Su dung b i e n do dia e h a n trong phuong phap phan tieh AVO
TS. Nguyen Dire Khanh DH Tong hap Faroe, Dan Mach TS. Nguyen Thu Huyen Vien Diu khi Viet Nam
Tom tat
Phwang phap phan tfeh AVO (Amplitude Variations with Offset) la phwo'ng phap tim kiem trwc tiep eae biy chira dau khi dwa tren ky thuat phan tfch bien do cua tai lieu dja chan trw&c khi eong. AVO tr& nen rat pho bien trong eong tae tim kiem tham do nh& kha nang lien ket bien do dja ehan v&i dae tfnh eua da chira. Cae dj thw&ng bien do (phan xa dja chan co bien do cao tren mat eat dja chin song dge) co the dwg'C nghien eiru trw&c khi eong de xem lieu chiing co dj thw&ng AVO hay khong?
Dieu nay giiip chiing ta phan biet eae dieu kien dja chat (eat ket chira khf, than da hay da nui Iwa) da gay ra dj thw&ng bien do.
AVO da dwg'C ap dung thanh eong tai mot so mo tren the gi&i, nhwng cung eo nhieu trw&ng hg'p that bai. Phwo'ng phap chju anh hw&ng rat l&n tir eae hieu irng thach hgc, do day cua da chira cung nhw dac tinh eua cac l&p phia tren. Cong tae thu no va xu' ly tai lieu dja ehan cung eo the gay ra eae dj thw&ng AVO gia. Tuy nhien, rat nhieu trw&ng hg'p ap dung khong thanh eong eo nguyen nhan tir viee sir dung bien do dja ehan khong ehinh xae chir hoan toan khong phai do ban chat eua phwang phap.
Trong bai bao nay, trw&e tien ehung toi chia ky thuat phan tich AVO thanh hai loai: Phan tich dinh tinh va phan tfeh dinh twg'ng. Ca s& ly thuyet va kha nang ap dung eua tirng phwang phap dwg'C khai quit & phan tiep theo. Cuoi eiing, sir dung ea s& toan hge eua AVO, ehiing toi thao luan viee sir dung bien do dja chan va anh hw&ng cua no t&i phan tieh AVO cung nhw phwang phap sir dung bien do dja chan chfnh xae trong phan tieh AVO ngwg-c.
fJ^^ ^ | y Sir dung tai lieu dia chan song dpc khong cho phep chung ta phan biet duge cac nguyen nhan gay ra dj thuang bien dp.
Trong khi do song ngang lai it chju anh Phuang phap tim kiem cac bay chira
dau khi sir dung dj thuang bien dp tren tai
lieu dia chan tra nen pho bien tu nam ^ 1972. Tuy nhien, co r I t nhiiu cac d i i u kien huang eua eae via chira khi do do rat huu
dja chat khac (via than, da carbonate hoae hieu trong viee phan biet eae dj thuang da nui lira) cung gay ra dj thuang bien dp. bien dp bai vi dj thuang bien dp khong gay
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ra bai khi se the hien tren ca 2 mat cat song dpc va song ngang. Tuy nhien, viee thu no song ngang phu'c tap han rIt nhiiu so vai song dpc. Do do phuang phap phan tieh AVO la mpt giai phap co the cung d p mat d t song ngang tir s i lieu song dpc.
Phuang phap phan tich AVO ra dai vao nam 1984 khi bai bao ciia Ostrander [1] dugc dang tren tap chi "Geophysics" trong do ong chi ra sy t i n tai cua khi trong t i n g cat k i t dugc phii bai tang set se gay ra hien tugng thay doi bien dp dja chan theo khoang each thu no (AVO). Ostrander cOng phat hien ra sy thay doi bien dp nay lien quan den sy suy giam ciia ty s i Poisson gay ra bai sy hien dien
ciia via cat k i t ehu'a khi. Mpt nam sau do Shuey [2]
chu'ng minh b i n g toan hpe thong qua viee sir dung cae phuang trinh g i n dung eiia he phuang trinh Zoeppritz r i n g ty so Poisson chinh la hang s i dan hoi tryc tiep nhat lien quan d i n s y phu thupc ciia he so phan xa dja c h i n (co goc tai len den 30°) vao khoang each thu no.
