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\author{Marc Wathelet (marc@geopsy.org)\\
        Cecile Cornou (Cecile.Cornou@obs.ujf-grenoble.fr)\\
	Matthias Ohrnberger (mao@geo.uni-potsdam.de)}

\title{Third draft array course outline \\
Using Ambient Vibration Array Techniques for Site Characterisation \\
Monday, April 3rd, 2006 to April 7th, 2006}
\date{\today}
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\textbf{{\Large
Using Ambient Vibration Array Techniques \\
\vspace{0.5cm}
for Site Characterisation \\
\vspace{0.5cm}
}
Monday, April $3^{rd}$ 2006 to Friday, April $7^{th}$ 2006 \\
Institute of Geosciences, University of Potsdam, Germany
}
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In recent years, the number of research papers dealing with
ambient vibration analysis methods has increased considerably.
Clearly, the interest in these methods originates from both
the economical attractive cost benefit ratio and the straightforward 
data acquisition. Being a non-destructive passive technique, these methods also 
complement geotechnical and/or active geophysical methods 
within highly populated regions.

Within the SESAME project (''Site EffectS assessment using AMbient Excitation'',
EU-Project EVG1-CT-2000-00026) detailed research has been
accomplished to identify the capabilities and limitations of
ambient vibration analysis techniques. Within this context a set 
of software tools has been developed to ease the processing
and interpretation of ambient vibration wave field recordings.

The main findings of the SESAME project however show, that ambient
vibration array analysis techniques have to be applied with care.
It requires not only a careful measurement, but especially 
the interpretation and the inversion of analysis results need a (self-)critical 
review. From these conclusions it has been agreed among SESAME-partners, that it
is highly necessary to distribute the software tools together with
adequate training.

The main purpose of this course is 
to achieve the necessary understanding among the 
course participants for the problems related to these techniques.
By doing so, we try to enable a correct usage of the software tools
and to avoid misuse of these methods (''black-box usage'').
The course fees are intended to support current and future improvements of
the software package, distributed under an open source and free license.

Due to the number of registrations we received with the first course in Grenoble 2005, 
we are organizing this second edition (and, who knows, a third one) to give everybody 
a chance to participate.

\section*{Contributions}

\begin{tabular}{p{3cm}p{12cm}}
organised by & IGUP and LGIT\\
hosted by & Institute of Geosciences at University of Potsdam\\
presented by & C\'ecile Cornou, Matthias Ohrnberger, Marc Wathelet\\
supported by & SESAME (EU-Project EVG1-CT-2000-00026) and Sismovalp (Interreg IIIB, Alpine
Space) and all participants of the first edition.
\end{tabular}

\pagebreak

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\section*{Course outline}

This is program which may be subject to slight changes in the future.

\newday{Monday}

\headline{9:00-9:30}
{Reception and welcome}{~}
\courseItem{Technical issues and program overview}

\headline{9:30-10:30}
{Physical background of ambient vibrations}{Lecture}
\courseItem{Overview of the physical background of ambient vibration studies.}
\courseItem{Basic assumptions and state of the art about the nature of the ambient vibration wave field.}
\courseItem{The linkage between subsurface structure and wave field propagation properties.}
\courseItem{The use of ambient vibration array analysis for observation and recovery of site characteristics (site response).}

\relaxtime{10:30-10:45}{Coffee break}

\headline{10:45-12:15}
{Single station measurement, H/V}{Lecture}
\courseItem{Interpretations for horizontal to vertical spectral ratio technique (H/V).}
\courseItem{Relationships between Rayleigh ellipticity and $S_H$ transfer function.}
\courseItem{Effects of experimental conditions.}

\relaxtime{12:15-14:00}{Lunch break}

\headline{14:00-15:30}
{Single station measurement, H/V}{Exercises}
\courseItem{A very short introduction to Geopsy database.}
\courseItem{Geopsy tools for H/V interpretation.}

\relaxtime{15:30-15:45}{Coffee break}

\headline{15:45-18:00}
{Single station measurement, H/V}{Exercises}
\courseItem{Geopsy tools for H/V interpretation (continued).}
\courseItem{Mapping H/V results with Geopsy.}

\pagebreak

\newday{Tuesday}

\headline{9:00-10:30}
{Basic array processing concepts (frequency wavenumber, f--k)}{Lecture}
\courseItem{Overview array processing methods.}
\courseItem{The intuitive shift-and-sum technique in time domain and its transposition into the frequency wavenumber (f--k) domain.}
\courseItem{Discrete spatial sampling of the continuous seismic wave field (by small groups of seismic stations - arrays) : concepts of resolution and aliasing.}
\courseItem{Resolution and aliasing of simple linear array layouts and generalisation to bi-dimensional array settings.}
\courseItem{Relation between array geometry and resulting estimation capabilities: rules of thumb and the array response function.}

