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D I C H C H U Y E N F - K V A E P ^ T I O P Y C l T C U E U T R O N G XU^ L Y T A I L I E U R A D A X U Y l l N D A T NGUYfiN THANH VAN, NGUYEN VAN THU/LN. DANG HOAI TRUNG
Khoa Vdtly- Vol ly Ky thugt. Trucmg Dgi hgc Khoa hpc Tg nhiin.
DHQG TPHCM. Nguyin Vdn Cu. P.S, Tp. HCM
Torn tdt: Viic sirdgng cdc phuang phdp dich chuyin trong dia chdn dixulv T9 9)"urst:(783) Z'"'"^' "'''" '^ ^ ^ ' ^ «#"• & " . ^ c S /y/y;. ursin (1983). Ue va eac cpng su (1987); Zhdanov(1988) Ca U r,;„
C r ' / ^ - " ^ / "*" " ^ * ^""^ ""^ - ' ' -"^«"S -hridivJmJ,",Zl
phdp dieh chuyen F-K (frequeney-ivaveLmb:, Td mro^ ^ S 'diTili quyet vdn di trin. Nhu vgy, qud trinh xti ly sd liiu fiPff i 3 ,», t - f ^
bu&csa rhitrdidt. 'ipVgdiehclZSiPK:^'^^ i^i^^^^^^
t T.tTu"' * ' ' '"^^" ^"^"^ ^ "^^ ^n'ropyc^tiiu cJiI^"J-
' r " " " , C„!!;J?i?," *^""^^'' ''-•^ VA ENTROPY
Hi?n nay, phuang phip ra da xuyfin dit ^*f^^^^
dupc su dyng rfng rii frong ngWfin ciiu ^- "!«"' «shuy4n F-K
ciu hiic dja chit ting ndng, khio sit cfing Phfip djch chuyfin gdc ngWfing frong trinh xiy dyng, v5 bin d l cdng hinh ngim ™en F-K dupc fliuc Wfn bdi Stolt nim dd tfij, khio cl, khoa hpc Wnh sy ... Vi '^^^ t^^- ^J-
v|y, vifc xu I^ s l Ufu GPR dl tfnh kfch Gii tfiuylt d& Ufu frudng sdng P(x z t) tfiudc vi df siu dj v|t vd Cling cip tfiilt di dua vl d^ng zero - offset vi tfida'man [1.3,5]. phuong trtnh sdng vfi hudng:
Thyc tl tfil v£in tic ttuyin sdng difn tir f - i l + i l _ J _ i l l p .
frong mdi hudng tfiay dli phiic t?p, tfieo I * ' ' ^ ' v^ 9,2 JP(^'2'') = 0 (D phuong fliing diing vi phuong neanc nfin T
vifc xic djnh vln tic niy i S t h i n '°''^.^t^ 1^ vj frf hfi„ tryc nim Tm„» Kx-Tx T K ^ ^^^^- ° S ^ g ; ^ ^ cWlu siu; t l i tfldi Kian hai lin Tmng bil bio tic gii kit hpp phuong sdng fruyin; v Ii van tic t S ^ n sin^
phip dich chuyin F-K vi enfropy eye tilu hong mdi tiudng. ^
ttiudc vidf siu dj vit [2, 6, 7]. sang miln S n s l v i s d sdng: ™°"^ ^ " ^ P ( k „ z , ( D ) = / / p ( x , z , t ) e ^ - ' - ' ) d x d t ( 2 )
273
H ^ xic djnh frudng sdng bing phfip P(x,z,t)= ffp(k.,z,a))e"-'>«>dk do,
tnen dm Founer nguoc: ' JJ ^^» ' ' i"™
(3) Trong dd: k ^ la sd sdng iing vdi x; co Ii tin sl gdc.
