\relax 
\providecommand \babel@aux [2]{\global \let \babel@toc \@gobbletwo }
\@nameuse{bbl@beforestart}
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyField@AuxAddToFields[1]{}
\providecommand\HyField@AuxAddToCoFields[2]{}
\babel@aux{french}{}
\@writefile{toc}{\contentsline {section}{\numberline {1}Séismes}{2}{section.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {1.1}Introduction}{2}{subsection.1.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {1.2}Ondes P et S}{2}{subsection.1.2}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Ondes P}}{2}{figure.1}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces Ondes S}}{2}{figure.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {1.3}Différence de vitesse de propagation}{2}{subsection.1.3}\protected@file@percent }
\gdef \LT@i {\LT@entry 
    {1}{277.37936pt}\LT@entry 
    {1}{185.98767pt}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces 6 km/s (ondes P) vs 4 km/s (ondes S)}}{3}{figure.3}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {2}Théorie}{3}{section.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1}Principe}{3}{subsection.2.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2}DSP}{3}{subsection.2.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.1}Acquisition des données}{3}{subsubsection.2.2.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.2}Extraction des temps d'arrivée}{5}{subsubsection.2.2.2}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Exemple d'un enregistrement de sismographe}}{5}{figure.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.3}Convolution}{5}{subsubsection.2.2.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.4}Propriétés algébriques de la convolution}{7}{subsubsection.2.2.4}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces numpy confirme ce résultat}}{9}{figure.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.5}Moyennage}{11}{subsubsection.2.2.5}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.6}Transformée de Fourier discrète}{11}{subsubsection.2.2.6}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.7}Radix-2 decimation-in-time (DIT) - Factorisation Cooley-Tukey}{12}{subsubsection.2.2.7}\protected@file@percent }
\ExplSyntaxOn \cs_if_free:NT \pgfsyspdfmark {\cs_set_eq:NN \pgfsyspdfmark \@gobblethree }\ExplSyntaxOff 
\ExplSyntaxOn 
\char_set_catcode_space:n {32}
\tl_gset:cn {c__nicematrix_1_tl}{\seq_gset_from_clist:Nn \g__nicematrix_size_seq {1,2,2,1,3,3}}
\ExplSyntaxOff 
\ExplSyntaxOn 
\char_set_catcode_space:n {32}
\tl_gset:cn {c__nicematrix_2_tl}{\seq_gset_from_clist:Nn \g__nicematrix_size_seq {1,2,2,1,3,3}}
\ExplSyntaxOff 
\pgfsyspdfmark {pgfid20}{13910647}{38507454}
\pgfsyspdfmark {pgfid21}{14238327}{37758776}
\savepointas{mcoeffdiag1-t}{pgfid23}{0pt}{0pt}
\savepicturepage{pgfid23}{13}
\pgfsyspdfmark {pgfid23}{15200483}{37758776}
\savepointas{mcoeffdiag1}{pgfid23}{0pt}{0pt}
\pgfsyspdfmark {pgfid26}{15200483}{37758776}
\savepointas{mcoeffdiag2-t}{pgfid28}{0pt}{0pt}
\savepicturepage{pgfid28}{13}
\pgfsyspdfmark {pgfid28}{19039609}{37758776}
\savepointas{mcoeffdiag2}{pgfid28}{0pt}{0pt}
\pgfsyspdfmark {pgfid31}{19039609}{37758776}
