... vibrations¹

Also called ambient noise, microtremor, ...However, the word "noise" is ambiguous because it generally designates all apparently random variations not explained by the current scientific model. For ambient vibration methods the noise is separated in coherent and incoherent noise. The first category contains valuable information.

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... aperture^1.1

Maximum distance between any pair of sensors

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... GEOPSY^1.2

Database with a graphical user interface (Qt libraries, www.trolltech.com) dedicated to seismic prospecting and developed during this thesis. Its dynamic signal loader is able to work on very long recordings (hours) with an efficient memory and time consumption. It works on any desktop PC (Linux or Windows) or Mac.

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... values^2.1

Also called data curve, measurements, or target curve.

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... parameters^2.2

Also called unknowns or, simply, parameters.

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... constructed^2.3

This function is called the misfit, the cost, the error or the residual function. It is a real number

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... four^2.4

According to the time needed for one computation.

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...\space ^2.5

The number of dimension of the ensemble is $n=n_{param}$

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... cells^2.6

It is a unique decomposition of the space into $n$ cells around $n$ points $p_i$ . The cell around point $p_i$ is defined by the ensemble of points that are closer to $p_i$ than to whatever other point $p_j$ where $j \ne i$ .

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... parameters^2.7

For example, in the case of a one-dimensional ground structure (see chapter 4), the $V_p$ profile may be fixed from the results of a refraction survey. The thicknesses of the $V_s$ layers may be set independently, eventually with a more refined discretization. The conditions induced by the natural limits of Poisson's ratio have to take the depth parameters into account, besides usual $V_p$ and $V_s$ .

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... rules^3.1

The summation of indices take place when one or more indices appear two times inside a product. For instance, the formula $x_{ki} y_{il}$ is in fact equal to $\sum_{i=min}^{max}x_{ki} y_{il}$

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... indices^3.2

In the pair $(m,n)$ $m$ is always different from $n$ , and pairs $(m,n)$ and $(n,m)$ are strictly equivalent

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... root^3.3

In the computer sense, the perfect root is obtained when the values of the function are less then the internal precision.

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... 40\%^4.1

The depth of the best models is around 10 m. Considering a misfit of 0.05 as acceptable, the depth may varies between 8 and 14 m, which makes an error between 20 and 40%.

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... parameterization^4.2

For $V_s$ , the prior density of probability is not uniform in this parameterization, as explained at the beginning of section 4.2

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...figCaseC3layers^5.1

The range is extended to 4 Hz in this case to get larger frequency range for the fundamental mode. Tests with a limit at 5.5 Hz do not work because the velocity rise is not sufficiently marked.

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... coding^B.1

parameter values explicitly written in the code, compilation is necessary to change it

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