Imagerie microonde : reconstruction quantitative du profil de permittivité complexe d'hétérogénéités enterrées.
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(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Imagerie microonde : reconstruction quantitative du profil de permittivité complexe d’hétérogénéités enterrées. Cédric Dourthe — Armel de La Bourdonnaye — Christian Pichot. N˚ 3294 Novembre 1997. THÈME 4. ISSN 0249-6399. apport de recherche.
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(296) zty~ippi¸ x«ntu~ntuxiwup t°·N³p
(297) ~np1p
(298) ~z|pÆwyp
(299) 4o³
(300) z|l} p
(301) @, p
(302) z n} Vtyp
(303) ~z pÆwyx«z|p
(304) lb´ ~nty¯Dvnpvz|tuwuty³p8}vnotu~ntyotup
(305) Bw±x¹º}~n$z|tu}~n~np
(306) wywupi¸ wywup8
(307) }~npip8wupxi|x{
(308) z|m
(309) p~n}~ wytu~n³Gx{typ p4wyx¹º}i~n
(310) zty}~~npwuwyp8N}vwupBo³
(311) zln} p @, z|xi~ tuB¯Dv ® pwuwyp4wutu~n³Gxityp4wu}{´ Gxiwupop~zp
(312) wywup$´ðt xi~n,wupo³
(313) z|l} p
(314) B a® } \wup~n}io po³
(315) z|l} p
(316) t°z|³
(317) |x{ztuip pBzÉVNp B} ~ $¸ F ® x{vz|p,o&³$z|ln} p
(318) ,p3bnwytut°z|³
(319) p xi~n(w ® p
(320) x{p&wytu¡npn}i²nzp~z p w ® xinn}blpovnwuztuVvn2 p I}ivn
(321) p,p
(322) zGxizpvnz}vz,p~z|}ivn|xi~zw ® }¡bp$uz vìbz¢ wcp
(323) zovnwë´ z|t°¹º³¯Dvnp
(324) ~z|tupwuwy2 p v°*¢ Cw#}vn }i~n~np p&w ® }¡bp$zv~nptuo&xi¥p&vnp<´É³}iwyvzty}i~ ¸ ~²n~ È po&³$z|ln} p
(325) p,zÉbp}¡x{¡ntywutuz|p}~z³p
(326) oo&p
(327) ~z(³
(328) z³ ³$pwu}n³p
(329) t vu¢GÈ ¢Gqn$ È C+w⸠pzpln~ntu¯Dvnp t°z|³
(330) |x{ztuip p¼³}wyvbz|tu}~ È}vn#wyp
(331) ¯Dvnp
(332) wywupxivn
(333) vn~np typ
(334) zty}i~ p¼p3´ lnplnpB~ ® pz¼ntuVtuwy³
(335) ¥ty³
(336) p'µlxi¯DvnpBt°z|³
(337) |x{zty}X ~ I}bz|tuo&tu|xz|tu}~Æ¥wu}¡x{wy_p $Èf}~ vntup~z µ a® p3
(338) pwuwyp
(339) ~z|¼³vwuz|x{z| o&xitupz|p~zz|mL} [zpvnpp~z|p
(340) o& pxiwy
(341) vnwI¸ p
(342) zzp8x{z|tup8}}p ® x xizppzÉVp po&³$z|ln} p8xiv:xi p8w±xp
(343) }~nz|v$´. >. úúÄé`aûb.
(344) II I I$+
(345) D. z|tu}~ ® }¡bp$z|p~b¹º}vntu xi~n p4}wuµ:pzp
(346) ¸ ~ ® ty~z³p
(347) p\p
(348) ~ xiz|tuvnwutyp
(349) µ w ® p$Vz|p
(350) ~ntu}~Kovwuztu¹º³¯Dvnp~ztyp
(351) wywup ® v~Kxiwy¥i}t°z|lnop ® tuo&xi¥p
(352) tup pzÉVp @, vì£weÈNxiv Gxi p#}¡bp
(353) zp
(354) ~Dzp³tywuwyvo&tu~n³
(355) =xicvn~8lnxioty~n
(356) t p~z p ³p~ xi~n
(357) p¼xz|tu}{´ z|po}p
(358) wywup,xi¡tuz|xitup{¸ F¼xi~n=v~p
(359) }~ z|p
(360) o&Ènvn~p¼³
(361) ¥vnwyxitu|x{zty}i~pz }}³
(362) p(x{²~ a® xio³
(363) wytu}p
(364) =wup ³3´ vnw°zx{z=}¡zp~Dvn n³
(365) ³ p
(366) o&op
(367) ~Dz¸ ~8p(n}N}ip(xiwu} ® xinnwutu¯Vvp vn~npz|pl~nty¯Dvnp pn³p{x{zty}i~ p ty}~zty~Dvnt°z|³
(368) v D5waxinwytu¯Dvn³p¼³
(369) poop~zxGpvn
(370) m xi~nwup }o&xitu~np pw ® tyo&xi¥iptup ® }¡bp
(371) z xi~n w ® pxi
(372) pwuty¡p vì{È D5wâ¸. . 5 2-!4
(373) . !. * -- . 6
(374) ) " 2.