\pgfsyspdfmark {pgfid32}{13910647}{37382764}
\pgfsyspdfmark {pgfid33}{14238327}{36607872}
\savepointas{mcoeffdiag3-t}{pgfid35}{0pt}{0pt}
\savepicturepage{pgfid35}{13}
\pgfsyspdfmark {pgfid35}{15200483}{36607872}
\savepointas{mcoeffdiag3}{pgfid35}{0pt}{0pt}
\pgfsyspdfmark {pgfid38}{15200483}{36607872}
\savepointas{mcoeffdiag4-t}{pgfid40}{0pt}{0pt}
\savepicturepage{pgfid40}{13}
\pgfsyspdfmark {pgfid40}{19039609}{36607872}
\savepointas{mcoeffdiag4}{pgfid40}{0pt}{0pt}
\pgfsyspdfmark {pgfid43}{19039609}{36607872}
\pgfsyspdfmark {pgfid44}{13910647}{36231860}
\pgfsyspdfmark {pgfid45}{13910647}{36231860}
\pgfsyspdfmark {pgfid46}{16490319}{36231860}
\pgfsyspdfmark {pgfid47}{17171893}{36231860}
\pgfsyspdfmark {pgfid48}{20907325}{36231860}
\pgfsyspdfmark {pgfid49}{21153086}{37164039}
\savepicturepage{pgfid51}{13}
\pgfsyspdfmark {pgfid51}{21153086}{37164039}
\pgfsyspdfmark {pgfid52}{21153086}{37164039}
\pgfsyspdfmark {pgfid53}{21398847}{38507454}
\pgfsyspdfmark {pgfid54}{21726527}{37758776}
\savepointas{mrecurrence1-t}{pgfid56}{0pt}{0pt}
\savepicturepage{pgfid56}{13}
\pgfsyspdfmark {pgfid56}{22761690}{37758776}
\savepointas{mrecurrence1}{pgfid56}{0pt}{0pt}
\pgfsyspdfmark {pgfid59}{22761690}{37758776}
\pgfsyspdfmark {pgfid60}{26168950}{37758776}
\pgfsyspdfmark {pgfid61}{21398847}{37382764}
\pgfsyspdfmark {pgfid62}{22555375}{36607872}
\pgfsyspdfmark {pgfid63}{22761690}{36607872}
\savepointas{mrecurrence2-t}{pgfid65}{0pt}{0pt}
\savepicturepage{pgfid65}{13}
\pgfsyspdfmark {pgfid65}{26168950}{36607872}
\savepointas{mrecurrence2}{pgfid65}{0pt}{0pt}
\pgfsyspdfmark {pgfid68}{26168950}{36607872}
\pgfsyspdfmark {pgfid69}{21398847}{36231860}
\pgfsyspdfmark {pgfid70}{21398847}{36231860}
\pgfsyspdfmark {pgfid71}{24124533}{36231860}
\pgfsyspdfmark {pgfid72}{24806107}{36231860}
\pgfsyspdfmark {pgfid73}{27531793}{36231860}
\pgfsyspdfmark {pgfid74}{27777554}{37164039}
\savepicturepage{pgfid76}{13}
\pgfsyspdfmark {pgfid76}{27777554}{37164039}
\pgfsyspdfmark {pgfid77}{27777554}{37164039}
\savepointas{mcoeffpairs1-t}{pgfid79}{0pt}{0pt}
\savepicturepage{pgfid79}{13}
\pgfsyspdfmark {pgfid79}{29684055}{42422999}
\savepointas{mcoeffpairs1}{pgfid79}{0pt}{0pt}
\savepointas{mcoeffpairs2-t}{pgfid83}{0pt}{0pt}
\savepicturepage{pgfid83}{13}
\pgfsyspdfmark {pgfid83}{29684055}{41298309}
\savepointas{mcoeffpairs2}{pgfid83}{0pt}{0pt}
\savepointas{mcoeffpairs3-t}{pgfid87}{0pt}{0pt}
\savepicturepage{pgfid87}{13}
\pgfsyspdfmark {pgfid87}{29684055}{38859502}
\savepointas{mcoeffpairs3}{pgfid87}{0pt}{0pt}
\savepointas{mcoeffpairs4-t}{pgfid91}{0pt}{0pt}
\savepicturepage{pgfid91}{13}
\pgfsyspdfmark {pgfid91}{29684055}{37704098}
\savepointas{mcoeffpairs4}{pgfid91}{0pt}{0pt}
\savepointas{mcoeffimpairs1-t}{pgfid95}{0pt}{0pt}
\savepicturepage{pgfid95}{13}
\pgfsyspdfmark {pgfid95}{29684055}{36579408}
\savepointas{mcoeffimpairs1}{pgfid95}{0pt}{0pt}
\savepointas{mcoeffimpairs2-t}{pgfid99}{0pt}{0pt}
\savepicturepage{pgfid99}{13}
\pgfsyspdfmark {pgfid99}{29684055}{35454718}
\savepointas{mcoeffimpairs2}{pgfid99}{0pt}{0pt}
\savepointas{mcoeffimpairs3-t}{pgfid103}{0pt}{0pt}
\savepicturepage{pgfid103}{13}
\pgfsyspdfmark {pgfid103}{29684055}{33015911}