Thay he thiic (3) vao (1), ta dupc:
ll
^ P ( k . , z , ( o ) - | ^ - k M p ( k „ z , a ) ) e""-'=-'>dk.d(»=0 Thu gpn hf thiic (4):^ P ( k „ z , a , ) = k,^P(k.,z,(o)
2 (o"
1.2 _ " * .,2
Vdi: k , ' = ^ - k ^
V
(4)
(5)
(6) Tnrdng sdng quan sit vi trudng sdng djch chuyen dupc xic dinh bdi hf tfnic:
P(x,z = 0,t) = J|p(k„z=0,(o)e"'"-''>"'dk,dco (7) P(x,z,t = 0) = J J e ( k „ k „ t = 0)e'<''-^-->''dk,dk,
V d i : e ( k . , k „ t = 0) = V
+kl P(k,
,z = 0,(o=^Vk[7kf)
(8)
(9) Nhu v§y, qui frinh dich chuyin F-K
frong miln khdng - tfidi gian li phfip inh X? P(k„z=0,(o) tfiinh e ( k „ k , , t = 0) frong miln tin sl - sl sdng. Day cWnh l i nguyfin 1^ djch chuyin F-K.
Cdng tfnic (9) l i co sd dl tinh djch chuyfin frudng sdng bing phuomg phip F- K. Sau dd, dilng phfip biln dli Fourier ngupc frong cdng tfnic (8) dl xic djnh frudng sdng djch chuyin frong miln khdng thdi gian.
2. Entropy c^fc tliu [2,6]
Vfi mit toin hpc, cd tfil bilu dien tfn Wfu mit eit GPR tfieo hf tfnic:
X = R+S+B (10) Trong dd, X, R, S, B: Wlu diln tfn Wfu
dudi d?ng ming cd ki'ch tiiudc M x N. X li tin hifu ghi nhan frong mit cit GPR; R li nhieu nln; S li tfn Wfu cd ich phan xa rir vft tfifi; B li cic nWeu giao tfioa.
274
T ^ moi vj tri cua anten tfiu, ning lupng ciia cic tfn Wfu dupc ghi nh?n bdi hf thiic:
M
D(n) = 2]X'(m,n); n = l,2 N (II)
ni=l
Theo nguyfin l^f ho?t dfng phuomg phip GPR, v§t tfil chdn vJii cho nhilu tfn hifu phin \^ hom, do dd lim ting ning lupng tfn Wfu ghi nhin tai anten tfiu.
Chfnh vi viy, nd cho bilt vj frf vft tfil bj chdn viii. Tuy nWfin, ning lupng tfiudng bj inh hudng bdi nhieu do d^c vi nhiJu hon lo?in frong mit cit GPR. hi ting tfn hifu cd fch, ta phii loai bd cic nhilu hin lo^n R. Cic phuong phip tfiudng sii dyng frong lo^i nhieu hon lo?n Ii phuong phip trung binh hda, hoie frung binh cfng sdng so lifu thu tfilp.
Trong xii If inh, enfropy chi df hin loan cfia dilm inh vi xic djnh khoi lupng tfldng tin ngiu nhifin cung cip frong mH cit GPR. Enfropy Idn iing vdi df bin lo?n
i ldn vi ngupc Iai. Gii su, mit cit X (cdng tfnic 10) cd cic gii fri roi rac 1, 2, 3... vdi xic suit hiong ling l i p,, p^, p, ... tW enfropy dupc xic djnh flieo bilu tfnic (Shannon, 1948):
E(X)=-2]p.iogp. (12)
j
Enfropy tfnh tfieo cdng tfiiic (12) cd hai vin de: tfni nhit, nd mit nWlu tfidi gian dfi tfnh toin xic suit pi nlu Wnh inh Idn- tfni hai, khi gii hi rod rac X dupc xac djnh tfli xic suit Pi = 0, do vay khfing tfil tfnh toin enfropy. Dfi loai bd hai vin di frfin chiing ta sii dyng cdng tfnic xip xi enfropy gpi li chi sd Win tfiifin eye hi:
1 E ( X ) = t.Zx\m.n)
ZSx\m,n)
(13)Neu enfropjr dat eye tilu, cic nWlu loan li tfiap nhat. Qui hlnh ttfin dupc tdm tit tfieo cic budc nhu sau:
'. Budc 1: Hieu chinh, loc nWeu vi Icfaufich d$i.