(375) ³ ²~ntupn³
(376) ³ poop~z vu¢i¢Èf¢Q5wâÈ }~Np
(377) vz}~n~nx±zpwup,lnxio.z|}{zxiw2µ'w ® tu~z|³
(378) tupvn pw ® }¡bp$z_S. ~4vbz|tuwytu|xi~zwyp
(379) o op~n}izxz|tu}~n¯Dvnpp
(380) wywup. 3 U V 4 , .6:?@/ A . x ip. % F f >g, . 6:?@/
(381) 3U V , . 6:?@/u6|oB¢Èì j ? . t . A . A 6 6tu~n}~. p$z. f% A Z R K, ?@/bf=, .6 . 6:?@/$ . 6 j ? ^`. <¢ ¸. Tvtywup=lxio t°·axi
(382) z³ µ¼w ® p3bz³typ
(383) vn p w ® }¡Vp
(384) zp
(385) zTGx{wy
(386) vnwy³ vnwyx¼wytu¥~np p=opvnp {- xi~wupotywutyp
(387) v tuS. 3 U V # , .W6:?@/BA f >=, . 6:?@/ 3U V_, . 6b?@/z6 j . k2{@6 j ? . x ip. â . f A Z R ,d?@/:fg, .*6 . 6:?@/i$ . 6 j . k2{@ 6 j ? ^ `. p pvb³¯Dvxz|tu}~ni}~z=pop$zz|p p ³
(388) ²n~nty#w±x,p
(389) w±x{zty}i~¹º}~ xiop~zxiwup v8n}{´ ¡nwym
(390) op ® tyo&xi¥iptup¯Dvx{~Dztuz|x{z|t°p{¸ xi}vn
(391) t p,tuonwuty
(392) tuz³iÈawyx~}izx{zty}i~Æo&x{z|ty
(393) typ
(394) wywup pz¼ponwu}Qi³p{¸r pn}¡wym
(395) o&p'p
(396) zx{wy}³}iwyvKp~1vbz|tuwytu|xi~z(v~npBo³
(397) zln} p'tuz³|xz|t°p pzÉVp¥i|x tup~z#}~vn¥vn³{¸b»~np ix{tyxi~z|pµ,
(398) pnpotyp
(399) x{wy¥}it°z|lnoppzxivntfn}{´ N}³iÈ xG{xi~z a® ³$z|v tup,¯Dvnpwu¯Dvnpp$bponwup pp
(400) }~nz|v
(401) z|tu}~ntuovnwu³p
(402) ® }¡bp$z| p~z|p
(403) ³
(404) ¸. ÓºÕú2ÓºÒ.
(405)
(406) "!$#%'&(!) * +. . .