Phuang phap phan tich AVO dugc tien hanh sau khi tai lieu dja chan da d u g c xir ly theo 1 chu trinh bao toan bien dp. V l ca ban, phan tich AVO d u g c chia ra thanh 2 loai chinh (Hinh 1): Phan tich AVO djnh tinh (qualitative AVO analysis) va phan tich AVO djnh lugng (quantitative AVO analysis).
QUALITATIVE AVO ANALYSIS 1
CMP, Partial Stacks Analysis
1
LambdaRtio, MuRho Analysi!
1
RAW SEISMIC DATA (PP, PS)
i 1
AVO - PR SERVED PROCESSING
1
Intercept, Sradient Analysi;
1
AVO Cross-Plotting
WELL LOG DATA (Vp, Vs, p)
.L » -
1 QUANTITATIVE A V O ANALYSIS
1
1
A V O Forward Modeling
1 .._.._.'
iZoeppritzl 1 f-k i 'Modelingi jiviodelingi
1 A V O Inversion J Amplitude
Calibration
•/ PP Inversion
•' Joint PP, PS Inversion
Hinh 1. Sa do phan loai cac phwang phap phan tich AVO 1. Phan tich AVO djnh tinh
Phuang phap phan tich AVO djnh tinh bao gom cae phuang phap phan tich su' dung bang diem giO'a ehung (CMP gathers) va mat e l t cpng vai khoang each thu no khac nhau (partial stacks), cung nhu eae thupc tinh AVO khac (intercept, gra- dient...) d l tim ra di thuang AVO lien quan d i n eae via cat k i t ehu'a khi.
1.1 Phan tieh AVO sir dung bang diem giira ehung (CMP) va mat eat eong v&i eae khoang each thu - no khac nhau (partial stacks)
Quan sat tai lieu dja c h i n tren bang CMP va
mat d t cpng vai khoang each thu no khac nhau cho phep chung ta xac djnh sy thay doi ciia bien dp dja chan theo khoang each thu no. O i l u nay rIt quan trpng bai vi no cho phep chiing ta kiem chu'ng cac dj thuang AVO quan sat thay tren cac mat d t thupc tinh khac (intercept, gradient...).
Trong rat n h i i u truang hgp eae di thuang nay khong lien quan d i n sy thay doi eua bien dp dja c h i n theo khoang each thu no.
Ngoai ra, chung ta cung co the tao ra rat nhieu thupc tinh AVO khac tif eae mat cat cong vai khoang each thu no khac nhau. Vi du: Thupc tinh FN (duge tao ra khi l l y mat cat cipng vai khoang 28 DAU KH|-S(!) 12/2010
each thu no xa - far stack (F) tru' di mat d t cpng vai khoang each thu no g i n - near stack (N)) co tinh chit gan g i l n g vai thupc tinh AVO gradient (phIn 1.2) trong viec phat hien dj thuang AVO loai II (phan 1.3). Thupc tinh FNxF (F trir di N roi nhan vai F) cho phep phat hien tot han dj thuang AVO loai II vai N eo gia trj am nho va F co gia trj am lan.
Thupc tinh FNxN (F tru di N roi nhan vai N) cho phep phat hien t i t han dj thuang AVO loai III.
