Te Reer of Loper Ple Teo of e Er o e Be of D of Seoo GPS Se e Solo of Prole of El Teor d e Erqe Predo L.. glo Ie of Me of S of re SUMMRY: Moder ee oe e re of rog erqe e Loper Ple eo of e Er 95% of e erqe. Te eee of dee e of eoo d oder elle GPS e per o follo e eor of e Er Loper Ple d epre pr perel prlrl o ere e dplee of po o e fl rfe of e Loper Ple d epre pr d follo er ge e. I r per o deere e re-r e of e ple d follo ge e ge e erl. Te orrepodg oll ree-deol prole of el eor oled. I proed e olo eoe ell e e e fo eerg e odr odo rele o dplee re polol. ollog e d of e re-r e ge of Loper Ple pole o gle o ore eodgero oe of e Er e ge oe. Keord:Teo of Loper Ple GPS e predo of erqe.. ITRODUCTIO Te oder ee oe e re of rog erqe e eo of Loper ple of e Er 95% of erqe Po e l 97 Kr 98. d re e Loper ple of e Er? I o e ple Er o oogeeo e Er rd = 678 d o of e er r pper d loer le; oer d er erel eled o e e of e geologl d oer ego. rle e eell dffere peed of propgo e ler of logdl Vp d ro er e V re e de fere of dfferee of ee ler. Te poer e of e er r o e oe ge fro o 7 e oe fro 5 o 5. Te er r oled fro e pper le Mooro Moo erfe.e. e order o e peed of e logdl el e ree p-le p o e le oer 8e. ere e er r ll 6-7 e. Vp=74e. I e od of e er r ree lere re oled e rer: I edel ler Vp 5 e. = 5 II gr ler Vp 6 e. = 4 III l ler 65 Vp 74 e. =5. Te er r d pr of e pper le p o e order o o pere lled Lopere. Te Lopere pl o oe g pee re lled ple. Te ere of e ple ge fro dred p o oe od. Te gge Loper ple of e Er re:
rd Er Id-rl fr So-er or-er Pf lppe ol r d oer Loper ple. Te geogrp of e e of e errerl gloe po o e f e oerelg or of e erqe re groped o relel leder oe e oe e d eo e of re l red o er o of dere o e oer Loper ple re eed o rele dplee log er og rfe. To pe of eo oee re dged: lo er d q p-le oeed e erqe. I e e of e e proe of lo ro deforo e reg rl le -4 d Re d 47-5 rg o glol dero e pr of e lo of e gre poel of eerg oled e for of olе P logdl or prr d S eodr or er e pred peed Vp d V. V p E V G E.5 V V. 7V l Vp V. p W e elp of e peed Vp V e epeer of e erqe fo deered. Hg e d for ree e o o lg e e ple e epeer of e erqe deered gre ee. ro e ed oe e derled pore of deero of re-r e of e Er Loper ple d e oorg of ge e follo. or pole o e erg d of e rer dee e of e eg eoo d elle GPS e prlrl ere e le of e po dplee of e Loper ple rfe. I e pper e olo of e orrepodg ree-deol prole of el eor for oelered ple d llered pe fro ple perg o fd re-r e of e ple or e pe o e e of e d of eoo d GPS e re fod. Te orrepodg prole oll odr-le prole e odo e re re ol ge o e fl rfe of e ple or e pe e orrepodg ree eor opoe re eql o ero e le of e po of rfe e d of eoo d GPS e re o. B e fod olo e e oppor o follo e ge of e re-r e d reel e rl e e ell ple.. THE BSIC EQUTIOS D ORMULTIO O THE BOUDRY-VLUE PROBLEM Le e pe fro ororop ler opg re D { : } g.. I reqred o fd e olo of e eqo d orrelo of ree-deol prole of el eor g o o e ole fore prlrl e eg of e ler d eperre o Del-e odel glo 997 Le 98:
... e ; 44 66 e. der e odr odo. d der e odo of fll o eee e ler for ler re re e for of H H H... H H. ere re e ree eor opoe re e ee of e ler re e o of el re e dplee eor opoe re e oeffe of e eperre eeo e eer e odo Eq.. preer rerg e ree d dplee le for efored ge e.e. e oe of e e e deo of e o d GPS e ere oded. gre. Pe fro ororop ler
Te odo o e lerl rfe of e pe re o defed oreel ler ll e o e olo of odr ler pe orrepod o e.e. olo deree ql epoell e reog fro e lerl rfe o e de e pe. I prl pplo e odr ler ll egleed.. THE SYMPTOTIC SOLUTIO O THE PROBLEM I order o ole e e p odr-le prole e eqo d orrelo Eq.. e p o deole rle d dplee. rel glrl perred e rele o ll preer oed. Te olo of e Eq.. oed of e olo of e er prole I d e odr ler I glo 997 fe. 976. Te olo of e er prole og e for of glo 997 glo 8 M. ere d ler e oo M e g e repeg de egеr le fro ero o e er of pproo M. Sg Eq.. o e rfored ordg Eq.. e Eq.. d eqlg e eqo e oeffe der e e degree for deero e ge e e... ; ; ; e. 66 44 Se Eq.. per egro rel e e
