Broadband Constraint Based Simulated Annealing Impedance Inversion

Transcription

1 Joural of Comuaoal Scece & Egeerg 8 (213) 3-34 Joural of Comuaoal Scece & Egeerg Avalable a h://wwwasocseorg SSN Broadbad Cosra Based Smulaed Aealg medace verso Guagxua Che 1, a, Yahu Du 1,b, Pae Q 2,c ad Le Zhag 3,d 1 Peole s Publc Secury Uversy of Cha, Bejg, Cha 2 Bejg Uversy of Poss ad Telecommucaos, Bejg, Cha 3 The Logscs Academy, Bejg, Cha Arcle formao Arcle hsory: Receved 26 July 213 Revsed 7 Augus 213 Acceed 2 Augus 213 Avalable ole 5 Seember 213 Keywords: Broadbad cosra Global omzao medace verso Smulaed aealg Absrac order o ehace he accuracy ad mroved he resoluo of he verso resul gas hydrae exlorao, hs aer roosed a ew verso mehod By roducg broadbad cosra based smulaed aealg medace verso, he ew mehod allows for a more exesve search for he omal soluo ad s more effce ha exhausve eumerao solvg global omzao roblems Comared o oher verso soluos as cosra sarse se verso ad model based verso, he ew mehod o oly solved he global omzao roblems, bu also mroved he resoluo of he rofles ad ehaced he verso accuracy, whch s helful o he laer erreao 1 roduco Sesmc wave medace verso s a effecve meas for reservor redco as here s a commedable corresodece bewee wave medace ad hydrocarbo reservor medace verso s acually a hyscal arameer medace of elmag he fluece brough by sesmc wavele ad maag he coeffces whch are furher used o calculae he hyscal chages of he sraa Corresodg auhor: a erccgx@163com, b dyh6889@gmalcom, c qae@gmalcom, d zxcv123o@163com 213 The Amerca Comuaoal Scece Socey All rghs reserved

2 Che e al / Joural of Comuaoal Scece & Egeerg 8 (213) There are may ways of medace verso The mos commoly adoed s geeralzed lear verso whch has hgher verso accuracy However, durg he verso, he hgh-frequecy ose ca brg grea fluece o solvg he morbd equaos; eve regularzao facors are added, he fluece ca be elmaed So, hs aer roosed broadbad cosra based smulaed aealg medace verso Smulaed aealg algorhm orgaed from he smulao of aealg rocess meallurgy, s a geerc robablsc meaheursc for he global omzao roblem of locag a good aroxmao o he global omum of a gve fuco a large search sace, esecally whe he search sace s dscree [1] value comared o eergy f of a radomly seleced o he model sace, e, f f f, he ew model wll be acceed ucodoally; f he f s a large value, e, f f f, he acceace robably of he ew model s ex( f / T ) Here, T s he corollg arameer As for a fxed emeraure, he es of acceace rocess wll be reeaed ul he objecve fuco s cosa As he acceace robably of heag s always greaer ha zero, he oeraor ca always reach o he global omum [3] 22 The secfc ses of smulaed aealg algorhm are as follows: Se 1: Secfy coolg schedule arameer 2 Smulaed Aealg Algorhm ad s Alcao Gas Hydrae Exlorao 21 Prcle of Smulaed Aealg Algorhm Smulaed aealg algorhm uses a se of arameers amed coolg schedule o corol s rocess ad oba he global omum soluo of he combaoral omzao roblem whe he corol arameer s coolg ad eds o zero Here, a soluo ad s objecve fuco of he omzao roblem are corresodg o a mcrosae ad s eergy E The descedg corol arameer s used o descrbe he emeraure T he rocess of aealg of he maeral Smulaed aealg algorhm s a adaao of he Merools-Hasgs algorhm [2] As for each whch clude he al value of he corollg arameer, aeuao fuco, fal value ad Maob cha legh L ; secfy al soluo of he erao f ( ) Se 2: Whe, carry ou L mes of searches accordg o he followg mehod: Geerae radom vecor Z (as for couous varable) or radom offse m (as for dscree varable) accordg o roery of he curre soluo o he eghbourhood, hereby oba he ew es Z, ( m m ), couous varable dscree varable (1) value of, he erao of geerag ew As for dscree varable, s he value sequece soluo- judgg- acce or abado s ogog ad m s he dscree locao of he curre ul reach he balace o uder ha soluo emeraure Geerae a radom umber G ha uformly Durg he rocess of smulaed aealg dsrbued o (, 1), calculae he raso algorhm, f he ew o s eergy f s a small robably P ha corresodg o Merools 213 The Amerca Comuaoal Scece Socey All rghs reserved