1.2. Phan tieh AVO sir dung he so ehan (inter- cept) va gradient (gradient) eua ham so tuyen tinh
Nhu da noi trong p h I n tom t i t , ky thuat phan tich AVO eho phep chiing ta xac djnh dugc cac thong so cua da chira thong qua viee phan tieh sy thay doi bien dp dja chan theo khoang each thu no. He so phan xa cua song dan h I i dugc mo ta bing he phuang trinh phirc tap Zoeppritz [3]. Su' dung phuang phap b i l n doi t u y l n tinh gan dung va chi giO' lai thanh p h I n bae 2, Shuey [2] dua ra phuang trinh sau:
R(Q)=Rp + Gsm"Q (1) Trong do: R(9) la he so phan xa ciia song dpc CO goc tai 6
AV, Ap
la he so phan xa eiia song dpc CO goc tai 90°
G-. 2 V, V'
Ap ^AK,
+ 2- ^ t h i hien sy thay doi p V,
tai cac khoang each thu no trung gian
Phuang trinh (1) la t u y l n tinh khi bieu d i i n R(6) dual dang ham so eua b i l n sin2 0. Khi do chiing ta eo the tien hanh phan tich bien dp dja chin dual dang h I i qui t u y l n tinh de xac djnh he so chan Rp va gradient G ciia ham t u y l n tinh. T i i n hanh phan tich nay cho tat ca cac mach dja chan se cho k i t qua la 2 mat d t thupc tinh AVO: Thupc tinh he so ehan Rp ehinh la mat e l t cpng eiia song phan xa dpc Kp vai goc tai 90°, thupc tinh gradient G chira dyng thong tin v l song phan xa dpc Kp va ngang Vs.
Gia thilt rang ty s i Fp/Fs = 2 thi cong thu'c tinh
G = R,-1R, (2) gradient G se tra thanh:
Al-', A p '
Trong do: ih la he so phan xa eua song ngang co goe tai 90°
Phuang trinh (2) eo the viet dual dang: Rs = iRp - G)/2. Ro rang la hieu s i ciia thupc tinh he s i ehan va gradient sau khi hieu chinh bien dp se la thupc tinh t h i hien g i n dung mat e l t song phan xa ngang. Dieu nay eho phep chiing ta sir dung phan tich AVO d l danh gia dj thuang bien dp: Neu 1 dj thuang bien dp x u l t hien tren thupc tinh he s i chan Vp (mat e l t song phan xa doe) ma khong x u l t hien tren mat d t gia song ngang Ks (lly thupc tinh he s i chan tru di gradient) thi dj thuang bien dp nay eo the lien quan tai via eat k i t chira khi.
Phuang trinh (1) dugc Verm va Hilterman [4]
b i l n doi thanh:
R{e)=Rp cos'e+PRsm'e (3) Aa a he s i phan xa Trong do: PR =
Poisson
Aa la sy thay doi eua ty so Poisson Og^.g la ty so Poisson trung binh
Gia thilt r i n g a^,^^ = V^ ta co PR = % AO va phuang trinh (3) tra thanh:
R{Q)=R^+i'^ &a~RAsm'd (4) So sanh phuang trinh (1) va (4) ta eo G = %
Aa - Rp hay:
Aa = {Rp+ G)*% (5) Phuang trinh (5) cho thIy n l u lay thupc tinh
he so ehan cpng vai gradient se cho k i t qua la sy thay doi ty s i Poisson ACT. Ty so Poisson a lai lien quan d i n (Vp/Vs)2, do do 1 sy thay doi ty so Poisson CO gia trj am se lien quan den noe ciia via eat k i t chira khi trong khi sy thay doi ty so Poisson CO gia trj duang se lien quan den day ciia via cat k i t chira khi.
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Ngoai ra, n l u l l y tich s i ciia 2 thupc tinh he so ehan va gradient (Rp * G) ehung ta se duge 1 thupc tinh mai r I t huu hieu trong viee phat hien cac via eat k i t chira khi co dp r i n g cao (gay ra dj thuang AVO loai III). Cac via cat k i t dang nay co ca 2 thupc tinh he s i chan va gradient vai gia trj am lan do do tich so ciia chung se co gia trj duang r I t lan trong khi cae via cat khong chira khi se eo bien dp y l u va tich s i (Rp * G) co gia trj am.
Thupc tinh nay cung cho phep phan biet eae dj thuang bien dp lien quan d i n khi vai cac dj thuang bien dp khac.
1.3. Phan tfeh AVO su' dung do thj Phan tich AVO sir dung do thj la mpt phuang phap hO'u hieu d l minh giai eae thupc tinh AVO. He so ehan Rp dugc bieu dien cung vai gradient G tren do thj la mpt eong eu tryc quan bieu d i l n cac dj thuang AVO giup chung ta xae djnh ro han cac dac tinh ciia da chira.
