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Etudes sur le comportement du champ magnétique terrestre durant les périodes de polarité stable

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(1)Etudes sur le comportement du champ magnétique terrestre durant les périodes de polarité stable Claire Bouligand. To cite this version: Claire Bouligand. Etudes sur le comportement du champ magnétique terrestre durant les périodes de polarité stable. Géophysique [physics.geo-ph]. Institut de physique du globe de paris - IPGP, 2006. Français. �tel-00676769�. HAL Id: tel-00676769 https://tel.archives-ouvertes.fr/tel-00676769 Submitted on 6 Mar 2012. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(15) j. ¾. |. kmlonSp. qrpts. u. kwvQxSytzQp{s. }>~-Y€2C‚:ƒD„ Y†"e~ ‡ ˆ ‰Šˆ ‹VŒŽ ‘R’“•”Q–˜—&™ šœ›š™ Ž Rž>Ÿh ”•’¡“•’¢£™O¤:’9Œ¥Œ’ ‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰ ¦ ˆ ‰¨§ ©C’–˜—&™ šœ›ªš*™ Ž •ž>Ÿ‘ ”•’¡—•«¥Ÿh¬ Œ‘ ”•’‰i‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰ ­ ˆ ‰¨§K‰Šˆ ®R™š’>«”•Œ¥’“•‘Œ¥’9–>Ÿ’t‰)‰i‰)‰)‰i‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰ ­ ˆ ‰¨§K‰¨§ ®K’9«#¯°™ Œ¥£™°Ÿ‘¬ •«=Ÿh’9šœ›e¬ Œ’>¢‘¢‘’>« ‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰ ± ˆ ‰¨§K‰³² ®K’9«#¯°™ Œ¥£™°Ÿ‘¬ •«,«›&™°Ÿ£™ ¢’9«´‰)‰i‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰rˆYµ ˆ ‰³² ©C’–˜—&™ šœ›ª›&™ ¢‘ž>¬ š™ Ž •ž¶Ÿh‘ ”•’i‰i‰)‰)‰i‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰rˆ2¦ ˆ ‰³²R‰Šˆ ®R™š’>«”•Œ¥’‘•“•Œ’>–>Ÿh’·‰i‰)‰)‰i‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰rˆ2¦ ˆ ‰³²R‰¨§ ®K’9«#¯°™ Œ¥£™°Ÿ‘¬ •«=Ÿh’9šœ›e¬ Œ’>¢‘¢‘’>« ‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰¸§ µ ˆ ‰³²R‰³² ®K’9«#¯°™ Œ¥£™°Ÿ‘¬ •«,«›&™°Ÿ£™ ¢’9«´‰)‰i‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰¸§ ¹ ˆ ‰º »6Œ¬ ¼•¢‘ž>š*™°Ÿ‘ ”•’V’¶ŸP¬ ŒŽ4™°•‘«™°Ÿh¬ A“•”Qšž>š¬ ‘Œ’w‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰½º§ ¿ ƒ<À·~:eƒ:ÁªÂRÃDÃ:€2ÀK~:~<ÀK~eQÄ"ÀÅÁAÁ †"ÆǃDÄ[ÂR2†[e~DÁœ~Sƒ:ÆÉÈ€†ËÊSƒ<ÀÅÁA‚<À·ÌWȁC‚CÍ<~:•ÆɁtÁ9ƒ:€Ä" œ ÆɁS‚:ÈÅÄ"†ËÁ9ÂK2†"e~HÁ>YÂR2†"Á>2†"ÊSƒ<ÀQ‚DƒÎ„Ï:•ÆÉÃ{Ã:Â&Ä"ȁeÆÉ•Ìe~<È42†ËÊЃ:ÀÑ Ò-‡ §K‰Šˆ »6Œž>«’>Ÿh™°Ÿh¬ Q“•’9««šO”•¢‘™°Ÿh¬ •«,”•šœž9Œ¥‘ ”•’>«r‰i‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰½º4­ §K‰¨§ ¤:’9«ÓŸ“•’>«D—4Ôśe¬ Ÿh—•Õ>«’>«DÖ[¬ •“•™ š’>4Ÿ˜™ ¢’9«C“•’>«Dšœ¬K“RÕ9¢‘’>«C›&™ ¢ž9¬ š™ Ž •ž¶Ÿh Å”R’9«C«¥Ÿh™°Ÿh«¥Ÿ‘ ”•’9«É¦Kˆ §K‰¨§K‰Šˆ ×,¬ šœ›-¬ ŒÓŸh’>š’>ŸP™°¢‘ž ™Ÿh¬ Œ’؉i‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰¸¦Kˆ §K‰¨§K‰¨§ ®ÅŸ˜™Ÿh‘¬ •&™ Œ¥Ÿhž ‰)‰i‰)‰i‰)‰)‰i‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰¸¦°º §K‰¨§K‰³² ٍ‘«ÓŸhŒ¥‘¼•”RŸ‘¬ ÚŽ ™ ”•««¥‘’>••’‰)‰i‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰¸¦ ­ §K‰¨§K‰º Û,‘¢‘™ ´‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰¸¦ ± §K‰³² »6Œ¬ ›•Œž>Ÿhž>«“•’«¥ÔŚž¶ŸhŒ¥‘’¡“•”Q–˜—&™ šœ›ªš¬YÔ ’>’¶ŸP“•’¢£™›&™ ¢ž9¬Y¯°™ Œ‘™°Ÿh¬ *«¥ž9–9”R¢£™ Œ’ ‰¸¦ ± §K‰³²R‰Šˆ ®ÅÔŚž¶ŸhŒ¥‘’9«#’¶ŸP–9¬ •“RŸh¬ •«#«¥”•Œ¢‘’9«#–>¬K’¶Üœ–9‘’>4Ÿh«P“•’iÝ)™ ”R««Þ‰)‰i‰)‰i‰)‰)‰i‰)‰¸¦ ± §K‰³²R‰¨§ ®ÅÔŚž¶ŸhŒ¥‘’9«#“•™ •«¢‘’>«P«¥‘šO”R¢£™°Ÿ‘¬ •«=”•šž>Œ Å”R’9«ß‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰à­ µ.

