Tro cM D I A C H A T . I n « A. s6 352-354. 7 - l 2 g 0 1 5 . tr 217-2211
XAC DINH VAN TOC TRONG THAM DO DIEN TlT TAN SO CAO BANG THUAT TOAN DICH CHUYEN
NGUYEN THANH VAN', NGUYEN VAN THUAN', DANG HOAI TRUNG' VO NGUYEN NHU- LlEU', V6 MINH TRIET', NGUYEN TIEN H6A^
Truang Dgi hpc Khoa hpc Tg nhien. DHQG-HCM 227 Xguyin Van Cir. Q.5. Tp. Hd ChiMinh Lien doan Bdn do Dia chdt mien Nam. 200 Ly Chinh Thdng Q.3. Tp. Hd Chi Minh
.- ^^.""f*' ^^"'^'^^".'""g^ieitu Id thdng s6 quan trong nhdt trong xir ly du li?u tham do dien tu tdn sd cao (radar xuyen ddt - GPR). Thudt todn dich chuyen. phu thupc nhieu vdo dgi lupng van tdc dupc sir dgng nhdm hpi tu cdc tin hifu tan xg trong mien x-t hodc khdng gian dnh trd vi ddng vi tri cua chiing.
Muc ueu cua bdi bdo nay Id trinh bdy ca sa ly thuvit. quy trinh vd cdch thuc fu?n cac phuang phdp dich chuyen. Su dung cdc md hinh todn hpc. cdc tdc gid da Chung minh su cdn thiet phdi cd mat cdt da dich chuyin. sg tuang duang giua vgn toe tinh dupc vd van tdc cdn qudn phuang din dinh di vdt Di tdi uu hoa cac thudt todn^ dich chuyen. chung tdi di nghi su dgng entropy Id tieu chudn dexac dmh vgn toe truyen sdng di?n tir chinh xde. Kit qud thuc ti chi ra rdng mgt cat sau dich chuyen vai van tdc ddng cd chdt lupng tdt nhdt. tuang img vai entropy dgt cue tteu. Nhd vgy. kich thuoc cung nhu dp sdu eda cdc di thudng dupe xae dfnh vdi dp tin egy eao.
I.Mt^OAU
Trong xir ly sd lipu, thujt todn djch chuydn dupe sir dyng de dua cdc mjt ranh gidi phdn x j vd diing hinh djng vd vj tti ciia nd, tang cudng dp phan gidi vd cdi thipn ty Id tin hipu frdn nhieu. Thdng so quyit djnh tinh chinh xdc cua thujt todn djch chuyin Id vjn tdc truyin sdng dipn ta frong mdi ttirdng. Day Id dji lupng vjt ly quan frpng, giiip xdc djnh dung dp sdu ciia cdc doi tapng phdn xj tten mdt cdt radar xuydn dit [1, 5, 8]. Cd nhiiu phucmg phdp tinh vjn tdc ttnyin sdng, nhung dp chinh xdc thudng chua cao hojc khd thyc hign ngodi hien ttirdng. Bdi bdo se ttinh bay cdc phuang phdp djch chuygn cd kit hop vdi ky fliu jt entropy eye tidu nhdm phdt huy tdi da hipu qud xdc djnh vjn toe truyin sdng dipn tir phye vy cdng tdc xii ly sd lipu radar xuydn ddt.
II. PHirONG PHAP 1. Djch chuydn dja chdn
Djch chuygn dja chin la budc quan ttpng vd phiic tjp nhit frong quy ttinh xii ly dii lipu dja chin phdn xj. Trudc budc djch chuyin, dii Upu dja chin tiiudng dupc bieu diln dudi dang bing ghi ttirdng sdng phdn XJ fliu dupc tji mjt dit frong hp tpa dp flidi |ian - khodng cdch [9, 10]. Vi m0t so ydu td tdc dpng ddn qud ttinh lan ttuyen sdng ttong mdi ttirdng dit da md flidng tin vg ttirdng sdng frong bang ghi chua dupc chinh xdc: tin hipu van cdn d djng tdn xj hyperbol, yi tti mjt phdn xj bj sai Ipch so vdi tiiye ti, cd djng rdi rjc durt quang vd khdng rd net Chinh vi vjy, qud ttinh xu ly dli lipu cin din budc dich chuvin di gidi quya cdc vin dg frgn [4]. Kgt qud cuoi cung ciia (juy ttinh xu ly Id dua ra dupc mjt cat bidu dien hmh flidi, ciu tao ranh gidi dja chit dung ben dudi mjt dit. Bgn cjnh do, dich chuygn dja chin cdn cd tdc dyng tich liiy tin higu vd lpc nhieu.