Budc 2: Dich chuyin s l Ufiu vdi van tdc Vi.
• Budc 3: Tinh enfropy Ei.
Budc 4: Lap lai cic budc 2 vi 3 vdi cic van tdc Vj, i = 2, 3,4...
• Budc 5: Xay dyng bilu dd bilu difin su tfiay ddi E tfieo v; xic djnh enfropy cue tilu E„, vi van tdc ddng v,„
tuong ung.
Budc 6: Djch chuyin sd Ufiu vdi gii frj van tdc Vo,.
Budc 7: Xic dinh dd siu, kfch thudc dj v i t
™ ' L ! * ° ? ^ ^ ^ TR§N M 6 Hll#t LV TWYtrvAnvCTeDe DANH GlA Ker QUA
1.Md hinh ly thuylt
HWh la bilu dien md Wnh hai Idp cd dj vit Ii fry bfi tdng. Md hinh hai ldp gim:
- Ldrp 1: dp sau tur z = 0 m din z = 0,2 m, van tdc fruyin sdng v, = 0,122 m/ns. '
Khoing cich[ni
Hinh 1. (a) M6 hinh hai l&p; (b) - Ldp 2: df siu tii z = 0,2 m din z = 5 m. vin toe fruyin sdng vj = 0,075 m/ns Ldp tfni hai cd dj vit li fry bfi tdng cd dudng kfnh * = 160 mm, tpa dd tam tai
(X = 3 m; z = 0,8 m).
Quan sit mit cit GPR (Hinh lb), ta xic djnh rfi tin Wfu hyperbol t^ vj hi x = 5 m, 1 = 17,9 ns. Dya vio tfidng tfn hfin, ta tinh dupc v|n tic cin quin phuomg cua mdi hudng bfin frfin dj v|t Ii V = 0,0859 m/ns.
Mgt cdt GPR mo hinh hai l&p.
Djch chuyin mit cit vdi vin tic cin quin phuomg, ta dupc kit qui HWh 3a.
Su dyng nguyen 1^ enfropy eye tilu dl xic dinh van tdc fruyin sdng, ta chpn gidi han v|n tdc fruyin sdng fliay dli trong khoing 0,05 m/ns din 0,15 m/ns vdi budc nhiy 0,001 m/ns. Bing cic budc tfnh toin trong myc 2.2, ta bilu diln enfropy tiieo van tdc bing do tfij Hlnh 2.
275
V$n coc [mis]
Hinh 2. D6 thi biiu diin sg thay ddi entropy theo vgn tdc truyin sdng.
Hinh 2 cho tfiiy enfropy lifin tyc tfiay vdi van tic can quin phuang tfnh dupc.
ddi tfieo van tdc truyin sdng. Enfropy dat Thuc hifn djch chuyin m|t cit vdi v|n eye tifiu kW van tdc fruygn sdng v = 0,09 tic vita tim dupc, ta dupc kit qui nhu m/ns. Van tdc niy khdng lfch nWlu so Hinh 3b.
Hlnh 3. Mat cdt dich ehuyin: (a) v Hlnh 3 cho tfiiy hai mit cit djch chuyin khi hromg ding vl van tic djch chuyin frong hai mit cit Ifcli nhau nhd.
Sai sl tinh dupc frong trudng hpp niy Ii 4,77%. Dl dinh gii df chfnh xic cic kit qui frfin, ta tfnh ning Iupng hai frudng hpp tfieo cdng tfnic (11). Ning lupng hromg ling vdi van tie cin quin phuang vi v|n tic tfnh theo enfropy eye tilu lan lupt Ii 0,0282 vi 0,0277. Ning Iupng tfnh tfieo vin tic cin quin phuang Idn ban v|n toe ti'nh toin khdng ding kl. Do dd, van tdc tinh tiieo entropy eye tilu hoin toin dupc chip nhin vi nim frong gidi ban sai sl cho phfip (dudi 10%).