(16) §. á•âã ä<åÎæVåèçéâá:ê?ëdìPåèç §K‰º. §K‰¨¦ §K‰³­. ,ÀÅÁ>‚:ÀÅÁOÆ·C‚

(17) ÅÄ[ÀÅÁiÃ:Â&Ä"ÀeÆÉ•Ìe~<À42†ËÊЃ:ÀÅÁÁ¶YÂR2†"Á>2†"ÊSƒ<ÀKÁÿÃ:•€Y2†[€‚<ÀKÁÆÉÀÅÁ ƒ:€2ÀÅÁ‚<À ‚:†"€2Àń 2†[-~ |e‡ ²R‰Šˆ î K›•Œ’>««¥‘¬ “•’¢£™O“•«¥ŸhŒ¥‘¼•”KŸh‘¬ Ú“•’9«“•Œ’9–¶Ÿh¬ •«#›&™ ¢ž9¬ š™ Ž Rž>Ÿh ”•’9«=‰i‰)‰i‰)‰)‰i‰)‰ˆYµ ­ ²R‰¨§ ×,¬ šœ›&™ Œ™ ‘«¥¬ Ú“•’>«P“R‘«¥ŸŒ¼•”RŸh¬ •« ›RŒž9“RŸh’>«’>ŸP¬ ¼•«¥’9Œ¥¯ ž9’>«/‰)‰)‰i‰‰)‰i‰)‰i‰)‰)‰i‰)‰ˆYµ ± ²R‰³² »6Œ«’’9Q–9¬ š›RŸ’¡“•’9«’>ŒŒ’>”•Œ«P“•’šœ’9«”RŒ’ ‰‰i‰)‰)‰i‰)‰i‰)‰)‰i‰‰)‰i‰)‰i‰)‰)‰i‰)‰ˆ ˆ2§ ²R‰º è™ ¢‘“&™Ÿh‘¬ *’>Ÿ$™ ›R›•¢‘– ™°Ÿ‘¬ A“R’)¢‘™Ošž¶Ÿh—•¬Å“•’ª‰‰i‰)‰)‰i‰)‰i‰)‰)‰i‰‰)‰i‰)‰i‰)‰)‰i‰)‰ˆ ˆ2§ ²R‰¨¦ î5Ÿh”R“•’“Rž>Ÿ˜™°‘¢‘¢ž9’A ï -ø˜ô¶ñ"ó3üÅûªô¶ñò ñ"ó‘ô¶ñ"óBõò ö-÷Rò ö‘ø˜ùúœòYû üÐø¶ñËóBõ,ý ø¶öŠþú*ù9þÅø¶ö¨ôòYû4ò ó3üRô¶ñ$þ ó  hø˜õ¶ñ"óBùüeò ö<þ4ò ñòÚ ò Vø˜õ¶ñø þ   ú*øòô hø¶ú*ø¶ü&ñ ø hù ˜ô,‰)‰i‰)‰i‰)‰)‰i‰‰)‰i‰)‰i‰)‰)‰i‰)‰ˆ ˆ º. Ò. ×,¬ R«ž9 ”•’>•–9’>«V›e¬ ”•Œ#¢£™šœ¬K“Rž9¢‘«h™°Ÿ‘¬ «¥Ÿh™°Ÿh«¥Ÿh ”•’¡“•”Q–˜—&™ šœ›Q›•™ ¢‘ž>¬ š*™°Ž •ž>Ÿ‘ ”•’P‰à­ º §K‰º•‰Šˆ ‹VŒ‘Ž ‘•’V“R’9«Œ”•›KŸh”•Œ¥’9«P“•’«¥ÔŚž¶ŸhŒ¥‘’ ‰i‰)‰)‰i‰)‰i‰)‰)‰i‰‰)‰i‰)‰i‰)‰)‰i‰)‰à­ º §K‰º•‰¨§ ×,¬ •«¥’9‘¢C›e¬ ”•Œ#¢‘™Oš¬Å“•ž>¢‘‘«™°Ÿh¬ A«ÓŸ˜™°Ÿ‘«¥Ÿ‘ ”•’i‰i‰)‰i‰)‰)‰i‰‰)‰i‰)‰i‰)‰)‰i‰)‰à­4í î5Ÿh”R“•’*“•ž¶Ÿ˜™ ¢‘¢ž9’ªïèðWñBò ñ"ó‘ô¶ñËóBõò öS÷Rò öŠòÅø˜ùúœòYû üÐø¶ñ"óBõ#ý ø¶öŠþÿú*ù9þÅø¶ö3ö ó3üÅûÿò üeþô  úú*ø¶ñ   õ˜ùüRô¶ó"þÅø ¥ò ñ"óBùüRôɉ)‰)‰i‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰‰i‰)‰)‰i‰)‰i‰)‰)‰i‰‰)‰i‰)‰i‰)‰)‰i‰)‰à­ ± î5Ÿh”R“•’“•ž>Ÿh™ ‘¢¢‘ž9’ï•ðWñò ñ"ó‘ô¶ñËóBõò ö ÷Rò öŠòÅø˜ùúœòYû üÐø¶ñ"óBõSý ø¶öŠþ)ú*ù9þÅø¶ö3ö ó3üÅûOò üeþþ  üeò ú*ù¡ü  ú*ø ^óBõò ö-ô¶ó3 ú ÅöŠò ñËóBùü ‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰‰i‰)‰)‰i‰)‰i‰)‰)‰i‰‰)‰i‰)‰i‰)‰)‰i‰)‰à­ ±. 