Vd mjt todn hpc, dich chuydn thyc chat la bdi todn giai phuang tiinh lan tiiiydn sdng. Trong thyc te, xu ly du lieu can thyc hidn budc dich chuydn frdn he thing mdy tinh vd phin mem ljp ttinh, didu nay ddi hdi phdi diing cdc thujt todn gidi tich sd di xip xi nghigm phuang ttinh sdng. U'ng vdi mdi djng fliuat todn nhu vjy, ta cd mot phuang phap djch chuygn. Cd ba trudng phdi giai tich sd phd bien nhit duac dp dung vdo dich chuydn, gdm: phuang phdp cpng trudng sdng tan XJ - tieu biiu nhu djch chuyin Kirchhoff, phuang phdp chuyen midn bing bien ddi Fourier - djch chuydn F-K, djch chuydn sai phan hihi hjn (FD) vd dich chuydn ddi pha npi suy taydn tinh (PSPI) thudc tnrdng phdi hj trudng.
a) Djch chuyin Kirchhoff:
Ca sd ly fliuyit ciia phuomg phdp ndy dya vdo nguydn ly Huyghen-Fresnel va
bai todn Kirchhoff: cdc ranh gidi phdn xj duprc xem nhu tap hpp cdc diim tan xj^
khi sdng tdi kich ddng vao, chiing ttd thanh cac ttnng tdm phdt sdng ciu fliir cap, phat ra cdc dao dpng tan xj giii ve cac didm khac nhau dpe flieo taydn quan sat X. Dao dpng sdng ta cdc didm tdn xj khac nhau (ndm frong mjt cit dia chit) khi phat ttidn din mjt dit, se giao flioa vdi nhau va tjo thanh ttirdng sdng tdng ghi duac dpe tayin quan sdt dudi djng cdc sdng phdn xj.
Nhu vjy, cd thd xem cdc xung sdng phdn XJ ghi dupc tji diim xi bit ki trgn tuygn quan sdt Id tdng ciia cdc phan dong gdp do cac diim tdn xj khde nhau nam tren ranh gidi phan xj giri vi diim quan sat.
Bai toan Kirchhoff da dupc Sneider (1978) va Scales (1995) gidi cho ttirdng thd vd hudng sdng dpe cd dang:
PD(XD,Z„,t) = ; l f
7 i r J
COS 8 ,
P X - X o , Z = 0 , t -r 1 cose d „,
- + — P X - X „
vy rv a
frong dd: (XD, ZD): tpa dp cua diim tdn x j sdng; (x, 0): tpa dp ciia diim quan sat; r:
khodng each hi diim quan sdt ddn diem t d n x j , vdi r ^ = ( x - X o ) ' + z ^ ; 0: gdc giiia tia 16 vd phuong phdp tayin ciia mjt quan sdt; P(x, z=0, t): ttirdng sdng fliu dupc ttdn mjt dit [6, 7].
Ve mjt ly fliuyit, phep biin doi tan xj cho phep cdi fliipn chit lupmg cdc ldt cdt dja chin nhd ba hipu iing sau:
Higu ling djch chuyin khdng gian ddm bdo dua ttudng sdng phdn tan khdng phdn gidi d mjt dit vd ttirdng sdng hpi ty tji cdc didm phdn xa;
Hidu ling phan gidi ddm bdo phan chia ttirdng sdng tong thdnh cac ttirdng sdng ridng bipt lidn quan din tiing diem phdn XJ sdng frong mdi trudng;
z = 0 , t - I Jx (1) - Hipu ling khii nhidu djc bipt Id khii cdc nhidu nglu nhign do cpng tich liiy.
De djt dupc cdc hi$u irng mong muin frgn thi ba yiu td cin dupc lya chpn mpt cdch hprp ly la dp rpng day cpng, frpng si cpng vd vjn tdc cpng.
b) Dich chuyen tdn so - sd sdng (F-K):
Ca sd cua djch chuyin F-K Id jihuang frinh (2). Phuang tiinh ndy chi ra ring, de djch chuygn tt^c dong pha sdng CD' vi mjt cat thyc CD (Hinh 1), chiing ta phdi quay dojn CD' tir gdc d i t„ ve gdc £,.
t g ^ = sin43 (2)
Neu tdc dp ttnyin sdng ciia mdi ttirdng Id khdng doi thi frong khdng gian (t, x) mjt sdng se ndm nghidng mpt gdc nhat djnh, nghla Id sdng cd tdc dd biiu kiin hay so sdng K nhit djnh. Tuang img.
ttong khdn| gian F-K, sdng ciing duac djc frung bang dp ddc nhit dinh. Theo he flnic (2), budc dich chuygn ttxmg mien F- K chi dom fliuan la fliyc hign tinh todn di quay dich gdc nghigng cua mjt sdng ta
^.vd gdc ^ , sau do dung tich phdn Fourier ngupc chuyin frudng sdng ta midn F-K vi lji miin (t, x) [8].