3 Che e al / Joural of Comuaoal Scece & Egeerg 8 (213) acceace rule uder curre erao o ad emeraure [2] 1, P ex ) ), ) ) (2) f dfferece of objecve fuco s less ha zero, e, f, he ew soluo wll be acceed, oherwse, reserve he curre soluo f he es searches s less ha L ) ), reur o se 1, oherwse go o se 3 Se 3: The curre soluo wll be used as aroxmae omal soluo f he ermao codo of he erao s sasfed, ad he he algorhm s comleed; oherwse, go o se 4 Se 4: Geerae ew emeraure corollg arameer 1 ad Maob cha legh L 1 accordg o he gve emeraure aeuao fuco, ad reur o se 2 for he balace o omzao of he ex emeraure o Smulaed Aealg Algorhm for medace verso The roagao of he sesmc wave he rasverse homogeeous acousc meda s a aroxmae covoluo model, as show Eq 3 S ( ) R( ) W ( ) d (3) Here, S() s wo-way ravel me sesmc race; model dcaes he relao bewee os-sac sesmc record ad uow model arameers, such as velocy, desy ad medace However, he acual sesmc daa s affeced by geomercal aeuao, vscoelasc absoro, wave dserso, as well as he loss of covered wave ad mulle reflecos Thereby, roer correcos are eeded o he acual sesmc daa he sesmc wave verso, low frequecy wave medace cosra ca reduce he o-uqueess of he soluo of he verso Here, we ca ado L1 model o esablsh objecve fuco, whch, he frs em s he absolue error bewee he acual sesmc race ad model sesmc race, he secod em s he absolue error bewee ror wave medace ad model wave medace ha eables verso resul close o he varao red of he low frequecy wave medace The objecve fuco s show Eq 4 So Sm So 1 W ( ) s sesmc wavele; R s sesmc refleco coeffce sequece Tycally, sesmc wavele s uow ad ca be obaed hrough varous mehods should be oed ha he covoluo 213 The Amerca Comuaoal Scece Socey All rghs reserved f Here, 1 1 m (4) So refers o he acual sesmc daa; Sm s he syhec sesmogram; s ror wave medace ad m s model wave medace The amlude of he sesmc wave mus be well mached wh he syhec sesmogram geeraed by loggg curves ad he objecve fuco mus be ormalzed before he verso A hs mome, he weghg facor s 1 The omzao rocess requres a fg sadard o esmae he qualy of each es model The oe ha ca mae he objecve fuco reach o global omum s he bes model Varous cosras ca be added o he model, hs s

4 Che e al / Joural of Comuaoal Scece & Egeerg 8 (213) esseal o reduce he o-uqueess of he soluo of he verso 3 Exermeal Resuls Aalyss order o exame he effec of he ew mehod roosed, we desged a seres of verso exermes The sesmc daa s acqured from a arge gas hydrae exlorao area he Souh Cha Sea Broadbad cosra based smulaed aealg verso covers he ow codos o secfc cosras, so as o corol he verso rocess The desged verso rocess s show Fgure 1 Here, we carred ou wo dffere versos o he daa acqured from he arge area, e, seudo-loggg medace ad medace whou loggg corol As for he frs verso, we ca oba seudo-loggg medace resul hrough smulaed aealg algorhm ha adoed al model; as for he secod verso whch s less deede o seudo-loggg daa ad more deede o sesmc daa, we ca drecly oba he verso resul hrough he calculao of he al model Fgure 2 ad Fgure 3 showed he rofles of hese wo versos of he es le he arge area Fg 1 Process of broadbad cosra based smulaed aealg medace verso Fg 2 Profle of seudo-loggg cosra medace of he es le order o reduce he o-uqueess ad ehace he sably of he soluo, ror medace formao ha adoed seudo-loggg curves ca be added o he algorhm as cosra em of he objecve fuco The cosra em ca comesae he mssg low frequecy formao of he bad-lmed sesmc daa The verso s called seudo-loggg verso f he cosra em s adoed or verso whou well corol f o adoed The al model ad sesmc wavele used broadbad cosra based smulaed aealg verso are he same as some oher verso mehods, such as cosra sarse se verso ad model based verso Fg 3 Profle of he medace whou loggg corol of he es le As ca be ow from he smulaed aealg medace verso resuls, rofle wh loggg daa (Fgure 2) refleced he hgh medace of he ossble gas hydrae reservor ad he low medace of he free gas; whle he rofle whou loggg daa (Fgure 3) ossesses hgher vercal resoluo ad ca reflecs he relave relao 213 The Amerca Comuaoal Scece Socey All rghs reserved

5 Che e al / Joural of Comuaoal Scece & Egeerg 8 (213) bewee he gas hydrae reservor ad he uer ad lower sraa, ad hus ca more fely reflec he occurrece ad saal dsrbuo of he gas hydrae solved he global omzao roblems, bu also ehaced he accuracy ad mroved he resoluo of he verso resuls uder he cosras 4 Cocluso Ths aer roduced he smulaed aealg algorhm o medace verso gas hydrae exlorao, where smulaed aealg s more effce ha exhausve eumerao Broadbad cosra based smulaed aealg verso allows for a more exesve search for he omal soluo Comared o cosra sarse se verso ad model based verso, o oly Refereces [1] S Krarc, CD Gela, MP Vecch, Scece, 22 (1983) [2] M Ncholas, WR Araa, The Joural of Chemcal Physcs, 21 (1953) [3] V Gravlle, M Krvae, JP Rasso, Smulaed Aealg: A roof of Covergece, EEE Trasacos o Paer Aalyss ad Mache ellgece, 16 (1994) The Amerca Comuaoal Scece Socey All rghs reserved