66.4... 44 ere d.5 44 d d d... Q I geerl e e olo Eq..4 Eq..5 o 6 o fo.. re qel deered fro odr odo Eq.. d 6- odo of e o Eq... We oder e proe of lo of rl deforo q e eqo of eqlr e ee ed Eq... Te eod per o oder d prole ell. We dere e proedre of fo of odo Eq.. Eq... fr e le of e fr ler re deered e of e fo of e odo Eq.. glo. Ug e forle Eq.. Eq..4 Eq..5 d fg e odo Eq.. e e
.6 Hg e olo Eq..6 e orrepodg forle Eq..4 Eq..5 e ree re deered. So e le of e fr ler ere opleel deered fer e fo of e odo Eq... Hg e le of e ree d dplee of e fr ler e of fo of e o odo Eq.. eee e fr d eod ler ll e dered le of e eod ler re deered. Te g e o odo Eq.. eee e eod d rd ler e ree d dplee of e rd ler re deered d ler e e e le of e re of e ler re deered. I geerl e e fo of e odo Eq.. for rrr ler rg o e olo of e follog rerre eqo 44 ; ; ;.7 H H fro ere d fro e forle Eq..4 follo ; ; 44.8...
or e fr ler e e e olo Eq..6 e fro Eq..8 e olo for e eod ler ll e deered e olo of e rd ler deered e.. T e odo Eq.. Eq.. red o o e ffe for deero of ll e dered le of ll e ler. ro ere follo e olo of e odr ler I ll e deered depedel d ll reoe oordo e fg e odr odo o e lerl rfe. deoed oe prl pplo rle e odr ler egleed. 4. O MTHEMTICLLY EXCT SOLUTIOS If e fo eerg e odr odo Eq.. re polol fro e ered proe of deero off o er pproo depedg o e degree of e polol. rel e o ell e olo e er prole. or e llro of ee d oe e olo of e odr prole Eq.. Eq.. ll e rog d 4. Ug e forle Eq..6 Eq..8 e o e oed e pproo ll e dffere fro ero. Cllg ee pproo for ree-lered pe ordg o e forle Eq.. Eq.. e follog e olo ll e oed: e le of e fr ler 66 4. e le of e -rd ler...
66 4. O e e of e oo reglre forle Eq. 4. Eq. 4. o dffl o re o e e olo of e er prole for -lered pe. or e pe of e fe gel deo loe o e lerl rfe o olo e olo of e odr ler old e dded. Te oe rog proper of e olo e por ppled gfe. Rell le for e oe of e e d of e o d GPS e o po of e fl rfe of -lered pe fodo-e. Te e dplee of e fl rfe e repreeed e for of Lgrge polol 4.4 ere e prod. Sg Eq.4.4 o e forle Eq.. Eq.. Eq..4 Eq..8 fer e fl er of ero e deere ell e olo of e prole orrepodg o e deo of e o d GPS e.e. e re-r e of e ole pe orrepodg o e. Moder opol ool deere olo fe e. Codg e oorg of e olo e d oerg e ge of e re-r e of repole rre oro re e dgero oe e fll repreeo o e oro re e e opoed d e pol of rl o re e reeled. 5. COCLUSIO Moder ee l rele e eergee of rog erqe o Loper ple eo of e Er 95% of erqe. I pper e prole of deerg re-r e of Loper ple ed o eqo d relo of e ree-deol prole of el eor d d of e o d GPS e odered. Te orrepodg o-ll ree-deol prole oled e po eod. Te d fro GPS e d e o o e le of dplee of po of e fe rfe of ple pproed Lgrge polol d e orrepodg ell e olo of e erl prole dered. Trg e eor of re-r e of Loper ple oer e oorg prode oppor for elg e ple d e of rl re-r e ledg o glol
dero. Togeer e l of olo peoe opg erqe ope for predo rog erqe. KCOWLEDGEMET Te ego flflled e ppor gr -46 of Se Coee of See of re. REERECES Po X. Le ree J. Bo J. 97. Ple eo. Eleer. Kr K. 98. Erqe Me. Crdge Uer. Pre Crdge. glo L.. 997. po eor of orop ple d ell.. Moo. Le S.G. 98. Teor of el of orop od.. Moo. glo L.. 8. po Meod for olg ree-deol odr le prole of d d of T Bode. Proeedg of e UTM Spo o e Relo of Sell Ple Be d D Model. Sprger -. fe. K. 976. Meod of perro. Mr. Moo. glo L... O oe l of ree-deol prole of el eor for ple. Proeedg of. Rde Mel Ie of Georg. Vol. -.