Hinh 1. Sg-djch chuyen lir CD', ve mfit CD thuc
Phep djch chuyen gdc nghigng ttong miin F-K dupc fliyc hign flieo di xuit cua Stolt nam 1978, xuit phdt tii phuang ttinh sdng phdng, ttvc x nim ngang, tt\ic z hudng xudng:
(3) Niu su dyng tich phdn Fourier hai chieu ddi vdi bien x, z cua hdm "P (x, z t) dli:
4'„(k..k,.t) = JJ4'(x.z,t)e'"-'^'dxdz W Neu ^di hjn bdi todn doi vdi sdng phdng didu hda thi phd F-K cua "P^j cd djng:
4 ' „ ( k . , k „ t ) = 4 ' „ ( k . , k , , 0 ) e J " ' (5) Bidu thiic di tinh djch chuyin trudng sdng trong midn F-K cd djng:
.0t.,k„0) = v4'„(lc.,0,<o) (6) Cong thiic (6) la co sd dd tinh dich
m
chuydn trudng sdng bdng phuong phdp F- K. Sau dd ta dung phep Fourier ngupc di chuyin hdm 4'„(k„k^,0) trong midn F- K sang miin khdng thdi gian [10].
Phuong phdp F-K chu ydu dupc sir dyng dd tmh dich chuyin ttudng sdng cho nhiing mdi trudng cd tdc dp truyin sdng khdng fliay ddi hojc fliay ddi khdng dang kg theo phuang ndm ngang.
c) Djch chuyin sai phdn hiru hgn (FD):
Djch chuyin sai phan hiiu hjn la phuomg phdp gidi phuomg ttinh sdng di hj tiudng xudng phia dudi. Nd hodn todn gidng phuang phdp hj ttudng tti vd frpng lyc bing phuomg ttinh Laplace theo djng:
V^>P=0.
Phuomg phdp djch chuyin sai phdn huu hjn gdm hai budc: ngoji suy va hpi ty trudng sdng [I].
Ly thuyet ngogi suy truang song: Ly tiiuyet ngoji suy sdng dupc bdt diu ta gid fliuyet dii lipu ttudng sdng p(x, z, t) da dua vd djng zero offset, dupc xdc dinh ttong midn (t, x) va ttida man phuang trinh sdng vd hudng sau:
I a'p
Vst^
(7)O day X, z Id biin khdng gian, t Id thdi gian, V la vjn tdc. Dua vdo hai dji lupng kx vd 0) lan lupt Id sd sdng ngang biiu kidn vd tan sd gdc, ttudng sdng cd the bidu didn ttong midn tin sd - sd sdng bdng bidn ddi Fourier hai chidu:
p(x,z,t) = 2;2^P(k„z,co)e'"''-'""J (8)
Gid sii van tdc chi thay ddi theo dp sau z, V = v(z). Thay phuang ttinh (8) vdo phuang ttinh (7) chiing ta thu duac phuang ttinh vi phan thdng thudmg sau:
(9) Phuomg ttinh (9) cd nghidm gidi tich:
P(k„z-i-Az,(B) = P(k„z,o))e<*'^* (10)
frong dd: k = + = ± - 1
- ( ^
(11)Nghidmndy vln diing vdi v biin fliidn flieo z, midn Id dji lugmg Az du nhd. Dd ngoji suy ttudng sdng xudng dudi ddi hdi Az > 0, tiic la kz vd oo se ciing diu (bidu
flnic 11 lay ^ d tri kz duang), taong iing vdi sdng ttuydn flieo chieu dm cua tt^c t.
Phuang ttinh (10) la nghidm phuomg trinh sdng mdt chieu sau; cua dP(k^,z,(o)_.((o
dz I V (0
Ddy Id phuomg trinh ngoji suy sdng ehinh xdc frong miin (k„ z, oo).
Hpi tg tru&ng song: Thujt todn dich chuygn FD ddi hdi khdi lupng tinh toan ldn ndn nhiiu gid fliuyit dupc sir dyng di xdp xi phuang frinh sdng (12) nhdm gidm fliieu flidi pan chjy cho mdy tinh. Thyc chat, vipc xip xi taong duomg vdi liy gin dung bieu flnic cin bjc hai frong phuang trinh (12) (gpi Id todn tii ngoji suy) flieo hai cdch: khai ttien Taylor vd khai ttidn phan sd lidn tyc [9].
Gidi phuang ttinh vi phan bing phuang phdp sai phdn hihi han ehiing ta se tinh dupe cdc gid tti d dudi sau. Cudi cung, bing cdch lay tdng fliyc hipn cho tit cd gid tti CO ta fliu dupc hinh dnh tai dp sau
Z-HAZ:
P(x,z + Az,t = 0) = ^P(x,z-(-Az,Q)) (13)
(D
d) Phmmg phdp djch chuyin d&i pha npi suy tuyen linh:
Phuang phdp ddi pha npi suy tayin tinh (PSPI) la mpt frong nhimg phuang phdp hudng ddn gidi quyit vide xem xdt bidn fliien vjn tde flieo dp sdu vd phuang ngang, cd y tadng tdch bdi todn djch
1/2
P(k^,z,to) (12)
chuyen flidnh hai fliu jt todn taang iing vdi hai budc chinh nhu sau:
Bu&c T. Ngoji suy tiudng sdng tiieo dp sau bang phuang phdp ddi pha frong mien F-K, chi xet den tinh biin fliien flieo dp sau ciia vjn tdc.