2ƒ:‚<À ‚<ÀKÁ ƒD„ 2ƒ<ÂR2†[e~DÁÚYÀÅÆÉÃ6W€2ÀÅÄËÄ[ÀÅÁڂ:ÀÞÄ"!Š†Ë~eYÀÅ~DÁ †3YÈ ‚:ƒw„°Ï<Â&ÆÉÃwÌWȁeÆÉ•Ìe~:È$# 2†"ÊSƒ<ÀQÀÅ~- €ÀÄ[ÀKÁ„°Ï<€2-~:Á% & &€œÀ4ª|('•€*),+& #ÒD|.-wÂ0/1ÇÃD•€Y2†[€œ‚:ÀÅÁOÃ:€2&2Ä"ÁÆÉ•Ìe~:È$# 2†"ÊSƒ<ÀKÁƷ•€†Ë~:Á ‚:À1Á9ƒ:4€ 3Â&„ À |ŇC| º•‰Šˆ ©C’9«šœ’9«¥”•Œ’>«$š™ Ž •ž¶Ÿh Å”R’9«#š™ Œ•’9«w‰)‰i‰)‰‰i‰)‰)‰i‰)‰i‰)‰)‰i‰‰)‰i‰)‰i‰)‰)‰i‰)‰ˆ2¦ § º•‰Šˆ ‰Šˆ 5#–9 ”•«Ÿ‘¬  ‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰‰i‰)‰)‰i‰)‰i‰)‰)‰i‰‰)‰i‰)‰i‰)‰)‰i‰)‰ˆ2¦ § º•‰Šˆ ‰¨§ ‹VŒ‘Ž ‘•’V“R’9«P™ •¬ š™ ¢‘’9«=š*™°Ž •ž>Ÿ‘ ”•’>«Pš™ Œ¥‘•’>« ‰)‰)‰i‰‰)‰i‰)‰i‰)‰)‰i‰)‰ˆ2¦ ² º•‰Šˆ ‰³² 6¬Å“•ž9¢‘«h™Ÿh‘¬ A“•’¢£™«¬ ”•Œ–>’)“R’9«$™ •¬ š™ ¢‘’9«=š*™ Ž •ž>Ÿ‘ ”•’9« ‰i‰)‰i‰)‰)‰i‰)‰ˆ2¦ í º•‰Šˆ ‰º ©C’9«P™ •¬ š™ ¢‘’9«=š*™°Ž •ž>Ÿ‘ ”•’>«P“R’)–>¬ ”•ŒÓŸh’¢‘¬ RŽ ”•’9”RŒ#8“ 7³¬ •“•’ ‰i‰)‰i‰)‰)‰i‰)‰ˆ2¦ ¹ º•‰Šˆ ‰¨¦ 9Pž>«¬ ¢”RŸh¬ AŸh’>š›e¬ Œ¥’9¢‘¢’V“•’>«P›RŒ;¬ :&¢«#“•’«”•ŒÓÖ"™ –9’i‰i‰)‰)‰i‰‰)‰i‰)‰i‰)‰)‰i‰)‰ˆY­ µ º•‰¨§ Ù¬ ••ž9’>«$’¶ŸŸhŒh™°Ÿh’>š’>4Ÿ ‰i‰)‰i‰)‰)‰i‰)‰i‰)‰‰i‰)‰)‰i‰)‰i‰)‰)‰i‰‰)‰i‰)‰i‰)‰)‰i‰)‰ˆY­ º º•‰¨§K‰Šˆ ®Kž9¢’9–¶Ÿh‘¬ Q“R’9«“•¬ •Rž9’9«Ú‰)‰)‰i‰)‰i‰)‰‰i‰)‰)‰i‰)‰i‰)‰)‰i‰‰)‰i‰)‰i‰)‰)‰i‰)‰ˆY­ º º•‰¨§K‰¨§ 9Pž>“•”•–¶Ÿh‘¬ ™°”=› < ¢‘’ ‰i‰)‰)‰i‰)‰i‰)‰‰i‰)‰)‰i‰)‰i‰)‰)‰i‰‰)‰i‰)‰i‰)‰)‰i‰)‰ˆY­ º º•‰¨§K‰³² × ™ ¢£™°Ž ’¡’9ªŸh’>š›•« ‰)‰i‰)‰)‰i‰)‰i‰)‰‰i‰)‰)‰i‰)‰i‰)‰)‰i‰‰)‰i‰)‰i‰)‰)‰i‰)‰ˆY­4í º•‰¨§K‰º ®K¬ šœš*™Ÿh‘¬  ‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰‰i‰)‰)‰i‰)‰i‰)‰)‰i‰‰)‰i‰)‰i‰)‰)‰i‰)‰ˆY­ ± .