(407)
(408) wyp~n}io¡np p}tu~Dz p ty³
(409) z|tu|xz|tu}~ p )#@6 ! .#8 " wup~n}o¡np pN}ity~z| popvnp,v{@z6 sV}typ
(410) ~z % . $ wyp~n}io¡np p,}tu~z| }vp,v{@z6 '&( wup~n}o¡p p(¹º³
(411) ¯Vvp~n
(412) pvbz|tuwytu³
(413) p. ~ ³
(414) ²n~ntuzÈN}vnlxi¯Dvnp¹º³¯Dvnp
(415) ~npp
(416) zN}vlx{¯VvpBN}it°z|tu}~ p}vp{ÈNwupp
(417) $´ z|pv vnt°{xi~z|TS 3 U V 4 , .6:?@/
(418) +*,* # A 3 U V # , .6:?@/
(419) ) +*,* )4 A. ´ F tyop
(420) ~ntu}~ . poxz|tup
(421) xi}b
(422) ty³
(423) p¼. x{vb-0 /. 3U V, .6:?@/
(424) +*,* A >g, .W6:?@/
(425) +*,* . ) A. 4 1. . t°·a³
(426) p
(427) ~Dzlnxionµ'vn~p¹º³¯Dvnp
(428) ~np+S. 243Èo&x{z|ty
(429) plxio.tu~n
(430) t p
(431) ~z p tuop~nty}i~# 657 .8$ 2BÈno&x{z|ty
(432) plxio.z}izxiw p tyop
(433) ~ntu}~9 :5 .8$ 2< ; Èno&x{z|ty
(434) plx{o& t°·axi
(435) z³ p tyop
(436) ~ntu}~9 = .#"57 .%$ ´ F tyop
(437) ~ntu}~ poxz|tup
(438) pA @ pp~.µ'vn~np¹º³
(439) ¯Vvp~n
(440) pHS >'? Ao5f%
(441) ++*,*,* * È oxz|tup pA( @ p
(442) p~ ty~z|³
(443) ¥|x{wyp ¡bp
(444) z´ ¡bp$z p tyop~tu}~9 657 >A@ A!5f
(445) + *,* 4 È oxz|tup pA( @ p
(446) p~Bty-0~/ z|³
(447) ¥|x{wyp ¡bp
(448) z´< p
(449) pzpvn p tuo&p
(450) ~ntu}~! ! .9" 57 ´ bnptu}~ p
(451) z tyop~tu}~ pwyx&o&x{ztup,xi}Vtu³pxiv}~z|xizpHS D > % A 6FE A n nG C z|p
(452) wywup,¯Vvp > % A 1 6 E A n nG0 6IH A n nJq 6IELAM K H oxz|tup p
(453) }~z||x{z|p p tuop~nty}i~# NONPNONONPNONPNONONPN. vno³ty¯Dvnp
(454) op~zGÈ#lxi¯DvnpÆo&x{ztuppz8xi~n¥³
(455) p.wutu¥~npxiwuty¥~pi¸c"xip3p
(456) onwyp{È#wup p$z|p
(457) vn p
(458) z}~z|vnt°zp
(459) ~¹Ixitu|x{~Dz {xityp
(460) wup}ty~z p )#Yvnt°ix{~DzRQ p~²xi~z. 1. úúÄé`aûb.
(461) II I I$+
(462) . ¢*?. ¸Fp=o opiÈH34Tpz}i~nztuzvn³p. xo&x{z|ty
(463) p3 4. p .8$ }iwy}~~np p
(464) }bp
(465) typ
(466) ~z|}io&wyp3p
(467) ¸ p|x,|xi~¥³p p~&²xi~zwup~Vvo&³
(468) } pwutu¥~npp
(469) zcp~&ix{tyxi~z#wup~Vvo&³
(470) }. p }wu}~n~np{¸ "xi,}vt p8tyonwuty
(471) tuz³iÈ }~:~n}{z|px p8wyx.o op8o&xi~tym
(472) p8wupo&x{z|ty
(473) p}vn,wup tu·N³p~z|p
(474) ,¹º³¯Dvnp
(475) ~np
(476) ¸N 2po&x{z|ty
(477) p}~zp
(478) ~\¹Ixit°z(
(479) }~nt ³
(480) ³p
(481)
(482) }oo&p p
(483) (wytuzp po&x{ztup
(484) }i~nzvnt°z|p
(485) (µ&¹º³¯Dvnp~p²b³
(486) pi ¸ p,~n}o¡np p¹º³¯Dvnp
(487) ~np
(488) ³
(489) zpo&tu~np w±x'wu}~n¥vnp
(490) vn pw±x'wutyz|p{¸. . 7
(491) 7 7
(492) < . ~Kvztywutyxi~z,wyp
(493) (~n}izxz|tu}~n¼n³
(494) ³ .
(495) p ~Dzp
(496) È }~1pvbz³³
(497) typ&wup(³
(498) ¯Dvx{z|tu}~n}vn ¹º}opÆo&x{ztutupwuwyp1}vnlxi¯Dvnpƹº³¯Dvnp
(499) ~npKxi~¥vnwyxityp ? A ¸ ~ }i¡z|tup~z4wup VzmoHp S. D 2 3 A 2 ; A. , F > ? C /2 > @ C 2. I'. }¼p
(500) n³
(501) p~zpwyx&o&x{ztupt p~z|t°z|³ p tuo&p
(502) ~ntu}~! P5 \¸ T~ vnn}|xi~zwyx/o&x{ztu p F > ? C v&|xioop~z ³¥vwytumpiÈ }~ z|}vip«x{wy} w ® ³¯Dvx{zty}i~.o&x{ztutupwuwyp,~n}~b´ðwytu~n³xitypvnt°{xi~z|pHS. 2 ; A > @ C , F > ? C / 2 3 6 j ?. ºq]. .
