M Hnh Ha Tng

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Facies Modeling

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Bo co a thng k trong m hnh ha va GVHD: TS. T Quc Dng

Bo co a thng k trong m hnh ha va GVHD: TS. T Quc Dng

I. M hnh tng da trn Variogram (Variogram based facies modeling):1. Chn phng php thch hp:Cc tng c phn bit bi kch c ht khc nhau hoc qu trnh bin i to khc nhau. C nhiu s phn bit r rng gia cht lng va ct kt v st kt, gia vi v dolomite. Mi quan tm ca chng ta l khng phi cc loi tng c xc nh nh th no, nhng cch xy dng s phn b thc 3D ca cc tng c th c s dng trong chui ra quyt nh va.Cu hi u tin l liu c phi m hnh tng trc khi m hnh rng v thm. Xem xt mt s l do di y: Cc loi tng phi c kim sot ng k trn rng, thm hoc hm bo ha; mt khc m hnh 3D phn b cc tng s c li ch nh do bt nh s khng c gim v cc m hnh kt qu s khng c nng lc d on nhiu. Kim sot ng k: Biu phn phi tn sut ca rng hoc thm trong cc tng khc nhau nn c s khc bit ng k v gi tr trung bnh, phng sai, v hnh dng, v d, hn 30%. o lng hm bo ha gia cc tng khng nn chng ln nhau. Cc tng phi c nhn bit ti cc v tr ging, t d liu log ging cng nh t d liu mu li. Kim tra cn thn d liu mu li cho php nhn bit nhiu tng, tuy nhin, s c bt nh ln trong m hnh 3D ca cc tng chi tit ny nu chng khng th c xc nh t lng ln d liu log ging. S xem xt ny l d dng kim tra. Cc rng buc trong s la chn cc tng l chng phi c m hnh khng gian bin thin n gin. S phn phi cc tng nn c m hnh d dng nh d on trc tip rng v thm.La chn cc tng l mt trng hp kh khn m c th khng c gii php r rng. S n gin l c a thch. Hai tng, mt loi cha thc (net) v mt loi khng thc (non net) thng l . C ti a nm loi tng khc nhau (ba tng thc v 2 tng khng thc). Mt khi cc tng c xc nh, d liu thch hp phi c nh gi v cng ngh m hnh 3D c chn.S la chn cho m hnh tng l: M hnh a thng k da trn variogram (Variogram based geostatistical modeling). Thng k nhiu im (Multiple point statistic). M hnh ngu nhin da trn i tng (Object based stochastic modeling). Phng php bt chc (Process mimicking). Lp bn xc nh (Deterministic mapping).Lp bn xc nh lun c u tin khi c d liu v bng chng v s phn b cc tng loi b bt k s nghi ng v s phn b 3D. Trong nhiu trng hp, c bng chng v cc hng a cht, nn bao gm m hnh tng ngu nhin.Nm bc chnh trong m hnh tng ngu nhin, mi bc D liu ging thch hp vi cc thng tin khu vc v hng a cht thng ng phi c tp hp bn trong lp a tng c m hnh. Thuc tnh a chn thng lin quan n cc tng trong mt cch gn ng, nu c sn, d liu a chn phi c kim tra iu chnh xc sut cc tng. Decluster, i din khng gian, bt k m hnh tng no cng phi xc nh t l ton cc. Thng k khng gian nh variogram, hnh nh o to, kch thc phn b phi c tp hp nh u vo ca m hnh ngu nhin. M hnh 3D phi c xy dng v hp l.

K thut da trn Variogram thng c p dng to cc m hnh tng trc khi m hnh ha rng v thm. Tnh ph bin ca k thut da trn variogram l do: D liu cc b c m phng bi s xy dng. Cc kim sot thng k cn thit (variogram) c th c suy ra t gii hn d liu ging. D liu a chn mm v cc hng a cht t l ln (large scale) c x l minh bch. Cc kt qu thc t xut hin cho nhng thit t a cht ni khng c hnh hc tng a cht r rng khi cc tng ang kim sot qu trnh to hoc ni cc tng trm tch t c cu trc, bn knh ngn hoc cc m hnh bin thin b pha trn.Nhiu h thng trm tch (Multiple Depositional Systems/ Systems Tract)Mt h thng trm tch l mt thnh phn di mt t c suy ra t mt thit lp trm tch c trng v d, trm tch sng (fluvial), trm tch chu th (deltaic), h thng mt b - phn trng hnh lng cho, dc nhng ngn trong thm lc a (shoreface systems) hoc h thng trm tch nc su (deepwater depositional systems). Cc h thng trm tch c lin kt di truyn c nhm li thnh cc h thng trm tch (system tracts). V d, t hp ca h thng b bin v knh sng (fluvial and coastal system) hoc h thng chu th v nc su (deltaic and deepwater system). Nhiu va ri vo mt thit lp h thng trm tch n. Nh mt kt qu, cc tng bt ng nht vn nht qun, v vy, c nhiu la chn m hnh thch hp trn ton b va. Tuy nhin, h thng trm tch a cht c th thay i bng qua kch thc khu vc ca m hnh, bi v h thng trm tch chuyn tip c th c chuyn tip hoc va c th bao gm nhiu thit t trm tch. V d, cc tng sng v tng t lin quan c th chuyn tip r rng thnh cc tng chu th v tng bin khc. Nhng s thay i trong cc tng phi c tnh ton cho m hnh tng, s dng phng php m hnh da trn variogram hoc cc phng php m hnh khc.Hu hu cc phng php tng c th s dng thng k khng n nh (nonstationary statistics) tnh ton cho nhng thay i trong thit t trm tch. Cc phng php m hnh tng c th cung cp c hi ph hp tnh ton cho cc chuyn tip. Phng php nhiu im (multiple point based methods) c th lm vic vi nhiu hnh nh o to (training images) c cung cp trong mi thit t trm tch. M hnh da trn i tng (Object based modeling) c th quen vi vic x l cc hng i tng c xy dng tng dn thay i ngang qua va.Mt tip cn khc tnh ton cho nhng s thay i t l ln trong h thng trm tch l xc nh phn chia khu vc thnh cc vng hoc cc min t l ln. Khi , cc tng c m hnh ring bit trong mi vng. Cc vng c m hnh lin tc t gn nht n xa nht, vi iu kin d liu trng lp t mt vng n vng k tip. S m phng thay i theo mc tng dn trong cc tng ti cc bin ca cc vng. M hnh ring bit cho cc vng khc nhau c th gy nn tnh gin on nhn to ti cc ranh gii.2. M phng ch s lin tc (Sequential Indicator Simulation) (SIS):SIS c s dng rng ri cho kim sot cc tng trong qu trnh to do kt qu c s bin thin cao v c th c c tnh tt vi bt ng hng v o lng variogram tng quan khng gian. Xt K tng loi tr ln nhau sk, k = 1, , K. Ch s chuyn i (indicator transform) ti mt v tr c th uj cho mt tng c th sk l xc sut ca tng sk chim u th ti v tr : 1 nu n hin din v 0 nu ngc li. C K ch s chuyn i ti mi v tr d liu. SIS bao gm truy cp vo mi nt li theo mt trnh t ngu nhin. Ti mi nt li mt m tng (facies code) s c ch nh theo cc bc sau: Tm d liu gn v cc nt li c m phng trc y. Xy dng iu kin phn b bng kiging - tnh ton xc sut c mt ca mi tng ti v tr hin ti, p*k, k = 1, , K. V mt tng c m phng t b xc sut. Ton b qu trnh ny c lp li vi s ht ging ngu nhin khc nhau to ra nhiu s thc hin. Mt ng dn ngu nhin c xem xt trnh bt k s gi to m c th l kt qu t mt t hp ca mt ng dn thng xuyn v mt tm kim hn ch, n cn thit gii hn kch c ma trn kriging. D liu gc v cc gi tr m phng trc u c s dng thc hin ng cu trc khng gian gia cc d liu gc, gia d liu gc v cc gi tr c m phng v gia cc cp gi tr c m phng.