IQloang each [m]
= 0,0859 m/ns; (b) v = 0,09 m/ns.
2. S6 lif u thyc t l
a) Tinh kich thu&c 0^ sdu dng ci, nu&c tgi Tp. Hd ChiMinh:
Khoans cich (m)
0 1 -
g
Hinh 4. Mgt cdt GPR tuyin T84 tru&c sd nhd All dudng Nguyin Thdn Hiin.
276
Sd Ufu dupc do dac bing tfiilt bj Detector Duo (IDS, 10, tin sfi anten 700 MHz. Tuyfin T84 tfiyc Wen frudc nhi sd All dudng Nguyin Thin Hiln, Quan 4 Tp Hd CW Minh (ffinh 4). Quan sit mat cit GPR hiyen T84, ta xac dinh tm Wfu hyperbol tai vj tti X = 2 m, t = 14 ns.
^ Ap dyng dich chuyin F-K vdi cic van toe V = 0,09 m/ns; 0,1 m/ns; 0,105 m/ns;
n * , a * w ) ^
0,12 m/ns, ta dupc kit qua nhu Hinh 5.
Mnh 5a, b cd hypertiol cong xuong, cho tfiSy van tdc dich chuyin be hon v|n tie mdi frudng; Hinh 5d xuit Wfn hyperbol cpng lfin: van tdc dich chuyin ldn hon v|n toe fru)^ sdng frong moi ttudng; Hinh 5c cho fliiy hyperixil hdi tu: vin toe dich chuyfin dung vdi van toe ttuyin sdng frong mdi trudmg.
H i n h 5 . « , , c * * c . c / « ^ ^ v j ^ c ^ , , , ^ , ( , , ^ , ^ ^ ^ . f c; 0,105 m/ns; (d) 0,12 m/ns.
' " U 13 ,., - f s
V«nl4c[intel " ' " " ' " <.: IJ M I I V*it4c(nVs] •«'
HWh 6. (a) Biiu dd entropy; (b) Biiu dd ndng btgng
277
Ngoii vifc so sanh cic mat cit dich chuyin, ta cd thi su dung chuin entropy eye tilu va gian dd ning lupng (Hinh 6) dfi xic djnh vfn tfic truyin sdng. Vin toe mdi tnidng xic djnh dupc iing vdi entropy eye tilu vi ning Iupng eye dai Ii 0,106 m/ns. Kich thudc va dp siu duang dng tinh dupc Ii O = 185 mm vi 0,74 m.
Kit qui niy dupc Cdng ty TNHH Cdng trinh thoat nudc va Ha ting Dd thj M.A.T dinh gii cao vi hoan toin chip nhan dupc vi sai sl cW 7,5%.
b) Xay dumg ban do cong trinh ngdm tgi Tp. Hd ChiMinh:
So Ufu do d^c tai dilm khio sit tfni 23, tiiufc cdng trinh "Siia chOa tiiyln Ing cap n, dudng V5 Vin Tin - Nguyin Thj Minh Khai, Qu|in 3, Tp Ho CW Minh" do Cdng ty cip nudc Wadeco tfiyc Wfn tfiing 2 nim 2014. Cdng frinh gim 24 difim khao sit tfiu fli|p so Ufu bing tfiilt bj Detector Duo Qiang IDS, ^), kfio dii tii Cdng tiudng Qudc tfi din Nga siu Cfng hda. Dudi diy, tic gii xu Iy vi minh giii difim khao sit so 23 (ffinh 7): xic djnh vj fri, df sau vi kfch fliudc dj v|t, nhim phye vy cdng tic flu cfing sua chtia cing hinh ngim cu, lip d|t cdng hinh ngim mdi vi sau d6 xiy dyng bin dl cdng ttinh ngim t^ Tp. HCM.
s o D 6 VITRI KHAO SAT sfi 23
ffinh 7. Sa dd vi tri vd tuyin khdo sdt vi trt dd tim 23.