(18) áRâVã,ä:åtæVåèçféâá:ê?ëdìPå=ç. ². º•‰¨§K‰¨¦ º•‰³² º•‰º. ^. ‡. × ¬ šœ›&™ Œh™°‘«¬ *“•’$«¥Ÿ˜™°–?>Å«#–>¬ ŒŒ¥’9«¥›-¬ R“&™ 4ŸA@“•’>«,Ÿ˜™°”A“B7³’R›•™ •«¬ Ú“•DCОE , Œ’>Ÿ«Î‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰#ˆY­ ¹ 9ž9«¥”•¢Ÿh™°Ÿh«=‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰#ˆ2í § î5Ÿh”R“•’i“Rž>Ÿ˜™°‘¢‘¢ž9’G ï F$ø˜ùúœòYû üÐø¶ñ"óBõdý ø¶öŠI þ H;ò ^ó"ò ñËóBùüRJ ô ¶ø¶ñ K,ø˜ø¶üÉ?õ L(hùüR1 ô MNM$ò üeþ ONP; QSR M$T=OVUÇ ò WAXhùú ôYø;ò Bô (YX>òÅõ˜øVúœòYû üÐø¶ñËóBõ)ò üÐùúœò ö  =÷ hù?ýdö‘ø˜ôM‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰#ˆ2í°º. ie~D„4Ä"ƒ:Á †"e~:ÁÀœÃ6À€Á9Ã6Àń 2†[-ÀÅÁ ¾W¾C| ¦K‰Šˆ 6¬Å“•ž>¢‘‘«™°Ÿh¬ A«ÓŸ˜™°Ÿ‘«¥Ÿ‘ ”•’¡“•”Q–˜—&™ šœ›Q›&™ ¢‘ž>¬ š™ Ž •ž¶Ÿh‘ ”•’Þ‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰è§ §Kˆ ¦K‰¨§ î5¯ ¬ ¢‘”RŸ‘¬ \  @ ¢‘¬ RŽOŸh’9Œ¥š’¡“R’9A « ]&”•–>Ÿ”&™°Ÿ‘¬ •«#“R”–˜—&™°š›QŽ ž9¬ š*™ Ž •ž>Ÿ‘ ”•’ ‰)‰)‰i‰)‰è§ § ² ¦K‰³² Û,¢£™ Î‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰‰i‰)‰i‰)‰)‰i‰)‰i‰)‰)‰)‰)‰)‰i‰)‰i‰)‰)‰i‰)‰è§ § ¦ _. Z. -~<ÀÅÁ*‚G! ÈYƒD‚<À1Á9ÈÅÄ[ÀK„ Y†"e~:~:ÈÀÅÁOÃ6eƒ:€ÚÄ"! È42ƒD‚<Àÿ‚<ÀÅÁœÂ•~:eÆÉÂ&Ä"†[ÀKÁÚ|('•€` & •€. ¾& &'.

(19)

Figure

Fig. 1b); state III, corresponding to state I after reflection in the equatorial plane (i.e
Table 1. Model g: estimates of the typical correlation times τ m n for the Gauss coefficients with low degrees.
Table 2. Model g: time-averaged estimates ¯ g m n and ¯ h m n of µ (g m n ) and µ (h m n ) (at the surface of the Earth and down-continued to the core–mantle boundary, CMB) during the period of reverse polarity.
Figure 3. Model g: estimates ¯ K(x n m , x m n , 0) of the variances. The black dots represent the values for the x = g coefficients and the grey crosses the values for the x = h coefficients
+7

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Il a introduit le rapport anharmonique appel´ e aussi birapport de 4 points align´ es... On discute apr` es les cas

Proposition 2 Si f admet un extremum local ou global au point a, si f est d´ erivable au point a, et si a n’est pas une borne de l’intervalle I, alors f 0 (a) = 0.. Remarque

Ses ´ etudes ont principalement port´ e sur la th´ eorie de la mesure, les int´ egrales de Lebesgue, les s´ eries de Fourier et le calcul diff´ erentiel. Il apporta de