\savepointas{mcoeffimpairs3}{pgfid103}{0pt}{0pt}
\savepointas{mcoeffimpairs4-t}{pgfid107}{0pt}{0pt}
\savepicturepage{pgfid107}{13}
\pgfsyspdfmark {pgfid107}{29684055}{31891221}
\savepointas{mcoeffimpairs4}{pgfid107}{0pt}{0pt}
\savepicturepage{pgfid110}{13}
\pgfsyspdfmark {pgfid110}{2797020}{31023689}
\savepicturepage{pgfid111}{13}
\pgfsyspdfmark {pgfid111}{3036226}{31023689}
\savepicturepage{pgfid112}{13}
\pgfsyspdfmark {pgfid112}{3275432}{31023689}
\savepicturepage{pgfid113}{13}
\pgfsyspdfmark {pgfid113}{3514638}{31023689}
\savepointas{cdiagmult-d}{pgfid114}{0pt}{0pt}
\savepicturepage{pgfid114}{13}
\pgfsyspdfmark {pgfid114}{19598886}{26567239}
\savepointas{cdiagmult}{pgfid114}{0pt}{0pt}
\savepointas{crec-d}{pgfid118}{0pt}{0pt}
\savepicturepage{pgfid118}{13}
\pgfsyspdfmark {pgfid118}{22630732}{26567239}
\savepointas{crec}{pgfid118}{0pt}{0pt}
\savepicturepage{pgfid122}{13}
\pgfsyspdfmark {pgfid122}{2797020}{25249965}
\savepicturepage{pgfid123}{13}
\pgfsyspdfmark {pgfid123}{3036226}{25249965}
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.8}IFFT}{13}{subsubsection.2.2.8}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.9}Passage du domaine temporel au domaine fréquentiel}{14}{subsubsection.2.2.9}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.2.10}Corrélation croisée}{14}{subsubsection.2.2.10}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Modélisation de la propagation des ondes sismiques}{15}{subsection.2.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.3.1}Calcul du temps de propagation selon iasp91}{15}{subsubsection.2.3.1}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces TauPy}}{16}{figure.6}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {7}{\ignorespaces iasp91}}{16}{figure.7}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.3.2}Tabulation et interpolation}{16}{subsubsection.2.3.2}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {8}{\ignorespaces Visualization des deux tables précalculées}}{16}{figure.8}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.4}Multilatération}{16}{subsection.2.4}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.1}Fonction d'erreur}{17}{subsubsection.2.4.1}\protected@file@percent }
\savepointas{p1-d}{pgfid128}{0pt}{0pt}
\savepicturepage{pgfid128}{17}
\pgfsyspdfmark {pgfid128}{4631739}{39749686}
\savepointas{p1}{pgfid128}{0pt}{0pt}
\savepointas{p2-d}{pgfid132}{0pt}{0pt}
\savepicturepage{pgfid132}{17}
\pgfsyspdfmark {pgfid132}{6647904}{39749686}
\savepointas{p2}{pgfid132}{0pt}{0pt}
\savepointas{p3-d}{pgfid136}{0pt}{0pt}
\savepicturepage{pgfid136}{17}
\pgfsyspdfmark {pgfid136}{8296830}{39749686}
\savepointas{p3}{pgfid136}{0pt}{0pt}
\savepointas{p4-d}{pgfid140}{0pt}{0pt}
\savepicturepage{pgfid140}{17}
\pgfsyspdfmark {pgfid140}{10395929}{39749686}
\savepointas{p4}{pgfid140}{0pt}{0pt}
\savepointas{p5-d}{pgfid144}{0pt}{0pt}
\savepicturepage{pgfid144}{17}
\pgfsyspdfmark {pgfid144}{12487716}{39749686}
\savepointas{p5}{pgfid144}{0pt}{0pt}
\savepointas{p6-t}{pgfid149}{0pt}{0pt}
\savepicturepage{pgfid149}{17}
\pgfsyspdfmark {pgfid149}{18780438}{40593456}
\savepointas{p6}{pgfid149}{0pt}{0pt}