Bu&c 2: Thyc hipn npi suy tiing diem flieo phuang ngang di gidi quyit vin de vjn tdc bien fliidn ngang, cd sii dyng bd vjn toe tiiam chieu tinh todn dupc tir ttudng vjn tdc khodng, dua ttudng sdng d budc mpt vi dang ttudng sdng thyc ti.
Phuang ttinh ngoji suy ttudng sdng (10) chi dp dyng dupc frong ttudng hpp vjn toe V khdng thay ddi flieo phuang ngang. De xet din hudng biin fliidn ndy frgn thyc te, ttudc hit ta tdch phuong trinh ngoji suy djng tong qudt (10) thdnh hai thdnh phin [3,4, 5]:
P*(z) = P(z)e^'"^^
P(z -(- Az) = P'(z)e''^''"''^'''^-I (14)
(15) Vdi v'54 v(x, z) Id mpt phdp xap xi vdi v(x, z).
Phuong frinh (14) fliyc chit Id mdt phep ddi ttidi gian (time shift), thuc hi&i cho mdi xung sdng, vdi v = v(x,z).
Phuang frinh (15) khdng flii tinh todn ttyc tidp khi v'= v(x, z), do dd cin phai fliyc hidn gidn tidp flidng qua mdt so budc.
Tim hai vjn toe Vj vd Vj+, nhu Id chdn frdn vd chjn dudi ciia v(x, z). Cdc vjn tic ndy dupc gpi la vjn tdc tham chidu.
Thay hai gid tri vjn toe ndy vdo cdng ttiiirc (15), ta dupc hai hdm sdng fliam
P(x,z-HAz,t=0) = 2^P(x,z-i-Az,a)) (I7)
chigu trong mign tin sd - so sdng, sau dd thyc hien phdp bidn ddi Fourier ngupc, dua ham song vd midn (x, co).
Hdm sdng d n tim se Id:
P(x,z-i-Az,co) = Ae**" (16) Thuc hien cac budc tinh todn fren cho tiing diem toa dp, sau dd tinh tdng tnidng sdng theo oo dd thu dupc trudng sdng tji t
= 0, cimg la ttudng sdng cua cdc doi tapng phdn x j :
Nhu vjy, phqj djch chuydn ddi pha ndi suy tayen tinh PSPI da hodn tit viec dua dupc tin hipu phdn xj frong ldt cdt cpng vi djng mjt phan cdch ciia mdi trudng.
Nh^ xet: Giiia phuang phdp GPR vd phuang phdp dia chin cd mpt so diim taomg ddng: nguygn ly hojt dpng dya frdn sy phdn xj ciia sdng; cdc todn ta vd cdc bidn so fren hai phuang ttinh sdng ddng vai tt^ giong nhau (Zhdanov, 2002) [12].
Sy taomg dong cua cdc djc diem dpng hinh hpc giira hai ttudng sdng nhu thi se dupc khai flidc frong qud tiinh xu ly so lipu. Vi vjy, nhiiu phuomg phdp xu ly ttt)ng dia chin cd dii dp dyng ttuc tiip vdo so lidu GPR khi cdch fliu fli jp sd lipu taong ty nhau.
Phuang phdp djch chuyin sau cpng ddi hdi fliyc hipn ttdn sd lieu zero-offset.
Trong dja chin, chung ta khdng fliu dupc ttvc tiep sd ligu ndy md phdi chuygn ta sd lipu diem nd chung qua hai budc: higu chinh vd cpng sdng. Thdng fliudng, khi tien hdnh do djc trong thanh phd, dii ligu GPR dupc thu flidp flieo kiiu khodng cdch ehung (CO) vdi cdc anten cd mdn chin, vi vjy dp sai Igch do khodng each thu phdt (khodng 10-20 cm) gdy ra taong doi nhd.
Ty so giiia thdi gian higu chinh vd thdi
gian sdng ttuyin nhd hon 1-2% ngn cd flii bd qua qud ttinh hipu chmh md khdng dnh hudng din kit qud djch chuyin. Do do, mjt cat CO ttong GPR dupc xem nhu mjt cdt zero - offset frong dja chin.
Khi thyc hipn dich chuyen vdi vjn toe gan nhau, cdc mjt cdt cd djng rit gidng nhau. Do do, vipc chpn lya hinh dnh sau djch chuyin diing nhit khd khd khin, cin phdi cd mpt chuin di so sdnh. De nhjn dipn rndt cit chinh xdc flii chuin enfropy eye tiiu dupc ehiing tdi dp dyng frong bdi bdo nay.
2. Entropy cifc tl4u trong xir ly tdi ll$u GPR:
Mjt cit GPR hidn flij ttdn mdy tinh Id kdt qud fliu nhjn tin hipu tiieo cdc phuang phdp sd hda frong fliiit bj do dac GPR.
