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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{Second draft array course outline \\
Using Ambient Vibration Array Techniques for Site Characterization \\
Monday, 21st Nov. 2005 to 25th Nov. 2005}
\date{\today}
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\textbf{{\Large
Using Ambient Vibration Array Techniques \\
\vspace{0.5cm}
for Site Characterization \\
\vspace{0.5cm}
}
Monday, $21^{st}$ Nov. 2005 to Friday, $25^{th}$ Nov. 2005 \\
Universit\'{e} Joseph Fourier Grenoble, France
}
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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.

\section*{Contributions}

\begin{tabular}{p{3cm}p{12cm}}
organized by & LGIT and IGUP \\
hosted by & UJF-Grenoble\\
presented by & C\'ecile Cornou, Matthias Ohrnberger, Marc Wathelet\\
supported by & SESAME (EU-Project EVG1-CT-2000-00026) and Sismovalp (Interreg IIIB, Alpine
Space)
\end{tabular}

\afterpage{\clearpage}

\section*{Course outline}

\begin{tabular}{p{2.5cm}p{11cm}p{2.0cm}}
 & Monday & \\ \hline\hline
 & & \\
 13:30 & Reception and welcome & \\ \hline
 %& Technical issues and program overview & \\
 % distribution of course material
 & & \\
 14:00-14:45 & Physical background of ambient vibrations & Lecture \\ \hline
 %& Overview of the physical background of ambient vibration studies. The
 %  Presentation covers the basic assumptions about the ambient vibration wave field,
 %  the linkage between subsurface structure, wave field propagation properties, 
 %  the use of ambient vibration array analysis for observation and recovery of 
 %  site characteristics (site response).
 %& \\ 
% & physical background / introduction to ambient vibration analysis - Goals!
% \begin{itemize}
% \item what is known about the nature of noise - nature of ambient noise (overview/resume)
% \item link between measurement structure and site response
% \end{itemize} & Cecile \\
 & & \\
 \coffeebreak{14:45-15:00} \\
 & & \\
 15:00-17:15 & Basic array processing concepts (frequency wavenumber, f--k) & Lecture \\ \hline
 %& In this lecture the basic array processing concept is presented from
 %the viewpoint of general multi-channel filter operations. As underlying
 %operation, the shift-and-sum technique in time domain is used as point 
 %of departure before transferring the problem into the frequency wavenumber
 %(f--k) domain. 
 %& \\
% \begin{itemize}
% \item Overview of methods
% \item Arrays as multi channel filter operation (shift and sum)
% \item f-k domain
% \end{itemize} & Matthias \\
\end{tabular}
%\afterpage{\clearpage}
\vspace{1.5cm}