(503) p xi|xi$z|³
(504) tuz|tu¯Dvnp³
(505) wyp
(506)
(507) z|}o&xi¥~n³$z|tu¯Dvnp&p
(508) z p
(509) }o&xitu~np}~z¼tup(tu~ ³3´ Np
(510) ~ xi~z|p
(511) p¼wyx'¹º³¯Dvnp
(512) ~np{¸pp~ x{~DzÈw±xBnxiztyp(tuo&xi¥tu~xitup p
(513) ³wu³op~z| p(wyx oxz|tup p&
(514) }~z|xizp C }i~Dztyp
(515) ~z p(z|p
(516) op(¹º³
(517) ¯Dvnp~z|tupwuG ºp~ 3¸ ~ ³
(518) ²~nt°z ?%5R xiwy}iwyx{xit±xi¡wyp C ³p~ x{~Dzp pBwyx&¹º³¯Dvnp
(519) ~np{È p~ ¹º}~
(520) z|tu}~ pwyx{xityxi¡nwupx´ |xi$z|³tyz|tu¯Dvn p 2AJ, p6y /ty~ ³p~ x{~Dzp pwyxB¹º³¯Dvnp
(521) ~n= p C A C , /93¸ }izp(n}¡nwumop ® ³
(522) tuz ³}o&xitu p~¹º}~n
(523) zty}i~ p,wyxB{xityxi¡nwupGxixi
(524) z³tuzty¯Dvnp+S. 2 ; A > @ C , / , F > ? C , /:/ 2 3 6 j ?. ⤠. xB³}wyvbz|tu}~. p¼~n}~wuty~³Gxitup(p
(525) ~! :pop$z xitu~nt p(p
(526) }~nz|vtyp,wyxBpot°zztuVt°z|³ p
(527) zwyx
(528) }~ vn$z|t°Vtuz³ v'}v p}¡Vp
(529) z| p
(530) z }~nwup
(531) }~z|xizp xi~n"wyp }o&xitu~np ³
(532) tu¥~n³. ÓºÕú2ÓºÒ.
(533)
(534) "!$#%'&(!) * +. ¢¢. xi% #Èbµnxizty pwyx }i~n~n³p v4lx{o& tu·N|x{
(535) z|³}~~Vvvnwyxwutu¥~np popvnp {- pt p$z v.lxio tu~nt p~z(
(536) }~n~Dv1µ&w ® ty~z³tupv pw ® }¡bp
(537) z¸Y 2p
(538) }~~n³p
(539) v o&tuwutyp
(540) v }~zpwuwyp
(541) xivt vnn}³
(542) p}~n~Dvnp
(543) ¸ x,³
(544) }wuvz|tu}~ v8n}¡wym
(545) o&p typ$z=}ivnnwu³tItu~ptu}~ p¼wyxo&x{ztup F > ? C , /: pzp$·ap
(546)
(547) z|v³p,p~vz|tuwytu|x{~Dzvn~npo³
(548) zln} p typ$z|p p(zÉbpA@,x{vn<´i} xi~ ¸ }vn(z}vip TÈ2}~K³}vz po&xi~ntump&t°z|³x{z|t°p&p~\vztywutyxi~zv~np'z|pl~nty¯Dvnp p o&tu~ntuotyx{z|tu}~ pƹº}~
(549) z|tu}~n~pwuwypKµ w ® x{t p ® v~ x{wy¥}it°z|lnop p pp~zp p.zÉbp ¥|x typ
(550) ~Dz
(551) }~{vn¥vg ³ vÝ{5q we¸. .
(552) 4 +
(553)
(554) 7 M
(555)
(556) . . . . 4
(557) 6 . . 2p=}¡nwumop p
(558) n³
(559) p
(560) ~Dz³ xiw ® ³
(561) ¯Dvx{z|tu}~ e¤H pzp ³
(562) ²~txi³
(563) ¯Vvtu{xiwup~n
(564) p p~'vn~ n}¡wym
(565) o&p p otu~ntyotu|x{zty}i~ p ¹º}~n$z|tu}~n~np
(566) wywupi¸blnp
(567) lnp
(568) ƯVvt|x{zty¹Ixituz⤠"p$btup~z µlplp «oty~ntuotyxi~zwuptuzmpÈ}iv¹º}i~n
(569) zty}~~npwuwyp,}[zGÈ ³
(570) ²~nt x{ S %, / A . / , / C' `!