Qua ttinh luu ttii, hiin thj tin hieu nhdm qudn ly vd quan sdt di tii dd de ddng xu ly sd lipu. Cdch biiu dien hinh dnh thdng dung nhat hign nay Id md hinh raster, frong do, dnh dupc biiu didn dudi djng ma frdn cac diim, cd kich thudc (MxNi [2,11].
Vdi cdch biiu dien nay, cdc phin ta ttong ma tran taong img vdi cac diim dnh cd gid tti bdng bign dp sdng GPR thu
duoc. Ta cd thg dp dung chuin enfropy frong cdc phuang phdp xu ly dnh vdo dii lipu GPR: gia tri ldn nhit ciia enfropy bing 1 ddi vdi dudng ghi chi cd mpt xung tin hidu, cd gid tti la N ddi vdi tjp hpp N dudng ghi, cd nghia Id enfropy chi dp hdn lojn ciia didm dnh, enfropy cang ldn thi dp hdn lojn (dp nhieu) frong dnh cang ldn [8].
Do do hidu qud cua xit ly dich chuyin se cao hom khi kit hpp vdi ky thujt enttopy eye tieu.
III. N G H I £ N C I > U T R £ N M 6 H I N H L t
THUYET VA THVC Tg 1. Mo hinh ly thuylt
a) Mo hinh 1 (phan bift cac di vft rieng le v&i ranh gi&i uon nip):
Sur dyng so anten tan sd 700 MHz.
- Hinh 2a bidu dien md hinh gom 4 try kim loji tiit dipn ttdn, ttv A cd dudng kmh 0=2 m, tpa dp tam (2 m; 2 m), ttv B cd
<I>=1 m, tpa dp tam (4 m; 2 m), ttv C cd 0=2 m, tpa dp tam (6 m; 2 m), ttv D cd
<I>=2 m, tpa dp tam (8,5 m; 2 m). Tinh chit dipn ciia cdc ttv frdn: p=0,05 flm;
er=90; Hr=39,9 vd mdi ttudng: p=500 Om;
Er=9; p,=l ,0006 (v=0,1 m/ns).
- Hinh 2d biiu dien md hmh ranh gidi udn nip:
+ Ldp 1: ldp dit ddy 0,8 din 1,5 m;
p=500nm; Er=9; |i,=l,0006 (v,=0,l m/ns);
^ + Ldp 2: ldp dd phiin set ddy rir 4,5 m den 5,2 m; p=I00O Om; £,=7; p,=I,0006
(V2=0,ll m/ns).
Thdng thudng, doi vdi cdc ranh gidi udn nep, moi vj tri nip 16m se xuit hi^n mpt thdt na vd tin hipu hyperbol bdn dudi thit no dd (Hinh 2e). Nhung niu khdng cd thdng tin tidn nghipm, ta khd phdn biet dupc sy khde nhau giua tin hi^u phdn XJ tii cdc di vjt lign tiip nhau vd tin hieu phdn xj tii mpt ranh gidi dja chit udn nip (Hinh 2b, 2e). Bing cdch dp dyng djch chuygn sai phan hita hjn, ta cd flid nhjn dupc mjt cdt GPR sau djch chuyin tiid hidn ro tin hifu phdn xj ciia cdc dj vjt (Hinh 2c) hojc ranh gidi uon nip (Hinh 2f).
b) Mo hinh 2 (tinh dp s&u vd kich thur&c cua dj v^t):
Sii dyng anten tin s6 700 MHz, md hinh gom ba Idp c6 tinh chit dipn khde nhau. Dj vjt la ing kim loji, bdn frong Id khdng khi (Hinh 3a):
L&p 1: ldp nhya dudng ddy 0,2 m, dipn frd suit p= 100000 nm, Er=4, n,=1,0069 (vi=0,15 m/ns).
L&p 2: ldp dk dim ddy 0,4 m cd di^n frd suit p=1000 nm, er=10, ^^=1,0 (V2 = 0,095 m/ns).
L&p 3: ldp dit sdt ddy 4,4 m, didn frd p=500 nm, e,=16, n,=l,0 (V2=0,075 m/ns).
Di vgt: ing kim loji cd didn frd suit p=0,01 nm, er=81, Mr=39,69, dudng kinh ong 0,22 m, tam dudng ong tji vj hi (5 m, 0,8 m).
suit
ICboang each [mj
sdng theo hg thirc [9]:
Khoang cich [m]
tiei difn iron, (d) (e) (f) lan lupl la mo hmh. mat cdi GPR. kel qud djch chuyin FD ddi v&i Vanh giM udn nep.
