(b)
65. Reference model for auto-correlation inversion
66. Grids in frequency-slowness for auto-correlation pre-processing
67. Inversion of the auto-correlation curves
68. Inversion of the ellipticity alone
69. Join inversion of the dispersion curve and the ellipticity peak
70. Theoretical model for synthetic ambient vibrations
71. Spectral curves of the central station of array A to C
72. Array geometries and their f-k responses
73. Single source wavefield: signals
74. Single source wavefield: influence of window length
75. Single source wavefield: f-k for arrays A and C
76. Single source wavefield: array responses at 6.5 Hz
77. f-k analysis for array C: influence of window length
78. f-k analysis for array A and B
79. Average dispersion from f-k analysis
80. Inversion of average dispersion from f-k analysis
81. High resolution analysis for arrays A, B and C
82. Inversion of dispersion curves from high resolution analysis
83. Influence of time window lengths on auto-correlation curves
84. Azimuth-inter-distance plot
85. Calculated and selected auto-correlation samples
86. Grids in frequency-slowness for auto-correlation pre-processing
87. Inversion of auto-correlation curves
88. Inversion of Love and Rayleigh fundamental modes
89. Local map of the test site
90. Recorded signals for East-West $P-S_V$ refraction line
91. Refraction results for profile East-West
92. Refraction results for profile North-South
93. Triggered surface waves along $P-S_V$ profiles: spectra
94. Triggered surface waves along $P-S_V$ profiles: f-k analysis
95. Refraction results for $S_H$ profile
96. Array geometries
97. Spectral curves of the central station
98. Theoretical array response
99. Results of the frequency-wavenumber method
100. Average of apparent dispersion curves
101. Inversion of the average dispersion curve
102. Inversion of the average dispersion curve and ellipticity peak
103. Results of the high resolution frequency-wavenumber method
104. Calculated and selected auto-correlation samples
105. Azimuth-inter-distance plot
106. Grids in frequency-slowness for auto-correlation pre-processing
107. Inversion of auto-correlation curves
108. Prior information carried by parameterization: LVZ
109. Prior information carried by parameterization: velocity jump
110. Prior information carried by parameterization: interpolation
111. Prior information carried by parameterization: random interpolation
112. Prior information carried by parameterization: bissection
113. Prior information carried by parameterization: diagonal
114. Prior information carried by parameterization: scaled diagonal
115. Prior information carried by parameterization: scaled interpole