Figure 1: Tm nhn nghing vi mt ct ng phng, gc cm v lt ct a tng ca ca mt php th hin SIS da trn t l bin cc b v vi sinh vt ti ch (boundstone), ht (grainstone), dm kt (breccia) v bn (mudstone).Hnh 1 l mt v d ca SIS t va Carbonate t bn trng tng hp Paleo. M hnh gm bn tng vi sinh vt ti ch, ht, dm kt v bn. vi sinh vt ti ch v ht dc theo ng phng lin tc tt hn, dm kt lin tc tt hn dc theo gc cm. Chng l a cht c k vng v c m hnh vi ch s variogram nh hng (directional indicator variograms). T l variogram cc b c p dng p t cc hng trong m phng tng vi u th vi sinh vt ti ch trn nh m tiu (reef), ht v dm kt trn sn v bn tr nn ph bin hn v pha b t nh m tiu.

Figure 2: Tm nhn nghing vi mt ct ng phng, gc cm v lt ct a tng ca mt php th hin SIS v t l bin cc b cho ct (sand), lp kp ct v st (interbedded sand and shale) v st (shale).Hnh 2 l mt v d ng dng SIS cho va chu th (Deltaic Reservoir) t bn trng tng hp Paleo. Trong m hnh ny, ba ch s variogram c m hnh cho ct, ct kp, v st. T l bin cc b cho mi tng c p t cho cc hng vi ct chim u th gc chu th, lp kp ct v st trung tm chu th, v st ra chu th. Tnh lin tc ca ct v st thp hn ca lp kp ct v st c p t bi m hnh ch s variogram. Khng c th t tng r rng trong php thc hin SIS. Thm ch vi mt bn knh thng ng rt ngn cho mi tng, cc m hnh ha hng tng tp trung mi tng trong phn ring bit ca m hnh, v iu ny lm tng tnh lin kt theo chiu thng ng ca cc tng trong php thc hin.D liu a chn trong SIS (Seismic Data in SIS)D liu a chn thng l gi tr tuyt vi trong rng buc m hnh tng, n bao qut ton b va v c th nhy cm vi cc tng thay i. D nhin, cc tng bin i trn quy m nh hn khi lng o lng a chn v c s bin thin ca c tnh m hc trong mi tng ging nhau. Bc u tin s l hiu chnh d liu a chn thnh t l tng.C t d liu ging c trng v nhiu d liu a chn, Ch s variogram theo phng ngang cho SIS kh c xc nh ch t d liu ging. Mt gii php ph hp l s dng d liu a chn gip xc nh m hnh variogram 3D.Trung tm ca m phng ch s l s dng kriging xc nh xc sut c iu kin cho mi loi tng. Trong s hin din ca d liu a chn, mt vi thut ton cokriging v kriging khi phi c xem xt tnh ton cho d liu a chn. Bc th ba s l chn thut ton cokriging v tp hp cc thng s u vo cn thit.Hiu chnh d liu a chn thnh tngCokriging khng yu cu d liu a chn c hiu chnh r rng thnh t l tng. Cc n v a chn ban u c th c gi li v s hiu chnh c nhp vo thng qua hip phng sai cho gia ch s d liu cng v d liu a chn mm. Tuy vy, cc gi tr xc sut hiu chnh c u tin do: Cc gi tr xc sut c hiu chnh trong cc n v ngi dng hiu. Variogram cho hoc hip phng sai cho thng kh suy ra t d liu ging tha tht. S hiu chnh cho php tch hp nhng thng tin v rng buc khc.D liu a chn c gi l tr khng m hc (acoustic impedance) (AI) nhng n c th l bt k thuc tnh thch hp no c ngh n. Khng cn lm vic vi tr khng m hc, qu trnh tng t c th c s dng cho bt k o hm hoc thuc tnh a chn c th. Khong bin thin ca AI c chia thnh chui cc lp. Qu t cc lp th cc mi lin h quan trng b mt. Qu nhiu cc lp th khng d liu trong mi lp suy lun tin cy mi quan h ca n vi tng. Thng thng, 10 lp da trn thp phn v ca biu tn s AI l (hnh 3).

Figure 3: Biu tch ly tn sut v biu tn s ca thuc tnh a chn vi 10 lp c xc nh bi ngng thp phn v. C s lng d liu ging nhau trong mi lpQu trnh hiu chnh bao gm xc nh xc sut ca mi tng cho mi lp a chn:p(k|aij), k = 1, , K, j= 1, , NaVi p(k|aij) l xc sut ca loi tng k cho jth lp a chn th aij. Xc sut c nh gi ti cc v tr ging khoan. Cho mi mt chun ai, ti mt v tr ging, mi tng c mt t l thc t tng ng. Bng di l mt bng rng s hiu chnh cho K= 3 loi tng v 10 lp ai.

Quan tm c bit trong xy dng mt bng hiu chnh l phn gii theo phng ng ca d liu a chn. D liu a chn (ai gi tr) c th c ghi li ti mt tc mu nh (2 ms hoc thp hn), tuy nhin, phn gii thc theo phng ng phi th hn. Cn thit xem xt mt ca s thng ng ca kch thc thc t tnh ton xc sut trc. Mt khc, s hiu chnh s khng i din ng phn gii a chn v s nhiu quy m nh c th che du gi tr thng tin ca d liu a chn. D liu a chn mang theo thng tin khi s hiu chnh xc sut p(k|aij) khi hnh t xc sut ton cc ca mi tng, pk. S hiu chnh xc sut s chy t 0 ti 1, tuy nhin, khng bao gi c trng hp do s thay i quy m nh ca tng v s bin i c tnh m hc trong mi tng. Suy lun ch s Variogram (Indicator Variogram Inference)Phi suy lun mt tp K ch s Variogram m m t cu trc tng quan khng gian cho mi loi tng. Thch thc chnh trong suy lun variogram l theo phng ngang, thng c qu t ging tnh ton variogram ngang vi mt tin cy cao. phn gii theo phng thng ng thng cho php mt variogram ng ng tin cy c tnh ton. D liu a chn cung cp mt ngun thng tin tuyt vi hng dn la chn cc thng s theo phng ngang cho cc ch s variogram. Mi ch s variogram cho tng s c tnh ton ln lt. Bc u tin l tnh ton ch s variogram theo phng ng k(h) t d liu ging v chun ha n thnh sill n v bng phng sai pk (1 pk). Th hai, tnh ton variogram ngang t t l a chn tng ng, gi tr p(k|aij). Variogram t l a chn da trn loi tng k = 1, , K, tuy nhin khng th trnh khi s ph chng do t l n t cc c tnh bn dui c tr khng ging nhau. Variogram a chn cn c chun ha thnh sill n v. Cui cng, variogram ng v ngang c lm khp vi hnh dng ca ch s variogram theo phng ng. Ch c t l di, bn knh nh hng v bt k i bt ng hng l c ly t variogram t l a chn.C mt vi gi thit xc nh ch s variogram. Gi thit quan trng nht l variogram t l a chn cung cp mt s xp x hp l cho ch s theo phng ngang, bn knh nh hng i. iu ny l hp l nu a chn tng quan cao vi t l tng v nu trung bnh a chn theo phng ng l qu r rt. Phi xem xt s gim nh bn knh nh hng theo phng ngang bng vic ng h d liu a chn theo phng ngang do bn knh nh hng variogram a chn thng di hn ch s bn knh nh hng theo phng ngang. Nhiu gi tr trung bnh cc b (Locally Varying Mean)Thay v cokriging, xc sut d liu a chn c hiu chnh c th c s dng nh cc gi tr trung bnh cc b khc nhau cho kriging, l xc sut ca tng k c c tnh bi kriging:

Vi i(u; k), k = 1, , K, l xc sut cc b c c tnh c dng cho m phng, n l s d kiu cc b, , = 1, , n l trng s, l ch s d liu cc b, v p(k|ai(u)) l xc sut c suy ra t a chn ca tng k ti v tr u ang c xem xt. Khi c t d liu cc b, tng cc trng s ca d liu l nh v xc sut suy ra t a chn nhn mt trng s ln. Khi trng s cho d liu cc b l cao, xc sut suy ra t a chn c cho l thp.Tp hp cc xc sut i (u; k), k = 1, , K, phi c hiu chnh cho cc quan h trnh t, mt khc, th tc SIS khng b thay i. Th tc ny n gin v kh hiu qu. Khng c kim sot variogram r rng trn nh hng ca d liu a chn. Mt s hnh thc cokriging s c yu cu cho vic kim sot nh vy.Phng php tip cn cp nht Bayesian (The Bayesian Updating Approach)Hnh thc n gin nht ca cokriging l cokriging tun t (collocated cokriging) hoc phng php tin cn cp nht Bayesian (Bayesian Updating Approach). Phng php ny ph bin v tnh n gin v d dng ca n trong tnh ton d liu a chn.Ti mi v tr dc theo ng dn ngu nhin, ch s kriging c s dng c tnh xc sut c iu kin ca mi tng i*(u; k), k = 1, , K, ch t d liu cng i, v sau sa i cp nht Bayesian v cp nht xc sut theo cng thc sau:

k = 1, , KVi i**(u; k), k = 1, , K l xc sut c cp nht cho m phng, p(k|ai(u)) l xc sut suy ra t a chn ca tng k ti v tr u ang c xem xt, pk l ton b t l ca tng k, v C l mt hng s chun ha m bo tng xc sut cui cng l 1. Nhn t p(k|ai(u))/pk hot ng tng hoc gim xc sut, da trn khc bit ca t l tng c hiu chnh t t l ton cc. Khng thay i khi p(k|ai(u)) = pk, trong trng hp khi gi tr a chn ai(u) khng cha thng tin mi vt qu t l ton cc. C hai gi thit n gin pha sau cp nht Bayesian c th l quan trng: D liu a chn c xp tun t sng lc d liu a chn gn . T l ca d liu a chn n gin c gi nh ging nh kch thc li a cht. Mt s kim tra tng i n gin trn php thc hin m phng s phn xt liu cc gi nh ny c gy ra gi to hay khng. Bng hiu chnh c th c kim tra s dng d liu a chn v php thc hin SIS, mt tng thch cht ch vi xc sut tnh ton t d liu gc ch ra phng php ny lm vic tt. Vn s c khm ph bng xc sut cao c phng i cao hn nhiu gi tr trong m hnh cui cng, gi tr thp hn s l thp hn nhiu. Kriging ch s mm Markov Bayes (Markov Bayses Soft Indicator Kriging)Mt khi d liu a chn c hiu chnh thnh cc xc sut n v, ch s kriging c th c dng hp nht cc thng tin thnh cc gi tr xc sut c iu kin c ci thin cho SIS.Phng php tip cn Bayesian c trnh by trn l mt cch tip cn cp nht kt qu ca ch s kriging s ch s dng d liu ging. Cc ngun thng tin khc nhau nh l d liu ging v d liu a chn l c sn. Vi y d liu, c th tnh ton trc tip v m hnh ma trn hm hip phng sai v hm hip phng sai cho (mt hip phng sai cho cho mi tng k). Mt phng n thay th cho bi tp kh ny l c cung cp bi m hnh Markow Bayes. n gin, vit m hnh ny v mt hip phng sai. C ba hip phng sai c cn l CI(h; k), hip phng sai ca cc tng c ch s d liu cng cho tng loi k, c tnh ton t d liu ging hoc mt t hp d liu ging v a chn; CIS(h;k), hip phng sai cho gia cc tng c ch s d liu cng v gi tr xc sut a chn; v CS(h;k), hip phng sai ca cc gi tr xc sut a chn. Hai hip phng sai sau cng c cho bi m hnh:

H s Bk thu c theo cng thc di y:

Vi E{.} l ton t gi tr k vng hoc tr trung bnh s hc n gin. E{P(k|ai(u))|I(u;k)=1} gn 1 nu d liu a chn l tt, xc sut d on a chn ca tng ang hin din rt cao nu tng c mt. E{P(k|ai(u))|I(u;k)=0} gn 0 nu d liu a chn l tt, xc sut d on a chn ca tng ang hin din l rt thp nu tng khng c mt.Thng s K, Bk, k = 1, , K, lng xc sut a chn mm phn bit cc tng khc nhau. Tt nht l khi Bk1 v t nht khi Bk0. Khi Bk= 1, xc sut d liu a chn p(k|ai(u)) c x l nh ch s d liu cng. Ngc li, khi Bk= 0, d liu a chn c b qua, trng s kriging s l 0.Cokriging khi (Block Cokriging)Cc phin bn cokriging c trnh by trn u l phng php xp x c gng trnh: Tnh ton variogram cho hoc hip phng sai cho. Lp rp mt m hnh y ca coregionalization. X l d liu bn cht t l ln ca d liu a chn.C th lm ng cc cng vic trn v tt c m hnh variogram v variogram cho c th c tnh ton. Nhng m hnh variogram ny c th gim t l thnh im t l, gi nh rng d liu a chn cung cp thng tin trn mt trung bnh tuyn tnh ca d liu ch s tng. Mt m hnh ca hai vng c th c ph hp. Mt cokriging khi c th c thc hin bng SIS, s tnh ton cho d liu a chn t l thc t v d liu mm c hiu chnh t tr khng m hc thnh t l tng. Hu ht cc phn mm m hnh ha a thng k xem xt cc loi d liu khc nhau ti cc t l khng gian ging nhau. Tuy vy, khi m hnh t l nh ca hai vng c thit lp, trung bnh khng gian tuyn tnh ca variogram c th c s dng d dng trong phng trnh cokriging.Ch thch v s thc thi y SIS c th p dng c vi cc tng bt ng nht thay i trong qu trnh to hoc khng c hnh dng hnh hc r rng vi tnh khng lin tc trong c tnh thch hc. C mt s nhn nh nh sau: C mt s cn thit v t l i din ton cc c tnh ton thng qua declustering hoc t l cc b ng tin c xc nh thng qua m hnh xu hng (trend modeling). Mi loi tng cn mt m hnh variogram. C K-1 bc t do cn thit trong m hnh ch s variogram. Mt h thng nh phn ch cn mt m hnh variogram do tnh lin tc ca mt tng hon ton r rng so vi cc tng khc. Tnh ton v lm khp tt c K m hnh variogram khi K 3, s mu thun gia K m hnh variogram s c bc l lin kt cc vn . Loi kriging c dng trong khung m phng lin tc c thch ng x l d liu a chn. Cc ch s c lng vo nhau (Nested Indicators)Mt s thc hin thay th ca SIS l p dng chng lng vo nhau hoc phn cp chng. V d, xt mt SIS th nht chia cc tng thc v khng thc. Sau , mt SIS th hai c th c p dng trong cc tng thc phn bit s khc nhau gia cc tng thc. Th tc ny cho php quan h lng vo gia cc tng chn ra tng hiu qu.3. M phng Gauss ct ngn (Truncated Gaussian Simulation): tng ch cht vi m phng Gauss ct ngn l to ra cc php thc hin ca mt bin Gauss lin tc v sau ct ngn chng ti mt lot cc ngng to ra cc php thc hin cho mt loi tng. Hnh 4 l mt v d 1D v m phng Gauss ct ngn. Trc honh th hin phm tr m phng, c suy ra t mt m phng Gauss lin tc c cho bi ng cong mu en in m. Cc ngng ct ngn bin Gauss cho tng khng cn thit l hng s.