O f l S l T h i l , " ? ^ ':^^ l t r ^ ^ '^ ^ « P^^ '"*P ^^ * d i gian fruygn (ihrti 3b). Hai dudng fliang kdo dai tji flidi ----' - - * ^ diim ti=2,6 ns vd t2=IO,9 ns lin lupt Id tin
hipu phdn xj tii mjt ranh gidi thir nhit vd ranh gidi ttili hai; tji t =13,6 ns Id tin higu cua dj vjt kim loji (hyperbol). Di xdc djnh vjn toe truyen sdng trung binh din dinh ciia dj vjt, ta cd the sir dyng vjn tde cdn qudn phuomg v ^ (root mean square) (Yihnaz, 1987) nhd biit chinh xdc vjn
Trong md hinh ndy, vjn tdc can qudn phuang ciia mdi ttudng bdn frgn dj vat Id Vn,B=0,104 m/ns.
3 4 5 6 7
Khodng each [m] Khoang each [m]
Hinh 3. (a) Mo hinh 2; (b) Mgt cdt GPR mo hinh 2
(c) Mgi cat GPR sau khi sir dgng bp lpc background de khir nhieu ndm ngang (d) Mgt cdt GPR sau dfch chuyen v&i vgn tdc v = 0,104 m/ns.
^ Tigp theo, thyc hipn djch chuyen frdn so lieu md hinh kit hpp vdi biiu dd enfropy di tinh vjn tdc ttuydn sdng (luu y tin hipu phdn xj tii cdc mjt ranh gidi khd mjnh, cd flie gay nhieu hinh dnh sau djch chuyin. Do vjy, bp lpc nin dupc sir dyng dd khu cdc nhieu nim ngang frong mjt cit md hinh, Hinh 3c). Nham gidm flidi gian tinh todn, ta gidi hjn khoang vjn tic tii
0,075 (vjn tic ldp 3) din 0,15 m/ns (vjn tic ldp 1) vdi budc nhdy 0,001 m/ns. Ket qua ciia biiu dh enfropy dupc biiu dien ttdn Hinh 4, gid tii enfropy djt eye tieu tji vi tii Ve=0,104 m/s, kit qud ndy rit phii h(;rp vdi vjn toe Vnns tinh dupc d frdn, cho thay phuomg phdp dupc sii dyng rit ddng tin cjy.
Vjn t6c [m/s]
Hinh 4. Bieu do entropy.
2. S6 li#u thM« t l
a) Xdc dfnh bo cap du img luc trong be tong:
Nhdm flii cdng ldp djt he flidng mdi md khdng gay hu tdn cho cdng frinh 177 Hai Bd Tnmg, Tp. HCM, chung tdi da su dyng fliidt bj GPR Detector Duo (hang IDS - Y) vdi anten tin so 700 MHz cd man chdn, di xac djnh lji vj tti cac bd cap
Khoang each [m] 0 2 3 4 5
du ling luc dupc ldp djt trong Idp bd tdng sdn. Day Id vin di khdng de ndu cac bd cdp ndm xen lln hojc dudi ldp ludi thdp ddy djc (vi sdng didn ta se bi hip fliu hojc tan xj manh khi gjp mdi trudng din dign tdt). May min Id phan ldn cac bd cdp irng lyc (hyperbol ldn vd ndm d dp sau ndng, Hmh 5a) ddu ndm tt^n ludi flidp (cdc hyperbol rit nhd cdch diu va sat nhau).
3 15 3.25 3 35 3 45
Khodng each [m]
Hinh 5. (a) Mgt cdt GPR tuyin T20 (sau lpc nhieu);
(b) Vimg lin hifu quan tdm; (c) Bieu do entropy theo vgn tdc.
^ Ngodi vj tti, flidng tin ve dp sau ciing rat quan frpng, cd lidn quan tivc tiip din cdng tdc khoan dye sdn bg tdng md khdng dnh hudng din cdc spi cdp chju lyc ndy.
Sii dyng gid tti vjn toe ttuygn sdng dipn tir ttong bg tdng ddi vdi tin so 100 MHz [5] (v=0,122 m/ns), ta tinh dupc dp sau ciia cdc bd cdp khodng 0,17 m. Tuy nhidn, gid tti vjn toe chuin ndy khdng dang tin cjy vi vjn tdc ttuydn sdng cd flie fliay ddi theo tin so vd thdnh phin cau tjo, dp im vd dp rdng ciia bd tdng.
Vi vjy, frong trudng hpp nay, chung tdi se_ dp dyng phuang phdp entropy eye tiiu de xdc djnh Iji vjn toe truygn sdng, vdi myc dich ddnh gid diing dp sdu cdc spi cap irng lyc di hjn chi tdi da hiim hpa doi vdi sdn bg tdng khi thi cdng. Di minh chirng, chiing tdi sii dyng sd ligu tayin do T20 thu thjp tai tang 3 ciia tda nhd.