(571) " x ipcwypT³t v D , /BA ) # F > @ C , /T, F > ? C , /9/ ) 4 Gx{wy
(572) vnwy³cµ lxi¯DvnpT¹º³3´ ¯Vvp~n
(573) p}vn l x{ ¯V vp}t°z|tu}~ p}vp . ¸ p&z|p
(574) op n ³
(575) tu¥~np4wyxÆ~n}iop4xi}Vtu³p xiv:n} vnt°zBlnp
(576) ot°z|tup~ ,bn 6_n / ³
(577) ²n~nt vn(w ® p
(578) x{ p% $ !#" ,{@9/ p
(579) (¹º}~n
(580) zty}i~nµ4ix{wyp
(581) vn}io&wyp3p
(582) p&xi³'ty~z³¥!
(583) xi" ¡nwup&vn ` {-xiTS . ,&r6('a/ !#" A Z. & !
(584) ". , . / 'Y, .0/b$ .q6 j < & k)$ , {@9/u6 j g ' k*$ , {-9/ ` `. ⣠. } 'Y, .0/p
(585) n³
(586) p
(587) ~Dzpwup}onwup$bp,}~{v¥vn³ p+', .0/3¸ }vnotu~ntyotup
(588) wyx4¹º}~n
(589) zty}i~n~npwuwup,"È2wyp
(590) ,o³$z|ln} p p p
(591) p
(592) ~z|p8}~z,}~nz|vntuzp p~ln}tutuxi~z=µ(w ® t°z|³
(593) |x{zty}~ M vn~np tup
(594)
(595) z|tu}~ p p
(596) p
(597) ~z|p.- /wup wy}i~n¥ p w±x{¯Vvpwuwyp ³
(598) }iwyvnp /{Èp
(599) z vn~³
(600) p w 0/¼xin^ pwu³(¹Ixi
(601) zpvn ® ³lpwuwyp,}ztyo&xiw }vn wyx'oty~ntuotyx{z|tu}~ 1 p xi~nw±x tup
(602)
(603) zty}, ~ - / z|pwu¯VvHp S /(2. A. M. / 30 / - /. Ê 4 ÌâÏæQÌeòåâÏéÐâÏܱñ òßÚ3ÌâÐ ÏéÐâÌeÏÜÝÏßðãÚ$Ù=æà Û65ÌeÚ
(604) ßÉÐâòÙ=ÏåIáQÌeòÏ<Ð2ÜìÏTßðãÚ3Ù=æ¼à Û75ÌðÚ$ßÉÐeòßÚ3Üçß<áÜÝò. úúÄé`aûb. D'.
(605) II I I$+
(606) . ¢Q. } /(pn³p
(607) ~z|p,w±x'{xityxi¡nwup(Gxixi
(608) z³tyz|tu¯VvpBµ'w ® t°z|³x{z|tu}~ ¸ p
(609) ~n}io¡npvnp¼o³
(610) zln} p p p
(611)
(612) p~z|p ³
(613) Np
(614) ~ p
(615) ~Dz vÆln}i^ t° p
(616) xixiom
(617) zp p pp~zp - / ¸f}vn~n}iz|pn}¡wym
(618) o&p{Èfvn~npo³
(619) z|l} p p¥x tup~z}~{v¥vn³ p(zÉbp }wyx \´< ty¡tym
(620) ppzvztywutu³g p vÝ£ w⸠vnxi~z8x{v xixiom
(621) z) p 0 / Èctuw pz4pGx{wy
(622) vnwy³Æµ\lnxi¯DvnpÆ~n}ivp
(623) wywupÆt°z|³
(624) |x{zty}~ x{²~ p p~ poty~tyovnoÄwyp~n}ivpxivÆ
(625) t°z|mpi¸. O ÃI© à à 2 VÂiÀ32º¾ 0 V¨G 0 À. 5 G .. . - / . ~lnp
(626) lnpxiwy}i - / xi~nTwupw±xi~'¹º}o³ xiTwyp
(627) pvb typ$z|tu}~nc}zln}¥}~nxiwyp
(628) p$z / Èn} / p
(629) n³
(630) p~zpwup,¥i|x tup~z pwyx'¹º}i~n
(631) zty}~~npwuwyp¸ ~xxitu~nt S - /. x ip,wyp³pw. ³$²~nt2x{ /. S. . p z|p
(632) op n , vnw ® pxi
(633) p xi S. \ $. E. A
(634) . / 6 . / - / . . \ F \ / E / E `. I'. /. \. ¢P?'. ³ty¥i~npBwyx8~n}o&pxi}b
(635) ty³
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