\begin{tabular}{p{2.5cm}p{11cm}p{2.0cm}}
 & Tuesday & \\ \hline\hline
 & & \\
9:00-10:30 &  Array geometry and f--k response & Lecture \\ \hline
 %& The discrete spatial sampling of the continuous seismic wave field by 
 %small groups of seismic stations (arrays) has severe consequences regarding
 %the resolution and the uniqueness of propagation characteristics which are 
 %estimated from array data records. This lecture aims to demonstrate these
 %effects for simple linear array layouts as well as 2D-array settings and 
 %outlines the relation between array geometry and resulting estimation capabilities. 
 %As key concept for estimating the capability of an array layout, the array
 %response function is introduced.
 %& \\
% & Spatial sampling issues:
% \begin{itemize}
% \item Linear array example - relation, interdependence between N, D, d with array response
% \item extension to 2D - geometries  (sub-items here)
% \item limits of array resolution/aliasing -- wavelength criteria
%       (table display of relation D, N $\rightarrow$ $k_{min}$, $k_{max}$
% \item what a priori information can be helpful for estimating the target wavelength range
%\end{itemize} & Matthias \\
 & & \\
 \coffeebreak{10:30-10:45} \\
 & & \\
 10:45-12:15 &  Array geometry and f--k response & Exercises \\ \hline
 %& The practical will allow the participants to apply the acquired knowledge
 %about array geometries and to evolve a feeling how a change in array layout
 %is reflected in the corresponding array response. A software tool which facilitates 
 %these tasks is presented and its handling will be explained in detail.
 %& \\
%% \begin{itemize}
% \item Tutorial for array design - considering the previously discussed matter
% \item test behavior with single source (links to f-k computation and 
% grid sampling issues - parameter of f-k computation explained here)
% \item (all practical done with build\_array)
% \end{itemize} & Matthias \\
 & & \\
 \lunchbreak{12:15-14:00} \\ 
  & & \\
 14:00-15:30 &  Signal database software (GEOPSY) & Tutorial\\ \hline
 %& The core software module of the SESARRAY software package, named GEOPSY, will be presented.
 %The participants will be trained in a step by step tutorial to create
 %data bases and to use the standard tools for data visualization, manipulation and
 %standard signal processing. 
 %& \\
% & Tutorial for data base creation and capabilities / tools within GEOPSY 
%   (data examples used: M2- single/multi source wave field) & Marc \\
 & & \\
 \coffeebreak{15:30-15:45} \\
 & & \\
 15:45-17:15 \ldots &  Conventional f--k processing & Exercises \\ \hline
 %& Based on the data base example created in the previous practical, the standard
 %f--k algorithm will be applied to estimate dispersion curves. 
 %The discussion of the analysis results will give new insight into dependencies 
 %between the observability of dispersion curves, array geometries and the 
 %subsurface structure.
 %& \\
% & Tutorial for f--k analysis of single/multi M2 model data sets & Marc \\
% & Observation of frequency limits - connection with both array geometry 
%   and site structure (HP-filter effect) & Matthias\\
\end{tabular}
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\begin{tabular}{p{2.5cm}p{11cm}p{2.0cm}}
 & Wednesday & \\ \hline\hline
 & & \\
 9:00-10:30 &  High resolution f--k (Capon's method) & Lecture\newline and\newline Exercise \\ \hline
 %& This lecture introduces the background of a widely used method in the realm of
 %ambient vibration array analysis: the high resolution f--k method after Capon (1969). 
 %After method presentation, participants will apply the method to the introduced
 %data sets for deriving dispersion curves. The results are to be compared
 %with the standard f--k method.
 %& \\
%9:00-9:45 & Viewing f-k in the context of cross correlation (covariance) matrix & Matthias \\
% & Spatial weighting of sensor couple contributions $\rightarrow$ Capon's method & Matthias \\
% & Technical implementation - stabilization by block-averaging, sensor normalization and
%   diagonal loading before hermitian matrix inversion  & Matthias \\
% & & \\
%9:45-10:30 & hands-on - processing M2 data sets with Capon's method & Matthias \\
% & discussion of results - comparison to f--k  & Matthias \\
 & & \\
 \coffeebreak{10:30-10:45} \\
 & & \\
  10:45-12:15 & Spatial autocorrelation method (SPAC) & Lecture\newline and \newline Exercise \\ \hline
 %& The spatial autocorrelation technique (SPAC) was introduced by Aki (1957) 
 %and is probably the most widely used method for ambient vibration array analysis worldwide.
 %The background of the method is introduced and its differences to the f--k techniques are outlined.
 %Newer developments in recent times are based on Aki's original work and will be presented
 %in this lecture. After the method's introduction, participants will apply the method
 %to the data sets and a direct comparison with f--k results will be discussed.
 %& \\
%10:45-11:30 & Introduction to SPAC (Aki) -- Assumptions, etc. & Cecile \\
% & Extension for imperfect array-layouts (Bettig et al., 2001) & Cecile \\
% & Technical implementation -- Parameters, etc. & Marc \\
% & & \\
%11:30-12:15 & Hands-on - processing M2 data sets with SPAC  & Marc \\
% & Use of tools for comparing to f--k results -- discussion & Marc \\
  & & \\
  \lunchbreak{12:15-14:00} \\ 
  & & \\
  14:00-15:30 & Dispersion curve (DC) inversion & Lecture \\ \hline
%14:00-14:45 & Basics of Inversion \\
 %& Within this lecture, the fundamentals of inversion theory are introduced 
 %making use of the problem at hand - the inversion of dispersion curve data.
 %The lecture introduces the forward problem, the concept of parameter space, 
 %data space, misfit functions and, for the non-linear problem to be solved, 
 %the non-uniqueness problem. For the solution to non-linear inversion problems,
 %direct search methods will be reviewed with a special focus on the Neighborhood 