Mjt cdt GPR T20 sau khi khir nhieu dupc bidu dien ttxing Hinh 5a. Gid tti entropy vdi cdc vjn tdc khac nhau dupc tiie hign tt^ dd flij Hinh 5c. Enfropy eye tidu taomg iing vdi hinh dnh it nhidu lojn nhdt cho ndn vjn tdc ttong phdp djch ehuyin chmh la vjn tdc ttuyin sdng frong mdi trudng ddn dinh dj vjt (v=0,116 m/ns). Quan sdt ky hai mjt cit djch chuydn, ta flidy tin hipu cdc hyperbol tjo bdi bd cap ung lyc thi hidn khd rd. Vdi vjn tdc chuin, hyperbol tjo bdi Idp thep bdn dudi cd hinh djng cong ldn, chiing td vjn tdc chuin ldn ban vjn tic thjt (do enfropy eye tiiu) ciia mdi tiudng (Hinh 6a). Trong khi dd, Hinh 6b cho thiy tin hipu cap chju lyc hpi ty lji, chiing td day la vjn tdc dung. Sir dyng gid tti vjn toe flijt, ta xac djnh bd cdp dy iing lyc nim d dp sdu d = 0,15 m (hap ly ban so vdi d =
225
0,17 m khi dimg v = 0,122 m/ns vi sdn be tdng chi cd be day khodng 0,22 m).
0
£ , 2 0 in
gia n
j a 4 0
60
Khoang each [m]
0 1 2 3 4 5 6
b) Xiir ly sd lifu tuyin T14 (tnr&c so nha 123 dtr&ng Le Van Sy - Chi cvc Tdi chinh doanh nghifp):
Khoans each fml
Hinh 6. Kel qud djch chuyen: (a) v = 0,122 m/ns (vgn tdc chudn);
(b)v = 0,116 m/ns (van ldc khi entropy cgc lieu).
Tuyin do dupc thyc hipn bdng thiit bj Detector Duo vdi tin sd 700 Mhz cd man chin, cit ngang dudng Ld Vdn Sy, Qujn 3, Tp. HCM. Quan sdt mjt cit GPR sau khi khii nhidu (Hinh 7), tin hieu hyperbol CO djng phan eye n^jch tji vj tti 6,8 m.
Tign hdnh djch chuyin mjt cdt T14 (Hmh 7a) vdi vjn tic frong khodng 0,09 m/ns dgn 0,12 m/ns (budc nhdy 0,05 m/ns). Kit qud eho flidy gid tti enfropy djt eye tiiu tji vjn toe v=0,l05 m/ns chinh la vjn tdc
ttuyen sdng frong mdi ttudng din dinh dj vjt (Hinh 7b).
Sau khi djch chuyin Kirchhoff vdi vjn tic V = 0,105 m/ns (Hinh 8), ta tiiiy tin hipu hOi ty rd ndt. Dp sau vd kich fliudc dj vjt tinh dupc Id d=l,04 m, <D=0,14 m.
Theo thdng tin tidn nghipm tii Cdng ty ta van xay dyng MAT, ddy Id dudng cip nudc cd kich fliudc <I)=0,15 m. Nhu vjy, sai Ipch giua kit qud tinh todn kich fliudc vd thyc te rit nhd khodng 6,7%.
(a)
0 09! 0 1 0105
Vta 1^ (m/n») Hinh 7. (a) Mat cdt GPR luyin T14 sau khi khie nhiiu; (b) Bieu dd entropy.
226
Khoang each
Hinh 8. Mat cdt sau dich chuyin tuyen T14.
IV. K t r LUAN
Nhdn td quyit djnh sy thdnh edng eiia qua trinh djch chuydn Id dp chinh xdc cua md hinh vjn tdc d mdi tiudng dit dd.
Trong thyc ti, vjn toe truyin sdng biin thign rit phuc tjp flieo mpi hudng, cd flieo phuang thdng dting vd phuang ngang.
Vjn tdc mdi ttudng thay ddi cdng phiic tap flii qui ttinh djch ehuyin cdng gjp nhiiu khd khin. Do vjy, vipc lya chpn phuomg phdp djch chuyin iing vdi tiing mdi ttudng dja chit khde nhau ddng vai ttd quan ttpng frong vipc nang cao ehit lupng mjt cit djch chuyin.
Djch chuyin F-K Id thujt toan nhanh nhat, cd lidn quan din biin ddi Fourier ta mien thdi gian - khodng cdch (T-X) sang mien tin sd - so sdng (F-K) di biiu dien mjt cdt do djc vdi mpt gid tti vjn tic khdng doi. Khi vjn toe bien thidn flieo phuong flidng dimg vd/hojc flieo phuang ngang flii phuomg phdp ndy khdng cdn chinh xdc. Trong khi dd, cac fliujt todn d^ch chuydn thdi gian FD vd Kirchhoff deu xem vjn tdc RMS (root mean square) ctia mdi ttudng biin fliien flieo phuang tiling diing. Djch chuygn Kirchhoff tiin hdnh nhanh vd cho kit qud tdt niu sy thay ddi vjn tdc flieo phuang ngang khdn§ qud ldm, tay vjy thujt todn ndy lji hjn chd niu ddi tapng muon Idm rd nim qud gin mjt dat. Thujt todn FD dua ra dupc hinh dnh
chdt luang vdi mpi gdc nghieng cua ranh gidi phdn xj tay thudc vdo cdng thiic xip xi, nhung se tieu tdn thdi gian xii ly rdt ldn khi dp ddc tidm cjn 90°. Cdc thujt todn djch chu>en dp sdu nhu PSPI sii dung md hinh van tdc khodng, cd xet din sy thay ddi xan tdc theo phuomg ngang vd sy Igch phuang truygn sdng tji ranh gidi phdn XJ. Do vjy, phuang phap nay cho chdt lupng anh djch chuyen rd nhung cin thdi gian thyc hidn Idn vd rit khd dg xay dyng md hinh vjn tdc phii hpp mdi trudng thuc td.