Cic tuyin cit ngang xuit Wfn tfn hifu 10 ns (ffinh 8b), cic hiyln dpe khde hyperixil t?ii vj frf x = 1,4 m, t = 13 ns, x =
3 m, t = 11 ns vi X = 5,4 m, t = 12 ns (T82) (ffinh 8a). Tuyin dpe T84 xuit Wfn tfn^Wfu hyperixil tai vj frf x = 0,9 m, t =
Khoang each [m]
khdng cd tfn lufu hyperbol. Thyc hifn xii ly sd lifu bing djch chuyin F-K vi enfropy eye tilu, tic gii dupc cic kit qui nhu ffinh 9,10, II.
Khoang each [tn]
ffinh 8: Mat cdt GPR tgi vi trtdd tim 23: (a): tuyin ngang T82; (b): luyin dpe T84.
278
^ ^ ffinh 9. Kit qud xir If tin hiiu hyperbol thu nhdt
^ ^ S ^ t i ' S t ^ : ^ ^^<?^.^«vdihaidjv|tginnhau.Gii dupc sl lupng'di vl Kit q^ x u ? f ( £ fh^tS^i^JT.^ "•'"^ "^"^ ^^
9d)chofliiytinWfuhyperLhfi^E '^^ f T T < , V \ t T ^ ^ t
ffinh 10. Kit qua xu ly tin hiiu hyperbol thU hai
279
T^i h^rbol thu hai, ta tihh dupc v|n ngang. Kfch thudc vi df siu dj v|t tfnh tie fruyen sdng Ii 0,094 m/ns, cho tfiiy dupc li O = 88 mm vi 0,55 m (ffinh 10).
van toe mdi tiudng thay doi theo phuang
ffinh 11. Kit qud xir If tin hiiu hyperbol thii ba.
Tai hyperixil tfni ba, ta tfnh dupc vin Tuang ty, ta xur 1^ sl Ufu cic hiyln tdc ttuyen sdng li 0,102 m/ns. Ki'ch tfiudc ngang vi cic hiyln dpe cdn l^ii. Kit qui vi df siu dj vft tfnh dupc Ii «> = 124 mm xut I5? dupc ttinh biy tfieo Bane 1 vi 0,59 m (ffinh 11). ^ '
Bing 1. Kit qui xv ly dilm khio sit s6 23 TfinDV
DVl DV2 DV3 DV4 DV5
Vjfrf(m) 1.4 1,6 3,0 5,4 0.9
Vin toe (m/ns)
0,102 0,102 0,094 0,102 0,094
Ning lupng 112,6 112,6 148,9 76 136,6
Dudng kfnh (mm)
106 106 88 123
90
Df siu (m) 0,70 0,70 0,55 0,59 0,51
Tdng hpp kit qui bfin, to xiy dyng tw<7iig dj v|t cin siia chfta, cii t?o hojc ISp bin vfi cfing ttinh ngim nhu ffinh 12. Bin d|t cdng hinh ngim mdi. Nhd dd, qui dd cdng hinh ngim giup xic dinh vj tri vi h^nh tfii cdng sfi frinh dupc cic rui ro vi phuong kfio dii cua cic dj vit. Dya vio tai nan ding tile,
dd, cic dan vj tfii cfing xic djnh dupc dli
280
! •
M A T C A T n n r B - p
GmCHtJ:
- Don vi trong ban ve 14 m -OImHc6kichUmdc i m x im - D6 saa duoc Unh (Kn dinh duemg iSng - U : Lupt qua fliil i UBO phuong L - T l : Lacd q u « Ui(t i UKO phuong T - Z i : dft s4u rfch mit d4t i <m) MATCATNr.AA;r:A A
SO Dd C 6 N G TRiNH NGAM VI TRfKHAO SAT 23
Hlnh 12. Sa dd cdng trinh ngdm vi trt khdo sdt 23.