\relaxtime{10:30-10:45}{Coffee break}

\headline{10:45-12:15}
{Array geometry and f--k response}{Exercice}
\courseItem{Design of array geometry with build\_array software: optimum usage and functionalities.}
\courseItem{Building experience on how modifications in array layout affect the theoretical array performances.}

\relaxtime{12:15-14:00}{Lunch break}

\headline{14:00-15:30}
{Conventional f-k processing}{Exercises}
\courseItem{Data management for array processing with Geopsy.}
\courseItem{Application of the conventional f-k algorithm to estimate the dispersion curves from synthetic signals}

\relaxtime{15:30-15:45}{Coffee break}

\headline{15.30-18:00}
{Conventional f--k processing}{Exercises}
\courseItem{Building your own experience with f-k input parameters (frequency sampling, time window length, ...)}
\courseItem{From the discussion of the analysis results, new insight into dependencies between the observability of dispersion curves, array geometries and signal spectra (high pass filter effect and H/V).}

\pagebreak

\newday{Wednesday}

\headlineshort{9:00-10:30}
{High resolution f--k (Capon's method)}{Lecture and exercise}
\courseItem{Background of a widely used method, the high resolution f--k method after Capon (1969).}
\courseItem{Application of the method to the synthetic data set, previously mentioned.}
\courseItem{Comparison with the conventional f--k method.}

\relaxtime{10:30-10:45}{Coffee break}

\headlineshort{10:45-12:15}
{Spatial autocorrelation method (SPAC)}{Lecture and exercise}
\courseItem{Background of the spatial autocorrelation technique (SPAC) introduced by Aki (1957).}
\courseItem{Ongoing developments around Aki's original work.}
\courseItem{Application of the method to the synthetic data set, previously mentioned.}
\courseItem{Discussion of differences with f--k techniques.}

\relaxtime{12:15-14:00}{Lunch break}

\headline{14:00-15:30}
{Synthetic data sets, high resolution f--k and SPAC}{Exercise}
\courseItem{Comparison of the three methods used for array processing, advantages and limitations of each approach.}

\relaxtime{15:30-15:45}{Coffee break}

\headline{15:45-18:00}
{Dispersion curve (DC) inversion}{Lecture}
\courseItem{Short introduction to the fundamentals of inversion theory.}
\courseItem{Direct search methods based on a random sampling, and particularly the Neighbourhood algorithm.}
\courseItem{Specific issues solved for the inversion dispersion curves: robustness of the forward computation, non-uniqueness of the final solution.}

\relaxtime{20:00-\ldots}{Workshop Dinner}

\pagebreak

\newday{Thursday}

\headline{9:00-10:30}
{DC inversion}{Exercise}
\courseItem{Introduction to dinver software.}
\courseItem{Inversion of theoretical dispersion curve in order to identify critical issues.}
\courseItem{Model parameterisation and parameter range ($v_P$, $v_S$, $\rho$), a natural way to introduce prior information and to reduce the non-uniqueness.}

\relaxtime{10:30-10:45}{Coffee break}

\headline{10:45-12:15}
{DC inversion}{Exercise}
\courseItem{Inversion of the analysis results which have been obtained from f--k (standard and high-resolution) and SPAC computations the day before.}
\courseItem{Combining the results of arrays with distinct apertures and geometries: decision on the usable frequency range for the inversion target.}

\relaxtime{12:15-14:00}{Lunch break}

\headline{14:00-15:30}
{Discussion of inversion results}{Moderated discussion}
\courseItem{Comparison of the inversion results obtained by the course participants with the true underlying model.}
\courseItem{Discussion of the causes and the significance of apparent discrepancies between obtained inversion results.}

\relaxtime{15:30-15:45}{Coffee break}

\headline{15:45-18:00 \ldots}
{Array analysis and DC inversion of test data sets I}{Exercise}
\courseItem{Blind test experiment performed among the course attendees on a synthetic case.}
\courseItem{Choice of the array layouts, analyse the selected records with f--k and SPAC techniques and finally derive the underlying velocity model.}

\pagebreak

\newday{Friday}

\headlineshort{9:00-10:30}
{Discussion of results from data sets}{Moderated discussion}
\courseItem{Comparison of the individual results obtained during the blind test.}
\courseItem{General discussion of experience gained during this complete test.}

\relaxtime{10:30-10:45}{Coffee break}

\headline{10:45-12:15}
{Course summary}{Lecture}
\courseItem{Summary of the various steps involved for the task of ambient vibration array analysis and site characterisation by the inversion of one-dimensional earth models.}
\courseItem{Ongoing developments around ambient vibration techniques and currently open questions.}
\courseItem{Recall of the advantages and limitations of using ambient vibrations to site characterisation.}

\relaxtime{12:15-14:00}{Lunch break}

\headlineshort{14:00-\ldots}{Departure of Participants}{Open discussion}

\pagebreak

\section*{Suggested readings}

\begin{description}

\item Aki, K. (1957). Space and time spectra of stationary stochastic waves, with special reference to microtremors, \textit{Bull. Earthq. Res. Inst.} \textbf{35}, 415--456.