Nhung kit qua cd dupc tti md hinh vd sd lieu fliyc ti tji Tp. HCM cho fliiy vipc dp dung cdc phuang phdp djch chuyin Id cdn tiiiit. Vjn toe ttuydn sdng didn ta duac xdc djnh chmh xdc vd nhanh chdng hom ndu chiing ta kit hprp fliujt todn djch chuydn vdi ky fliujt enfropy eye tiiu frong xu ly dnh.
L&i cdm cm: Nhdm tdc gid xin chdn thdnh cdm om Sd Khoa hpc Cdng Nghp Tp. HCM di cip kinh phi fliyc hipn di tdi (HD so 283/2014/HDDH-SKHCN):
"Nghidn cihi phuang phdp dich chuyin, enfropy eye tiiu, bidu dd ndng lupng vd xdy dyng phdn mem xu ly dii lipu radar xuydn dit"
VAN Lifu
L Dang Hoai Trung, Do Thanh Hdi, Nguyen Thanh Vin, 2013. Ap dyng djch chuyin sai phan hiiu hjn vd xu ly s i lipu radar xuygn dit. TC Khoa hpc vd Cong nghi Biin, tap 13. sd 3A, pp. 120-126
2. Huilin Zhou, Xing Wan, Wei Li, Yuling Jiang, 2011. Combining F-K filter witii minimum enfropy Stolt migration algoriflmi for subsurface object imaging and background permittivity estimation. Procedia Engineer, vol 23 pp
636-641. ^^' 3. Jeno Gazdag, Piero Sguazzero,
1984. Migration of seismic data by phase
shift plus interpolation. Geophysics, vol.
49, No. 2. pp. 124-131.
4. Jeno Gazdag and Sguazzero, 1984.
Migration of seismic data. Proceeding of the IEEE, 72, pp. 1302-1315.
5. Le Hoang Kim, Nguyin Thanh Van, Dang Hoai Trung, 2014. Ap dyng phucmg phdp dich chuyin ddi pha npi suy tayin tinh vdo xir ly tdi lieu radar xuygn dat dg xdc djnh kich thudc va vj tri dj vjt, TCDia chdt A/34I-345:230-236 HdNpi.
6. Nguyen Thanh Van, Le Van Anh Cuong, Nguyen Van Giang, Dang Hoai Trung, 2012. Kirchhoff Migration for specifying velocity model in Ground Penefrating Radar mediod. Proceeding IEEE 14 Intemational conference on Ground Penetrating Radar (GPR).
Shanghai. China, pp. 419-424.
7. Nguyen Thanh Van, Nguyin Van Giang, 2013. Radar xuygn dat: Phuang phdp vd ling dyng. NXB. Dai hoc Qudc gia Tp. HCM, 222 tr.
8. Nguyen Thdnh Van, Nguyin Van Thujn, Dang Hodi Trung, 2014. Djch chuyen F-K va entropy eye tigu trong xii ly tdi lieu radar xuygn dit. TC Dia chdt, A/341-345:273-282. Hd Npi.
9. Ozdogan Yilmaz, 1987. Seismic Data Processing, Society of Exploration Geophysics, USA.
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SUMMARY
Using migration algorithm to determine velocities in high frequency electromagnetic prospecting
Nguyen Thdnh Van. Nguyin Vdn Thugn, Dgng Hodi Trung Vo Nguyin Nhu Lieu, Vo Minh Triet Nguyen Tien Hda Elecfromagnetic wave velocity is tfie most crucial parameter in processing high frequency elecfromagnetic prospecting (ground penefrating radar: GPR) data. Migration techniques tiiat sfrongly depend on velocity parameter have been used to refocus the scattered signals from tfie x-t domain or image space back to their frue spatial location m Uie object space. To optimize migration algoritfims, we propose using enfropy as a n^esTn^th r f- ^"^ f^'=°^^«=* propagation velocity. The goal of this article is to present tiie theoretical basis, the procedure as well as the necessity for combining r s ? . ?T^^-- ^'^^ "mathematical models, we demonsfrated tfie need of having flie migrated sections and the similarity between the estimated velocities and the Z ZlZiT^ ° ° ' ' V° * ' '°P °^°''-'"'=*^- T^« ^^^""^ ^^fi«» °n fi«'d data show flius flie size as well as tiie depfli of anomalies is deteimined wifli high reliability.
Ngu&i biin tap: TS Nguyin Vdn Nam.