Figure 4: Biu m t cch m phng Gauss ct ngn lm vic: mt bin lin tc Gauss b ct ngn ti mt lot cc ngng to ra mt loi bin thc hin.Th t ca cc tng (Ordering of Facies)Mt c im quan trng ca m phng Gauss ct ngn l th t ca cc m hnh tng tng hp. Cc m tng c sinh ra t mt bin lin tc di mt t. Trong v d ba tng hnh 5, hu ht s thy tng 2 gia tng 1 v 3. Him khi thy c m 1, sau l m 3, khi bin lin tc thay i rt nhanh t cc gi tr thp n cao.Th t ny mang li li ch quan trng cho m phng Gauss ct ngn khi x l cc tng c xp th t. V d, cc tng c th c xc nh bi s lng st: 1= st, 2= lp kp gia ct v st, 3= ct sch. M phng Gauss ct ngn c th lm vic tt cho trng hp ny. SIS s lm vic tt hn khi khng c th t r rng do iu kin rng buc tnh lin tc khng gian r rng ca mi tng.

Figure 5: Phn phi chun vi ba m tng. C hai ngng (y1t v y2t) v ba gi tr y lin tc cho mi tng (y1, y2 v y3). T l mi tng l vng nm ng phn phi chunT l, ngng v iu kin d liuT l tng c ly nh hng s hoc c m hnh nh bin cc b vi nhng k thut m hnh ha xu hng. Trong mi trng hp, gi thit rng t l ca mi tng th t c bit ti mi v tr u trong lp A, pk(u), k = 1, , K, u A. T l ny c th c chuyn thnh t l tch ly:

Vi cp0 = 0 v cpK = 1 do t l tng l 1 ti mi v tr. C K 1 ngng cho qu trnh chuyn bin lin tc Gauss thnh tng

Vi ykt(u), k = 1, , K 1, u A l cc ngng cho m phng Gauss ct ngn, y0t= -, yKt = +, G-1(.) l nghch o hm phn phi tch ly ca phn phi chun, v cpk(u), k = 1, , K-1 l xc sut tch ly cho v tr u. Cho mt lch chun hoc bin chun, nhng ngng ny c th c dng gn mt m tng:

Facies ti u = k nu Cc ngng bin cc b gii thiu thng tin xu hng. Cc gi tr Gauss y(u) c xem l n nh, E{Y(u)} = 0, u A.Cc loi d liu tng phi c chuyn thnh d liu lin tc Gauss c iu kin cho m phng c iu kin bin n nh Gauss, Y. C hai s xem st: Cc t l cc b v cc ngng tng ng phi c xem xt chc rng cc tng chnh xc thu c t vic chuyn i d liu v min ban u. Cc tng c phn loi v mt s quyt nh phi c thc hin v cc spikes (nhiu do s tng t bin) c gy bi loi d liu.Vic x l cc t l v cc ngng khc nhau l n gin: Mt thng tin cc b c s dng. Despiking (loi b nhiu spikes) yu cu cc quyt nh b sung.Despiking ngu nhin s a vo ngu nhin cc t l nh khng hp l. Mt despiking phc tp hn c th c s dng, nhng c li ch nh.Cc quyt nh lin quan n cc thng s despiking c th a ra nhng gi to khc. Gii php n gin nht l thit lp s im chun chuyn i cho mi tng thnh trung tm ca lp trong phn phi chun, ch cc spike khng thay i:

Vi y(u) l im chun chuyn i ti v tr u, k l m tng ti v tr u, v cpk l t l tch ly. Tt c s o lng tng c chuyn i v s dng trong m phng Gauss c iu kin.VariogramM phng Gauss ct ngn yu cu mt variogram n cho bin y. y l mt thun tin c ngha rng ch s variogram K khng cn c tnh ton v m hnh mt cch nht qun. iu ny cn l mt bt li do khng c kh nng kim sot s bin i cc m hnh khc nhau cho cc tng khc nhau. Thng thng, khng phi l mt tng tt tnh ton v lm khp trc tip variogram y vi d liu y do cc spike. Trong trng hp hai tng (mt ngng n y1t), hip phng sai im chun c lin kt trc tip, thng qua quan h mt vi mt cho cc hip phng sai ch s tng. Mt cch khc phc hn ch trn s c xem st mt lot cc hm ngu nhin Guass Yk(u), k = 1, , K, mi hm c dng m phng (sau khi ct ngn) mt tp hp lng nhau ca hai tng, l, m phng mi tp hp lng nhau vo mt tp hp c m phng trc . iu ny s l mt phin bn phc tp hn phng php tip cn ch s lng nhau c tho lun trong m phng ch s lin tc. Phng php tip cn ny khng c pht trin hn do cc tng him khi c mt m hnh ty ca bin c lng nhau. Phng php gn ng khc gm c nghch o m hnh hip phng sai n CY(h) t mt s trung bnh cc variogram ch s K. Trung bnh variogram ch s n (average indicator variograms) s c sao chp thng qua m phng, khng c bt k m hnh variogram ch s ca tng no. M phng Gauss nhiu trc (Pluri Gaussian Simulation) (PGS) m rng phng php Gauss ct ngn cho m phng nhiu tng khng lng nhau (K 2) cho nhiu hm ngu hin Gauss. Ngc li cho trng hp K = 2, m phng cho nhiu tng khng lng nhau c php nghch o khng phi duy nht. Cc th tc lp i lp li da trn la chn th v sai (trial and error) ca hip phng cho v hip phng sai im chun u vo gia nhiu hm ngu nhin Gauss c xem xt, nhng vi kt qu gii hn.ng dng gn y ca PGS chng minh tnh linh hot v hu ch trong vic c th tn trng mi quan h lin kt bc cao. Trong thc t, PGS c yu cu c tnh: Cc quy lut tng thng qua cc quyt nh v mi tng quan gia nhiu hm ngu nhin Gauss. S ct ngn ca khng gian bc cao hn vo trong tng K.Phng php tip cn c gii thiu l ly nhiu nht variogram ch s quan trng v nghch o s liu ca n thnh variogram im chun tng ng. Variogram im chun c tnh d hng v cng mt bn knh nh hng, hnh dng mt hn hnh parapol hoc Gauss ti khong cch ngn.

Figure 6: Mi quan h gia variogram ch s c chun ha (nt lin) v semivariogram im chun (nt t) vi cc t l n bin khc nhau.

Figure 7: Hu qu ca s dng variogram sai cho m phng Guass ct ngn. Php thc hin Variogram ch s c chun ha (bn tri) ng vi php thc hin Variogram im chun (bn phi). Kt qu ca variogram ch s c nh hng nugget qu cao. Ch thch v s thc hin y M phng Gauss ct ngn c th p dng c cho cc tng bt ng nht c thay i trong qu trnh to , c hnh dng hnh hc khng r rng v c th t trong mt s kiu c th d on c. Mt s ch thch: Nh vi SIS, cn thit tnh ton t l ton cc i din thng qua declustering hoc t l cc b ng tin c xc nh thng qua m hnh xu hng. Nhng t l ny xc nh nhiu ngng cc b v d liu iu kin. Mt m hnh variogram ch s c cn cho hu ht cc loi tng quan trng. Variogram ny c chuyn i thnh mt variogram cho m phng bin Gauss, trong thc t, hnh dng variogram c thay i thnh hnh Gauss. Thc hin m phng Gauss c iu kin c ct ngn bi nhiu ngng cc b to ra cc php thc hin tng.

