1\babel@toc {french}{}\relax 
 2\contentsline {section}{\numberline {1}Séismes}{2}{section.1}%
 3\contentsline {subsection}{\numberline {1.1}Introduction}{2}{subsection.1.1}%
 4\contentsline {subsection}{\numberline {1.2}Ondes P et S}{2}{subsection.1.2}%
 5\contentsline {subsection}{\numberline {1.3}Différence de vitesse de propagation}{2}{subsection.1.3}%
 6\contentsline {section}{\numberline {2}Théorie}{3}{section.2}%
 7\contentsline {subsection}{\numberline {2.1}Principe}{3}{subsection.2.1}%
 8\contentsline {subsection}{\numberline {2.2}DSP}{3}{subsection.2.2}%
 9\contentsline {subsubsection}{\numberline {2.2.1}Acquisition des données}{3}{subsubsection.2.2.1}%
10\contentsline {subsubsection}{\numberline {2.2.2}Extraction des temps d'arrivée}{5}{subsubsection.2.2.2}%
11\contentsline {subsubsection}{\numberline {2.2.3}Convolution}{5}{subsubsection.2.2.3}%
12\contentsline {subsubsection}{\numberline {2.2.4}Propriétés algébriques de la convolution}{7}{subsubsection.2.2.4}%
13\contentsline {subsubsection}{\numberline {2.2.5}Moyennage}{11}{subsubsection.2.2.5}%
14\contentsline {subsubsection}{\numberline {2.2.6}Transformée de Fourier discrète}{11}{subsubsection.2.2.6}%
15\contentsline {subsubsection}{\numberline {2.2.7}Radix-2 decimation-in-time (DIT) - Factorisation Cooley-Tukey}{12}{subsubsection.2.2.7}%
16\contentsline {subsubsection}{\numberline {2.2.8}IFFT}{13}{subsubsection.2.2.8}%
17\contentsline {subsubsection}{\numberline {2.2.9}Passage du domaine temporel au domaine fréquentiel}{14}{subsubsection.2.2.9}%
18\contentsline {subsubsection}{\numberline {2.2.10}Corrélation croisée}{14}{subsubsection.2.2.10}%
19\contentsline {subsection}{\numberline {2.3}Modélisation de la propagation des ondes sismiques}{15}{subsection.2.3}%
20\contentsline {subsubsection}{\numberline {2.3.1}Calcul du temps de propagation selon iasp91}{15}{subsubsection.2.3.1}%
21\contentsline {subsubsection}{\numberline {2.3.2}Tabulation et interpolation}{16}{subsubsection.2.3.2}%
22\contentsline {subsection}{\numberline {2.4}Multilatération}{16}{subsection.2.4}%
23\contentsline {subsubsection}{\numberline {2.4.1}Fonction d'erreur}{17}{subsubsection.2.4.1}%
24\contentsline {subsubsection}{\numberline {2.4.2}Méthode de Nelder-Mead}{17}{subsubsection.2.4.2}%
25\contentsline {subsection}{\numberline {2.5}Magnitude sismique}{18}{subsection.2.5}%
26\contentsline {section}{\numberline {3}Toutes les pièces mises ensembles}{19}{section.3}%
27\contentsline {subsection}{\numberline {3.1}Fonctionnement}{19}{subsection.3.1}%
28\contentsline {subsection}{\numberline {3.2}Résultats}{23}{subsection.3.2}%
29\contentsline {section}{\numberline {4}Précision et erreur}{25}{section.4}%
30\contentsline {subsection}{\numberline {4.1}Cas réduit avec propagation rectiligne dans un millieu transparent, homogène, isotrope, linéaire à longues distances et 4 detecteurs}{25}{subsection.4.1}%
31\contentsline {subsection}{\numberline {4.2}Méthode de Monte-Carlo pour les cas plus complexes}{28}{subsection.4.2}%
32\contentsline {section}{\numberline {5}Bonus}{30}{section.5}%
33\contentsline {section}{\numberline {6}Bibliographie}{31}{section.6}%