 %Algorithm (Sambridge 1999) being the core of the inversion software program package.
 %& \\
% & Forward problem -- inverse problem & Marc \\
% & Linear problems - overview - examples for data space, model parameter space & Marc \\
% & non-linear problems, overview of approaches & Marc \\
% & DC-inversion - our non-linear problem to be attacked & Marc \\
% & & \\
%14:45-15:30 & outline of NA-sampling - benefits - 
%    general problem of sampling techniques, etc.& Marc \\
 & & \\
  \coffeebreak{15:30-15:45} \\
 & & \\
  15:45-17:15 \ldots & DC inversion & Tutorial \\ \hline
  %& A step by step procedure will be applied to a theoretical 
  %dispersion curve in order to identify critical issues in the inversion
  %task. In particular the effects of 1D initial model parameterization
  %and parameter ($v_P$, $v_S$, $\rho$, \ldots) range restrictions on the
  %final outcome of the inversion will be demonstrated and discussed.
  % old
  %In a first tutorial to dispersion curve inversion, the participants will
  %be introduced into the use of software modules. A step by step procedure
  %will be applied to a synthetically computed dispersion curve in order to 
  %identify critical issues in the inversion task. In particular the effects of
  %1D-earth model parameterization and parameter range restrictions on the final 
  %outcome of the inversion will be demonstrated and discussed.
  % very old
  %Interdependence of 1D earth model parameterization,
  %limits on parameter ranges and available data will be studied as well as the
  %interpretation of the NA-model set result.
  & \\
% & use of na\_viewer (dinver!) & Marc \\
% & Tutorial for creation of synthetic DC and inversion & Marc \\
% & effects of restricting search ranges, type of parameterization, what are the pitfalls!& Marc \\
 & & \\
 20:00-\ldots & Workshop Dinner & \\
\end{tabular}
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\begin{tabular}{p{2.5cm}p{11cm}p{2.0cm}}
 & Thursday & \\ \hline\hline
 & & \\
  9:00-10:30 &  DC inversion & Exercise \\ \hline
  %& The course attendees will be guided to invert the analysis results
  %which have been obtained from f--k (standard and high-resolution)
  %and SPAC computations the day before. A combined interpretation of
  %analysis results is necessary and enter into the decision on the usable
  %frequency range for the inversion target (estimated dispersion curve).
  %& \\
% & Importing analysis results for M2 data sets (f--k, Capon, SPAC)& Marc \\
% & Combining/editing obtained results for inversion target & Marc\\
% & Inversion  & Marc\\
 & & \\
  \coffeebreak{10:30-10:45} \\
 & & \\
  10:45-12:15 & Discussion of inversion results & Moderated discussion \\ \hline
  %& The inversion results obtained by the course participants
  %will be compared with the true underlying model. 
  %The cause of apparent discrepancies between obtained inversion 
  %results and the true model, as well as the variability
  %of results will be discussed. 
  %A general discussion about the cause of the variability 
  %of the inversion results, its cause and its significance 
  & \\
%  & General discussion on results obtained for M2-model & Matthias \\
%  & Important: Pointing out frequency limitation, interpretation problems, etc. & Matthias \\
  & & \\
  \lunchbreak{12:15-14:00} \\ 
  & & \\
  14:00-15:30 & Array analysis and DC inversion of test data sets I & Exercise \\ \hline
  %& In this practical, a blind test experiment will be performed among the
  %course attendees. For a synthetically modeled ambient vibration wave field,
  %participants choose their own array layouts, analyze the selected records
  %with f--k methods and SPAC technique and finally derive the underlying velocity
  %model. 
  %& \\
% & Free practical for participants on predefined data sets (3 data sets) -- 
%   contains choosing array layouts from set of virtual sensor locations, analysis with 
%   all array methods and inversion & \\
 & & \\
  \coffeebreak{15:30-15:45} \\
 & & \\
  15:45-17:15 \ldots & Array analysis and DC inversion of test data sets II & Exercise \\ \hline
  %& Continuation of the previous practical. Now a real data set will be
  %investigated with the goal to derive the site characteristics. 
  %& \\
% & Free practical for participants on predefined data sets (2 data sets) -- 
%   contains choosing array layouts from set of virtual sensor locations, analysis with 
%   all array methods and inversion\\
% & & \\
% & data sets are 1 synthetic but no longer so easy than M2 and 1 real data example\\
 & & \\
\end{tabular}
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\begin{tabular}{p{2.5cm}p{11cm}p{2.0cm}}
 & Friday & \\ \hline\hline
 & & \\
  9:00-10:30 &  Discussion of results from data sets & Moderated discussion \\ \hline
 %& In a short presentation of 5 minutes, participants have the opportunity
 %to present their results for both synthetic and real data examples. 
 %the results shall be discussed among the group and an interpretation
 %of the results for both cases shall be given. 
 %& \\
% & Report of participants about their results & \\
% & general discussion of variations obtained for different data sets (M2, 2nd synthetic and real) & \\
 & & \\
 \coffeebreak{10:30-10:45} \\
 & & \\
  10:45-12:15 & Summary of SESAME findings & Lecture \\ \hline
  %& The final course lecture summarizes the various steps involved for
  %the task of ambient vibration array analysis and site characterization
  %by the inversion of 1D earth models. Important findings from the 
  %SESAME project as well as open questions in this field will be discussed.
  %& \\
%  & Presentation by Cecile, Marc and Matthias presenting the main findings within SESAME\\
%  & in particular: recommendations, what are the still open questions and: THIS is not a black box!\\
  & & \\
  \lunchbreak{12:15-14:00} \\ 
  & & \\
  14:00-\ldots & Departure of Participants & Open\newline discussion \\ \hline
 & & \\
\end{tabular}

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