\item Bard, P.-Y. (1999). Microtremor measurements: a tool for site effect estimation?, State-of-the-art paper, \textit{2nd International Symposium on the Efects of Surface Geology on Seismic Motion}, Yokohama,
Balkema, \textbf{3}, 1251--1279.

\item Bettig, B., P.-Y. Bard, F. Scherbaum, J. Riepl, F. Cotton, C. Cornou and D. Hatzfeld (2001). Analysis of dense array noise measurements using the modified spatial auto-correlation method (SPAC). Application to the Grenoble area., \textit{Bolletino di Geofisica Teorica ed Applicata} \textbf{42}, 281--304.

\item Capon, J. (1969). High-resolution frequency-wavenumber spectrum analysis, \textit{Proc. IEEE} \textbf{57}, 1408--1418.

%\item Krim, H. and Viberg, M. (1996). Two Decades of Array Signal Processing Research. The parametric Approach., \textit{IEEE Signal Processing Magazine}, \textbf{13}, 4, 67--94.

\item Sambridge, M. (1999a). Geophysical inversion with a neighbourhood algorithm: I. Searching a parameter space, \textit{Geophys. J. Int.} \textbf{138}, 479--494.

\item Sambridge, M. (1999b). Geophysical inversion with a neighbourhood algorithm: II. Appraising the ensemble, \textit{Geophys. J. Int.} \textbf{138}, 727--746.

\item Tokimatsu, K. (1997). Geotechnical site characterization using surface waves, \textit{Earthquake Geotech. Eng.}, Ishiliara (ed.), Balkema, Rotterdam, 1333-1368.

\end{description}

%A paper copy of these publications will be sent to the attendees before the beginning of the course.

All deliverables and reports of the SESAME project are available at (especially, D18.06, D19.06, D24.13 may be of interest): http://sesame-fp5.obs.ujf-grenoble.fr/SES\_TechnicalDoc.htm.


\section*{Registration and Fees}

To offer the best attention to each of the course attendees, the maximum number of participants is fixed to 15. A minimum of 8 registrations is required for the organisation of this cession.

Online registration (http://www.geopsy.org/arraycourse/login.php) is open until Friday March 10$^{th}$ 
2006. If the number of applicants is greater than 15, the organisers reserve their rights to select the participants. 

The fees include lectures, practical exercises, workshop dinner and coffee breaks. 
One computer per participant will be made available during the exercises. 
Profits will be devoted to the development and improvement of the SESARRAY softwares.

\vspace{0.5cm}

\begin{center}
\begin{tabular}{lcp{4cm}} \hline
Organisation & Number of participants & \centering Price \newline (euros, excluding VAT) \tabularnewline \hline
SESAME partners & 1                   & \centering 1000 \tabularnewline
                & 2                   & \centering 1500 \tabularnewline
                & n $>$ 2             & \centering 1000+n*500 \tabularnewline \hline
Sismovalp       & 1                   & \centering 1000 \tabularnewline
                & 2                   & \centering 1500 \tabularnewline
                & n $>$ 2             & \centering 1000+n*500 \tabularnewline \hline
Others          & 1                   & \centering 2500 \tabularnewline
                & 2                   & \centering 4000 \tabularnewline
                & n $>$ 2             & \centering 4000+(n-2)*1000 \tabularnewline \hline
\end{tabular}
\end{center}

\vspace{0.5cm}

Special discounts may be offered if really needed, please contact Pierre-Yves Bard \\ (pierre-yves.bard@obs.ujf-grenoble.fr).

\section*{Contacts}

\begin{tabular}{ll}
Marc Wathelet & marc@geopsy.org \\
Matthias Ohrnberger & mao@geo.uni-potsdam.de \\
 & \\
Geopsy  & http://www.geopsy.org \\
SESAME & http://sesame-fp5.obs.ujf-grenoble.fr \\
Sismovalp & http://www-lgit.obs.ujf-grenoble.fr/sismovalp
\end{tabular}

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