IV. KtT QUA-THAo LUAN
Vdi nhimg kit qui tfnh toin t?i Tp. Hi CM Minh, vifc kit hpp phuang phip djch chuyen F-K. entiopy eye tilu vi ning lupng li tfult tfurc vi hihi fch. Trudc tffin, ip dyng phuang phip djch chuyin F-K trong qui hinh xii Xf dUt Ufu GPR nhim nSng cao chit Iupng cic mSx. cit GPR.
Sau dd, tfnh toin enfropy vi ning Iupng tuong ling vdi tiing gii frj van tic dich chuyfin. Gii frj enfropy eye tilu vi ning lupng eye dai sfi dinh gii miic df hfi ty cua tfn Wfu frong mit cit GPR, rtr dd xic djnh v§n toe fruyin sdng difn rtr. Cudi cilng, bii toin xic dinh df siu vi kfch tfiudc dj v|t dupc giii quylt phye vy cic cfing tic ling dyng cua phuang phip GPR.
VANLI$U
1. Giang N.V,, Van N.T., Trung D.H., Jarzyna J., Zietek J., Sylwia- Suchon T , 2012. Wvestfgatfon of sinkholes on the roads by GPR:
AppUcation to HCM city, Viehiam.
Proceeding of Intemalional conference
on Ground Peneti-ating Radar (GPR) pp 443-447. Shanghai. China.
2. Huilin Xhou, Xing Wan, Wel Li, Yuling Jiang, 2011. Combimng F-K filter witfi mmunum enfropy Stolt migratfon algoritfmi for subsurf-ace object imaging and background permittivity stimation.
Procedia Engineer 23:636- 641.
3. Jol ¥LM, 2009. Ground Penefrating Radar: Theory and Applications. Oxford UK, P.365J. Clerk Maxwell, A Treatise on Electncity and Magnetism, Srded., vol. 2.
Oxford: Clarendon. 1892, pp.68-73.
4. Stolt ILH, 1978. Migration by Founer Transform. Geophysics: 43, 23-48
5. Van N.T., Giang N.V., 2013.
Giomid Penettating Radar - Fmidamentols and Apphcations. VNU Press, 222 pages.
6. Xiaoyin Xu, Eric L. Miller, 2002 Enfropy optimized confrast sfretch to enhance remote sensing imagery. Boston MA, USA.
281
7. Zhou H., Sato M., Senior Member, of Conunon-Transmitter GPR Dato. IEEE IEEE, and Liu EL, 2005. Migration transactions on geoscienee and remote Velocity Analysis and Prestack Migration sensing, vol 43, no. 1, pp.86-91.
SUMMARY
F-K migration and mmimum entropy in processing ground penetrating radar data Nguyin Thanh Vdn. Nguyin Vdn Thudn, D^ng Hodi Trung Using migration methods of seismic in processing ground penefrating radar (GPR) dato has been done by many scientists, such as Szaraniec (1976, 1979); Ursin (1983), Lee and coUeagues (1987), and Zhdanov(1988). The principles of tfiis metfiod is restoration of the observed wave field back to the correct position of the objects; Then, the energy of scatter points is converged and subsurface object will be clearly shown if applying accurate fravelUng velocity of tfie waves. However, determimng accurate velocity for migration is very difficuh and time-consuming. Therefore, we combined Uie F-K (frequency-wave number) migration and minimum enfropy to resolve above problem. Thus, tfie GPR data processing were done in tfie following steps: Firstiy, applying F-K migration into tiie data processing. Secondly, determimng accurate velocity based on mimmum enfropy value. Finally, tfie deptfi and size of objects are definedfor mapping underground consfruetion works in Hi Chf Minh City.
Ngu&i biin tdp: PGS. TS. Cao Dinh Triiu.
282