Figure 8: Va chu th vi tng ct kt, lp kp ct st v st. Tm nhn nghing vi mt ct ng phng, gc cm v lt ct ngang ca mt php thc hin SIS (trn) v m phng Gauss ct ngn (di). C hai trng hp, bn gc phng v cho bin cc b c p dng xoay hng ban u ca variogram cc b nhm sao chp m hnh nhnh sng. Ch rng s chuyn i cho Gauss ct ngn t ct n lp kp ct st v cui cng l st.4. Thc hin lm sch tng da trn li (Cleaning Cell Based Facies Realizations):Mt mi quan tm ca php thc hin tng da trn li l s hin din ca cc bin i t l ngn khng th trnh c, vi s xut hin a cht khng thc t. Trong mt s trng hp, s bin i nh vy nh hng n m phng dng chy v d bo tr lng, y mt l do chnh ng xem xt thc hin cc thut ton lm sch. Mt mi quan tm th hai l t l tng thng lch khi t l mc tiu u vo. c bit l, cc loi tng vi t l tng i nh (5 10%) c th km ph hp. Trong m phng ch s, ngun chnh ca s sai lch l vic iu chnh cc mi quan h trnh t (xc sut c c tnh c hiu chnh l khng m v tng bng 1). Khng c gii php r rng thng c dng

II. M hnh tng da trn i tng (Object Based Facies Modeling):1. Khi qut:Mt trin vng a cht thun tin nhn va t mt thi a tng trin vng. Kin trc trm tch c xem xt r rng qua mt biu phn cp a tng. Cc tng va c chia thnh cc nhp, nhp, cc lp, tp lp a tng. V d, bt ng nht trong mt h thng knh sng c m t bi cc lp va a tng, cc hc, rnh phc tp, cc knh (channel), cc (levee) v cc khe nt v (crevass) thng qua cc c im t l nh thm vo. Xem xt m hnh phn cp thnh to ca bt ng nht bng s chuyn i ta lin tip v i tng hnh hc i din cc tng lin kt. Cc m hnh rng v thm c xy dng sau ti mt t l thch hp s dng h thng ta c ng chnh vi trm tch lin tc ti mt t l c bit hoc thmch vi nh hng t nhiu t l. Cc m hnh da trn i tng c to ra hng ngy trong c tnh va. C ba vn ct li c ch ra trong s dng m hnh da trn i tng: Cc hnh dng a cht v phn phi thng s ca chng. Thut ton iu chnh v tr i tng. D liu thch hp rng buc kt qu thc hin.Cc m hnh da trn i tng c th to ra cc m hnh bt ng nht vi hnh hc gh gh m khng th thc hin bi phng php da trn li. Mt gi thit c bn vi m hnh da trn i tng l hnh dng ca cc n v trm tch c th l gh gh v c th c m t bi mt hnh hc c tham s ha. Trong khi qu trnh trm tch sinh ra cc dng hnh hc c th nhn bit c, sinh ra a cht phc tp do c gia cng li, s ph ln v qu trnh to c th dn n c im c nhiu ph v hoc ngu nhin trong hnh thc, thiu cc hnh hc r rng. Trong trng hp ny, cc phng php da trn li c th thch hp hn cho vic ci thin kh nng iu kin ca chng. Mc d cc m hnh da trn i tng c th c x l sau gim hnh hc g gh (vi iu kin nhiu), nhng n thng khng th c thm thng tin hnh hc m hnh da trn li. Cc m hnh da trn i tng l gi thnh to (pseudo genetic) trong ngha cc quy lut xm thc ( tr hn trn) v ngun gc a cht khc c s dng nhiu nht c th.Hu ht qu trnh bt chc (process mimicking) cc phng php m hnh tng u da trn cc i tng v b mt. Nu mt thut ton ni cc i tng khng c mt khi nim v thi gian nhp a tng, gi l m hnh da trn i tng. Nu mt thut ton ni cc i tng trong nhp a tng m khng c quy lut lin quan n mt i tng k tip, vn l m hnh da trn i tng. Nu mt thut ton ni cc i tng trong thi gian nhp a tng vi quy lut bt chc qu trnh trm tch, gi l m hnh ha qu trnh bt chc (process mimicking model).Cc dng a cht (Geological Shapes)Khng c gii hn vn c cho cc hnh dng c m hnh vi cc k thut da trn i tng. Hnh dng c th c nh r bng cc phng trnh, mt mu mnh (raster template) (trn mn my tnh, mnh l ton b cc dng qut ngang to nn hnh nh, trn mi dng l cc chm c th pht sng c lp vi nhau), hoc kt hp c hai. Cc hnh dng ny c th c t hp t mt tp hp cc thng s hnh dng c xc nh trc hoc thm ch c nh r hoc v t do trc khi m hnh. Cc hnh dng a cht c th c m hnh phn cp. Mt hnh dng i tng c th c s dng ti mt t l ln, v sau cc hnh dng khc nhau c th c s dng cho cho cc hnh dng a cht ni b t l nh. Mt s hnh dng r rng sau y: Cc knh sng lp y ct b ri (abandoned sand filled fluvial channels) trong mt khi trm tch st ng bng (floodplain shales) v trm tch ht mn. Nhng knh dng hnh sin c m hnh bi mt ng tm 1D v mt mt ct thay i dc theo ng tm. Nhng i tng (levee)v khe nt v (crevasse) c th c gn lin vi knh (chennel). Cc nt st (shale plugs), xi mng kt hch (cemented concretions), phin st (shale clasts) v nhng tng khng thc (non net) khc c th c b tr trong cc knh dc theo cc xu hng (trends) trong cc tng thc (net). Xp nhm ca cc knh vo trong knh hoc vnh ai phc tp c th c x l bi cc i tng t l ln hoc nh mt phn thut ton v tr i tng. Cc h thng sng ngon ngoo nng lng thp hn (lower energy meandering fluvial system) c th c m hnh nh cc thu knh ct trong mt nn tng khng thc. Thnh thong xem xt m hnh ha ton b tng sng v sau gn ct v st bn trong knh theo mt s cch thc t. Cc h thng trm tch sng ha khc (channelized depositional systems) bao gm h thng nc su v ca sng thng c m hnh bi cc k thut m hnh ha phng theo knh sng nhm xem xt h thng c th nh kch thc knh, t s b rng v b dy, v bt ng nht bn trong. Cc m tiu carbonate ra thm lc a (shelf edge carbonate reefs) c th c m hnh vi mt g li m tiu (mounded reef core) v dm kt thy che ph mi m tiu (breccia lobes draping the fore reef) v m m tiu phn tn (patch reef scatter) trong khu vc pha sau m tiu. Cc ht c th to thnh tm chn bao quanh m tiu. Trong bi cnh ny, s bin i qu trnh to c th ph v lng ln tm quan trng ca m hnh tng da trn i tng. Cc dng cn ct do gi (eolian dune shapes) l ng c vin cho m hnh da trn i tng. Mc d hnh hc 3D ca i tng ny khng quan trng xc nh phn tch, nhng c th cn thit cho gi nh v m hnh thc t. St tn d (remnent shales) c th c m hnh nh cc i tng hnh a hoc elip bn trong mt khi ct. iu ny c th thch hp trong cc va c t s thc/ tng cao (net to- gross). Mc d st c t l thp, nhng chng s nh hng ng k n thm theo phng ng, do ging khai thc ngang v to nn nc. Cc va chu th (deltaic reservoir) c th c m hnh nh cc n v ct hnh qut trong bn trong mt khi trm tch km cht lng. V mt lch s, cc k thut da trn li c s dng nhiu hn vi cc h thng nh vy. Mi trng mt b (shoreface) c mt s tin trin c h thng t cc tng gn b n cc tng xa b. V tr ca b bin c th c m hnh nh mt hm tui a cht (v tr trong lp a tng) v th t c th ca cc tng c lin kt vo v tr ny. Mt s m hnh hn hp da trn i tng v li s thch hp.D liu thch hpMt m hnh tng thc t nn sao chp tt c d liu c sn bn trong vng th tch h tr v chnh xc ca mi ngun d liu. D liu thch hp bao gm d liu ging cc b, d liu a chn, d liu khai thc v minh gii a cht gm c cc i tng xc nh, s kt ni v cc xu hng.D liu ging cc b bao gm cc m tng c nhn bit ti cc v tr bt k trong lp va 3D. Cc tng c th n t s quan st mu li trc tip hoc suy ra t nhiu d liu log ging. D liu ging cc b cng c ly t s giao nhau ca cc loi tng ti v tr v nh hng bt k.D liu khai thc v a chn hu ht thng khng ng khi thng tin t l ln. C nhiu cch khc nhau miu t nhng thng tin nh vy. Mt cch l tnh ton xc sut c suy ra t a chn ca mi tng:

Vi pk(u) l xc sut hoc t l ca tng k ti v tr uV, c k = 1, , K m tng, v ti v tr uV l c xc nh mi ni trong va A. Ch s di V l th tch m t l tng c xc nh. Nhiu thng tin t l tng cc b cn c th c c t mnh gii v lp bn a cht. Kin thc v h thng trm tch thng cho php c im k thut ca khu vc v t l ln ln v nh hn ca cc tng khc nhau.D liu a chn, khai thc v a cht c th khng phn bit c mt s tng. V d, cnh vt khe (crevasse splay) v ct (levee sands) c th khng phn bit c t d liu. Mt rng buc quan trng trong m hnh da trn i tng l sao chp t l ca cc tng c nhm. V tr ca mt s i tng a cht c th c bit chnh xc t s quan st a chn, minh gii th va (well test) hoc d liu khai thc, hoc t bn a cht. V tr ca nhng i tng nh vy phi c c nh v khng li mt thut ton b tr ngu nhin. C cc loi thng tin khc nhau lin quan n v tr i tng: Kin thc v v tr chnh xc ca mt s i tng. Kin thc v hai ging (hoc hn) giao nhau ca tng ging nhau khng th lin quan n i tng ging nhau. Mt xc sut o lng hai ging (hoc hn) giao nhau ca tng ging nhau thuc v i tng ging nhau.S kt ni trn n t minh gii a cht ca cc tng c bit c ly mu li v t d liu k thut lin quan n p sut cht lu lin tc gia s giao nhau trong cc ging khc nhau. Trong khi cc m hnh da trn li d dng sao chp dy c cc d liu ging, cc t l bin cc b v d liu th cp, th cc m hnh da trn i tng c mt s hn ch. D liu ging dy c c th dn n, hoc thi gian chy lu, hoc cc gi to nh s v tr i tng c th c gng vinh danh iu kin d liu. Thi gian chy lu c th n t s lp i lp li kt hp tng thch cc rng buc kh khn. S gi to thng bao gm: S khc bit ng thi m hnh ti hoc gn cc ging. Hnh hc khng thc t. S thay i khng thc t trong hnh hc.Mt kim tra c bn cho cc m hnh da trn i tng l v tr ca d liu iu kin khng th c xc nh t m hnh chnh n v hnh hc l n nh, nu khng n nh th khng c p t r rng. Tp hp d liu thch hp bao gm phn phi ngu nhin lin quan n kch thc, hnh dng, nh hng v tc ng qua li ca cc i tng. Cc thng s ny nh r cho mt vn c bit, nhng c c trng lin kt vi mt s ngu nhin. Rt kh thit lp cc phn phi tin cy cho cc thng s ny t d liu ging tha tht. S ci tin trong hnh nh a chn v s dng cc d liu tng t nng ci thin vn suy lun kh khn ny. Tuy nhin, suy lun t phn phi ny cn l mt hn ch ln ca m hnh da trn i tng.Cc thut ton cho v tr i tng Cc i tng phi c t v tr m chng xut hin thc t v tn trng d liu c sn. Thut ton qu n gin c th dn n gi to gn d liu iu kin. Thut ton cho iu kin gm c: cc thut ton phn tch c tc dng sao chp d liu (hai bc xc nh v tr ni d liu iu kin c sao chp u tin v sau phn cn li ca min c in), v cc thut ton kiu ti u ha m phng lp i lp li.Cc thut ton iu kin trc tip (Direct conditioning algorithms) iu chnh kch thc, hnh dng, hoc v tr ca cc i tng xy dng cc i tng tn trng d liu iu kin cc b. Th tc ny c th c thc hin cho nhiu hnh dng a cht, ph bin nht l cc knh sng.

Figure 9: M t m hnh bin 1D c ng tm ca mt i tng knh. Khi hnh t ng hng chnh c m hnh phn tch hoc vi m phng a thng k (Gauss). Khi hnh t ng tm c th c dng lm iu kin cho d liu ging cc b.

Figure 10: Hai v d v iu kin trc tip ca cc ng tm knh tn trng d liu cc b trong m hnh da trn i tng. Trng hp bn tri, khong cch d1 v d2 c s dng buc knh i thng qua hai ging. Trng hp bn phi, knh c b buc trnh xa ging, ni ging khng tn ti.Thng thng, thut ton iu kin trc tip c p dng trong hai bc: Thm i tng bao ph ni giao nhau gia cc tng cc b, l, kt hp tt c d liu iu kin m khng c tng nn tng. Thm i tng m khng lm vi phm ni giao nhau c bit ca tng nn tng, cho n khi t l chnh xc ca mi loi tng xut hin.Mt phng php tip cn khc nhau xc nh v tr i tng l lp i lp li. Mt tp hp ban u ca cc i tng c xc nh v tr trong th tch va kt hp t l ton cc ca cc tng khc nhau. S b tr c th vi phm d liu ging cc b v nhiu t l cc b. Mt hm i tng c tnh ton o lng s khng khp t d liu c o lng. Sau , m hnh b xo trn nhiu ln cho n khi hm i tng h xung gn bng 0. 2. St ngu nhin:Khi t s thc/ tng l cao r rt (80% tr ln), rt hp l m hnh st tn d (hoc cc tng khng thc thch hp) nh cc i tng bn trong mt khi ct. St tn d ny c th khng nh hng n thm ngang, nhng c th nh hng ng k n thm thng ng, nn nc, mi t v hiu sut d bo ca ging ngang. Yu cu u vo ca m hnh st ngu nhin l mt c tnh hnh hc ca hnh hc st, cc thng s nh hng, d liu ging v c th c thng tin trn nhiu t l st cc b. Hnh dng thng c ly nh hnh ellipsoid. Phn phi b dy c th c suy ra t cc v tr ging. T s chiu di/ chiu dy phi c thit lp t thng tin a cht tng t hoc kt hp t mt s loi d liu khc nh l d liu th va, khai thc. Mt s thng tin nh hng c th c sn thng qua kin thc v h thng trm tch. Khng chc rng c bt k thng tin no lin quan n t l cc b khc nhau nu t gy ca st l nh (t hn 20%).

Figure 11: Ba m hnh st ngu nhin da trn i tng. Mi mt ct c phn trm st (15%) v phn b b dy nh nhau. Kch thc ngang ca st ellipsoid c thay i t ng.M phng c iu kin c quan tm hn.

Figure 12: Ba m hnh st ngu nhin da trn i tng sao chp tnh lin tc ca ct v st ti mt v tr ging ng. Va chu th cung cp mt v d tt th hin m hnh st da trn i tng bi v t l thc/ tng cao vi cc mnh st b gii hn m c th c rng buc ng k trn nhy cht lu va. Cc tng va c nhm li v thit lp nh tng nn, v st c m phng c iu kin vi d liu ging.SIS c th c p dng xy dng cc m hnh lp ph st, nhng s khng sao chp hnh hc g gh. Tham s ha i tng c chn cho st l qu n gin v tuyn tnh. Mt ng dng hu ch hn ca cc k thut da trn i tng l cho cc knh sng hnh sin.