\savepointas{p7-t}{pgfid169}{0pt}{0pt}
\savepointas{p8-t}{pgfid175}{0pt}{0pt}
\savepicturepage{pgfid175}{17}
\pgfsyspdfmark {pgfid175}{31050814}{40593456}
\savepointas{p8}{pgfid175}{0pt}{0pt}
\savepicturepage{pgfid169}{17}
\pgfsyspdfmark {pgfid169}{29681813}{40593456}
\savepointas{p7}{pgfid169}{0pt}{0pt}
\savepointas{p9-t}{pgfid221}{0pt}{0pt}
\savepicturepage{pgfid221}{17}
\pgfsyspdfmark {pgfid221}{26597492}{39102523}
\savepointas{p9}{pgfid221}{0pt}{0pt}
\savepointas{p11-s}{pgfid226}{0pt}{0pt}
\savepicturepage{pgfid226}{17}
\pgfsyspdfmark {pgfid226}{38048280}{41317355}
\savepointas{p11}{pgfid226}{0pt}{0pt}
\savepointas{p10-d}{pgfid228}{0pt}{0pt}
\savepicturepage{pgfid228}{17}
\pgfsyspdfmark {pgfid228}{19858220}{34000750}
\savepointas{p10}{pgfid228}{0pt}{0pt}
\savepicturepage{pgfid232}{17}
\pgfsyspdfmark {pgfid232}{2797020}{32683476}
\savepicturepage{pgfid233}{17}
\pgfsyspdfmark {pgfid233}{3036226}{32683476}
\savepicturepage{pgfid234}{17}
\pgfsyspdfmark {pgfid234}{3275432}{32683476}
\savepicturepage{pgfid235}{17}
\pgfsyspdfmark {pgfid235}{3514638}{32683476}
\savepicturepage{pgfid236}{17}
\pgfsyspdfmark {pgfid236}{3753844}{32683476}
\savepicturepage{pgfid237}{17}
\pgfsyspdfmark {pgfid237}{3993050}{32683476}
\savepicturepage{pgfid238}{17}
\pgfsyspdfmark {pgfid238}{4232256}{32683476}
\savepicturepage{pgfid239}{17}
\pgfsyspdfmark {pgfid239}{4471462}{32683476}
\savepicturepage{pgfid240}{17}
\pgfsyspdfmark {pgfid240}{4710668}{32683476}
\savepicturepage{pgfid241}{17}
\pgfsyspdfmark {pgfid241}{4949874}{32683476}
\@writefile{lof}{\contentsline {figure}{\numberline {9}{\ignorespaces Implémentation de la fonction d'erreur}}{17}{figure.9}\protected@file@percent }
\@writefile{toc}{\contentsline {subsubsection}{\numberline {2.4.2}Méthode de Nelder-Mead}{17}{subsubsection.2.4.2}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {10}{\ignorespaces Une itération de Nelder-Mead sur un espace de dimension 2}}{18}{figure.10}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {2.5}Magnitude sismique}{18}{subsection.2.5}\protected@file@percent }
\@writefile{toc}{\contentsline {section}{\numberline {3}Résultats}{19}{section.3}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1}Tests}{19}{subsection.3.1}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {11}{\ignorespaces rs2025flrsdg - Mon estimation (avec les données RaspberryShake)}}{20}{figure.11}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {12}{\ignorespaces rs2025fwmrzv - Mon estimation (avec les données RaspberryShake)}}{21}{figure.12}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {13}{\ignorespaces rs2025fwmrzv - Estimation de l'USGS}}{22}{figure.13}\protected@file@percent }
\bibcite{convolution_video}{1}
\bibcite{fft_algorithm_video}{2}
\bibcite{fft_matrix_factorizations}{3}
\bibcite{eq_sources}{4}
\bibcite{seismic_waves}{5}
\bibcite{gfz-1-d-earth-models}{6}
\bibcite{earthquake_data_centers}{7}
\bibcite{cfcs_lecture}{8}
\bibcite{penn_state_anova}{9}
\bibcite{nelder_mead}{10}
\bibcite{broadband_magnitude}{11}
\@writefile{toc}{\contentsline {section}{\numberline {4}Bibliographie}{23}{section.4}\protected@file@percent }
\gdef \@abspage@last{23}