Figure 13: M hnh st da trn i tng cho va chu th. Cc tng va c n lm ni bt i tng st. St chim 10% th tch va.3. M hnh ha tng sng (Fluvial Modeling):Cc thnh to knh c lp y ct b ri (abandoned sand filled channel forms) vi mt khi st ng bng (floodplain shales) c m hnh da trn i tng.Nhiu hnh hc ct sng nh thnh to bi bi ca knh (channel bar forms), vng ct rng theo phng ngang (laterally extensive sand regions) do s bi t theo phng ngang v nhiu bi bi th ct khng lin tc (discontinuous point bar sand bodies) c xem xt s dng cng mt s vi cc m hnh trm tch hc phc tp hoc cc phng php qu trnh bt chc (process mimicking methods).Cc tng c lin kt nh ct (levee sands) ct nt v (crevasse sands) v cc i xi mng (cemented zones) bn trong cc knh ct c m hnh ti cng thi gian.

Figure 14: M hnh da trn i tng phn tng. (a) Mi lp va c trch ra, (b) ta a tng ca va c tnh ton, (c) mi knh phc tp c trch ra t lp, (d) h thng ta a tng cc b cho knh phc tp c thit lp, (e) mi knh c trch ra t knh phc tp, (f) mt h ta a tng cc b cho knh c thit lp, (g) thuc tnh thch hc c m hnh bn trong h thng ta cho knh thch hp, (h) cc ta knh c khi phc (xy dng) li, (i) knh c b tr v li knh phc tp, (j) cc ta knh phc tp c khi phc li, (k) knh phc tp c b tr v li lp, (l) cc ta lp c khi phc li, v (m) cc lp c b tr v li va.S chuyn i ta (Coordinate Transformations)Mt quan im ca m hnh da trn i tng l h ta c lp vo cho thch hp vi hng chnh lin tc. Hng lin tc da vo t l quan st v c im a cht c th c m hnh. Cc chuyn i ta khc nhau c p dng lin tc v ti cc t l khc nhau. V d: Mi lp hoc nhp a tng chnh c m hnh c lp. Mt lp c th lin quan ta a tng c xc nh t nh hin ti (existing top), nn hin ti (existing base), nh khi phc (restored top), nn khi phc (restored base). Php tnh tin v php xoay mt khu vc c thc hin c h ta c cn l (sp cho thng hng) cho khu vc , vi hng chnh l sn lc a c, l hng c trung bnh tnh lin tc tuyt nht. Cc knh sng thng xp nhm cng nhau trong cc knh phc tp hoc vnh ai knh (channel belts). Cc knh phc tp c th c gn sng t l ln c lm thng. Cc knh bn trong knh phc tp cn c lm thng cho m hnh thuc tnh thch hc bn trong chng. Cc knh phc tp c lm thng v cc knh khng rng nh nhau, mt lin h ta ngang lm cho cc ranh gii song song v n gin ha m hnh thuc tnh thch hc n sau.Mi s chuyn i c th o ngc v cc i tng a cht c th c nhn v lu di bt k h ta no.S dng h ta thch hp cho rng v thm bn trong mi knh. H ta thng ng c th c ly song song vi b mt cao nht ca knh hoc c lm t t l gia b mt nh v nn (top and base surface). Cc i tng tng sng (Fluvial Facies Objects) Loi tng u tin l nn st ngp lt khng thm (impermeable background floodplain shale), c xem nh mt khi trong cc i tng ct v va cht lng b kp vo. Loi tng th hai l ct lng sui (channel sand) lp y cc knh b ri hnh sin (sinouous abandoned channels). Tng ny c xem nh va cht lng nht do nng lng trm tch tng i cao v kt qu l kch thc ht th. Bn trong ct lng sui c cc c im c bit nh l: Bt ng nht ca vt liu lp y lng dn (channel fill), cha mt s vt liu khng thc ht mn. Mt tch t tn d trong lng dn (channel lag deposit) ti y Xu hng ht mn i ln (fining upward trends) bn trong vt liu lp y lng dn. Loi tng th ba l ct (levee sand) c thnh to dc theo ra lng dn. Loi ct ny km cht lng hn vt liu lp y lng dn (channel fill). Loi th cui cng l qut ct nt v (crevasse splay sand) c thnh to trong sut k ngp lt khi b thng v ct b trm tch xa knh dn chnh. Nhng loi ct ny km cht lng hn vt liu lp y lng dn (channel fill). Thng c hnh thnh ni cao knh dn cao.

Figure 15: M hnh khi nim ca tng sng. Gm nn st ngp lt (background of floodplain shales), ct b ri lp y lng dn (sand filled abandoned channel), ct (levee border sands), v qut ct nt v (crevasse splay sands).Mt i tng cho m hnh tng sng l mt knh dn (channel) v tt c ct (levee sand) v ct nt v (crevasse sands) lin quan. C th hn, tnh ton hiu qu cho cc i tng l mt mu li s c m ha nh ct lng sui, ct v ct nt v. Cc knh dn c xc nh bi gc nh hng v lch trung bnh t hng knh dn, chiu di bc sng hoc chiu di lin kt ca lch trung bnh, b dy, b dy gn sng (v chiu di lin kt), t l chiu rng/ b dy, v chiu rng gn sng (v chiu di lin kt). Mi thng s c th ly mt khong gi tr c th theo nh mt xc sut phn b.

Figure 16: Mt vi thng s c dng xc nh i tng knh dn: (a) Gc cho hng chnh v lch cho ng tm knh dn thc t, (b) bin thin chiu rng knh dn (v b dy) vi s kt ni khi ln gia cc lt ct knh dn.

Figure 17: Mt ct ca mt i tng knh dn c xc nh bi chiu rng, v tr ca b dy ln nht.Cc hnh dng hnh hc s c c nh v thay i kch thc. Thng thng, cc thng s kch thc nn ph thuc vo kch thc ca knh dn, mt knh dn ln c cc ln. Cc kch thc ca tri v phi c th khc nhau. Ba thng s khong cch (A) khong cch ngang ca , (B) chiu cao trn cao chun knh dn v (C) su bn di mt chun knh dn c dng xc nh kch thc.

Figure 18: Mt ct xuyn qua mt knh dn c lp y ct b ri (abandoned sand - filled channel) v ct (levee sand). Ba thng s khong cch (A), (B), (C) c dng xc nh kch thc ca ct (levee sand).Mt th tc ng i ngu nhin c th c s dng thit lp hnh hc nt v (crevasse geometry). V tr ca mt nt v thng ni knh dn cong nht. Mt s ng i ngu nhin c tung ra t v tr nt v thit lp quy m khu vc. Bn thng s kim sot l (1) khong cch trung bnh ca ct nt v (crevasse sand) t c tnh t knh dn, (2) khong cch trung bnh dc theo knh dn, v (3) tnh bt thng ca ct nt v hoc s ng i ngu nhin c s dng. B dy ca ct nt v gim tuyn tnh t mt b dy ln nht n knh dn.

Figure 19: Knh dn (channel) v nt v (crevasse) c thnh to do thng . Mt s ng i ngu nhin tung ra t l thng thit lp hnh hc nt v. S, chiu dy v khuch tn theo phng ngang kim sot hnh hc v kch thc ca nt v.D liu iu kin a cht (Geological Conditioning Data)Nhiu thng s kch thc i tng cho cc m hnh da trn i tng kh suy ra t d liu ging v a chn c sn. Cc ging cung cp thng tin v phn b b dy v t l cc tng khc nhau. Tuy nhin, thng s kch thc thng cn c o lng thch hp t cc vt l tng t, cc h thng trm tch hin i, v cc va c khoan dy c tng t. T l ca mi loi tng (channel sand, floodplain shale, crevasse splay sand, v levee sand) c th c nh r bng mt ng cong t l thng ng (vertical proportion curve), cc bn t l khu vc (areal proportion maps), v t l ton cc mu (reference global proportion). y l ba loi t l c th thu c thng qua mt t hp d liu ging v a chn. T l ton cc mu c k hiu l Pgk, k = 1, , K, vi K l s tng. Mt ng cong t l thng ng nh r t l ca mt tng k nh mt hm cao thng ng hoc hm thi gian v c k hiu l Pvk(z) vi z (0, 1]. Bn t l khu vc nh r t l tng nh mt hm v tr khu vc (x, y) v c k hiu l Pak (x, y).ng cong t l thng ng v bn t l khu vc c th ngm cha t l ton cc v chng hoc mu thun vi nhau hoc mu thun vi t l ton cc mu. Cc t l ny c th c chia cng t l.Hai c tnh ca cc thng s hnh hc hoc a cht l: Mi thng s c th ly mt khong gi tr c th theo xc sut phn b. Khong gi tr thay i vi v tr a tng z hoc thi gian.V vy, cc thng s xc nh mi knh dn c nh r vi mt lot iu kin phn b cho mt tp hp cc gi tr z gin on gia nn a tng v nh a tng.S nh hng, hnh dng, v kch thc ca mt knh dn phc tp phc v nh mt n v m hnh c bn. Cc phn b u vo di y c yu cu nh r hnh hc knh dn phc tp: Gc . lch t hng knh dn phc tp v chiu di lin kt ca lch ny dc theo trc ca knh dn phc tp. Chiu dy. T s chiu rng v chiu dy. T s thc v tng trong knh phc tp.Mt vi thng s tt hn c yu cu nh r hnh hc knh v b dy v b rng mi knh khng phi hng s: B dy trung bnh. B dy gn sng v chiu di lin kt ca b dy gn sng. T s chiu rng v chiu dy. nhm y knh dn.Cc tng c bit dc theo mi ging. D liu c th n t bt k ging no. D liu ging trong ta khng gian gc c chuyn i thnh cc ta thch hp ti mi giai on ca m hnh. Th tc m phngTt c u vo a cht c trnh by trn u phi c nh r trc khi m hnh. Cc thng s ny rt kh khn suy ra t d liu c sn. Mt vi thng s, nh t l chiu rng v chiu dy c th gi khng i ti mt s gi tr thc t. Nghin cu nhy c c xem xt trn cc thng s khc phn on quan trng v nh gi kh nng chp nhn trc quan ca cc kt qu thc hin.Th tc m phng l lin tc. u tin, s phn b knh dn phc tp c thit lp. Th hai, phn b ca cc knh bn trong knh dn phc tp. Th ba, rng c gn s dng ta knh dn thch hp. Cui cng, thm c gn iu kin vi tng v rng.Cc thut ton da trn variogram truyn thng c th c dng cho m hnh rng v thm. iu kin cho tng lin tc dc theo cc ging v d liu t l tng nn c hon thnh ngay nu c th. Mt th tc lp i lp li c th c s dng thc thi tng ti cc ging v ng cong t l v cc bn .4. Cc h thng trm tch khc sng (Nonfluvial Depositional Systems):M hnh tng da trn i tng c th p dng c cho nhiu thit lp trm tch. Hn ch chnh n t cc thng s thch hp cho i tng a cht. Cc thy (lope) chu th hoc thy nc su l v d ca cc i tng c th c xc nh. C by thng s cho mt hnh hc thy n gin. Tp hp cc thng s ny cung cp mt s cn bng gia hnh hc qu n gin (qu t thng s) v qu linh hot c lin kt vi nhng suy lun kh khn (qu nhiu thng s). By thng s nh sau: sw = chiu rng bt u (starting width); c trng cho rng pha cui knh dn. ll = chiu di thy (lope length); tng chiu di ca thy t knh dn n im cui. rm = v tr tng i ca chiu rng ln nht (relative position of maximum width); thy t chiu rng ln nht mt khong rm*ll t ni bt u thy. lwlr = t s chiu rng/ chiu di thy (lope width/ length ratio); chiu rng ln nht ca thy c cho bi lwlr*ll ti v tr c nh r b v tr tng i rm. st = chiu dy bt u (start thickness); chiu dy bt u ca thy k bn cnh knh dn (c th c lin kt vi chiu dy knh dn ti im ). y l chiu dy ti ng tm thy. ft = chiu dy cui cng (final thickness); chiu dy ca thy ti im cui (ti ng tm thy) so vi chiu dy bt u st. ct = mt ct chiu dy hiu chnh (cross section thickness correction); lng chiu dy gim t ng tm n ra ca thy.

Figure 20: Cc thng s cn thit m t hnh hc thy 3D.Theo quan im k hoch, cc rng buc hnh hc bao gm: Chiu rng bng vi chiu rng bt u ti im chuyn tip t knh dn y = w ti x = 0. Chiu rng l ln nht ti v tr tng i l y = W ti x = l. Chiu rng l 0 ti chiu di thy ln nht L y = 0 ti x = L. ng tip tuyn vi hnh dng thy c dc l 0 ti x = l. ng tip tuyn vi hnh dng thy c dc xc nh ti x = L.Phng trnh tha mn cc rng buc hnh hc trn l:

Vi y l khong cch t ng tm, x l khong cch dc theo ng tm, w = sw/2, l = rm*ll, L = ll, v W = (ll*lwlr)/2. Hnh dng l da trn hnh dng p(1-p) cho phn u tin (gn nht kt ni vi knh dn) v mt hnh dng elip cho phn hai. Hm v o hm phn u u lin tc ti tt c v tr xung quanh ng vin thy.

Figure 21: (a) hnh hc thy vi cc thng s khc nhau. T trn xung di t s rng/ di gim t 2:1 n 0.33:1. V tr tng i ca chiu rng ln nht l 0.65 bn tri v 0.85 bn phi. (b) hnh hc c bn W = 0.5, w = 0.01, L = 1, v l = 0.6 vi su m phng Gauss khc nhau.Cc thy c th c b tr ti cui cc knh dn. Hnh dng cui cng ca cc knh dn v thy trong bt k m hnh cui cng no cng c xc nh bi d liu iu kin v thut ton m phng. T l tng khc nhau v d liu ging c th cho ra v tr thy c u tin.

Figure 22: Mi quan h gia knh dn v thy.

III. M hnh ha rng v thm:1. Nn tng:Cc bin rng v thm l cc bin chnh cn c tnh va. Nhng bin khc nh th tch st, tr khng, vn tc v bo ha nc d cng c quan tm. rng l nng th tch ca khng gian rng. N l mt bin ng x tt do thng bin thin nh v trung bnh theo theo mt trung bnh s hc n gin. rng thng c m hnh theo rng hiu dng (effective porosity). Tng rng (total porosity) cn gm c th tch c th khng c truy cp thng qua c ch thu hi thc t. thm v mt s bin khc khng bn trong c tnh , chng ph thuc vo iu kin bin bn ngoi ca c im k thut hoc o lng th tch. Cc bin ny c th thay i ln mt vi bc. thm l mt hng s tc hoc c tnh hiu dng khng c trung bnh n gin cc gi tr t l nh. Mt s xem xt trong m hnh ha thm: D liu nn c hiu chnh theo iu kin p sut v cht lu va. Nhng iu kin ny l khc nhau t cc phng th nghim ni thc hin o lng v phi xem xt hiu chnh thm trc khi dng cho th va. Bt ng hng t ngang ti dc l mt nhn t quan trng, cc thnh phn hng chnh ca thm c th c m hnh hoc t s bt ng hng dc v ngang ton cc c th c p dng trn mt tng c bn. Cc t l khc nhauc tnh thch hc phi c gn cho mi li trong m hnh a cht. 42 SVTH: Nguyn Mnh Trng