Rutherford and Williams [5] dua ra mpt he thong phan loai cac dj thuang AVO tuang irng vai eae via ehu'a khi khac nhau (Hinh 2). 3 loai dj thuang AVO dugc djnh nghla dya tren viee xae djnh vj tri eiia t i n g noc va t i n g day eua via chira khi tren d l thj.
Sau nay, Castagna and Smith [6] djnh nghTa them dj thuang AVO thir 4 nhu sau:
- Dj thuang AVO loai I dugc ve a goc phan t u thir 4 vai he s i chan duang va gra- dient am. Loai dj thuang nay lien quan d i n cac ranh giai co tra khang am hpe lan va ty so V/Vs nho han so vai t i n g chan.
- Dj thuang AVO loai II lien quan den cac via eat k i t vai he so chan nho nhung lai CO gradient co gia trj am lan. Loai dj thuang nay r I t kho co the phat hien tren mat d t dja c h i n vi chung thuang la cac dj thuang bien dp y l u .
- Di thuang AVO loai III la dj thuang lien quan den cac dj thuang bien dp lan va n I m
m
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• o ra m O
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0.20 0.16 0.12
o.oa 004 000 -0.04 .0.08 -0.12 -0.16 -0.20
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Class II | a a s s l| \
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-0 20 -0 16 -0 12 -0 08 -0.04 0.00 0.04 0 08 0 12 0.16 0.20
AVO Intercept (A)
Hinh 2. Phan loai di thwang AVO theo Rutherford va Williams (loai I, II va III) cung vai loai IV ciia Cagtana va Smith. Hinh ve nay dwac sira tw [7] vai cac sd La Ma tai 4 goc thi hien sd thir tw cac goc phin tw tren dd thi
a goc p h I n t u thu" 3. Dj thuang nay the hien cac via cat k i t chira khi co dp rong lan.
- Dj thuang AVO loai IV n I m a goc phan t u thu' 2. Loai nay h i l m gap nhung x u l t hien khi cac via eat k i t ehu'a khi CO dp rong eao bj chan bai cac t i n g set cirng co ty s i K / F J cao han chut it so vai da chira.
1.4. Phan tfeh AVO sir dung eae tham so LambdaRho va MuRho
Goodway [8] giai thieu mpt phuang phap phan tich AVO sir dung cac tham so LambdaRho(Ap) va MuRhoijup) (phuang trinh 6) eho phep phan biet tot han cae dac tinh vat ly ciia da chira) so vai phuang phap phan tich AVO thong thuang sir dung ty s i F/Ks (phuang trinh 7):
^pp(e) = - [ l + t a n ' e ]
^pp(e)= - 4 ^ s i n F„-
A(X + 2[i)
X + 2ii F„-
• ^ + i r i -
u 4L
tan-e
l ' ^ ( 6 )
1 _AF,
2 c o s ' e F„ F„- F. (7) Trong do: ?. va n la eae tham s i Lame va p la mat dp.
Cac thupc tinh nay cho phep chung ta hieu biet sau sac han da chira vi chung chia tach cac dae tinh cua da chira nhu dung djch va thach hpe theo eae tham s6 Lame dya tren phan xa dja c h i n .
30 DAU KHi -S6 12/2010
2. Phan tich AVO djnh lu'O'ng
Trong dja c h i n phan xa, nhu d u tinh toan cac tham s i : Van toe song dpc va song ngang cOng nhu mat dp cua cac lap dat da dual sau su' dung s i lieu dja chan thu no tren mat d I t la 1 moi quan tam nghien ciru tu' lau. Viee tinh toan dugc eae thong tin nay 1 each djnh lugng cho phep chung ta tien hanh phan tich thach hoc chinh xae gop phan vao viee tham do d i u khi tryc t i i p sir dung tai lieu dja chan.
Phan tieh AVO djnh tinh dya tren cac thupc tinh he so chan va gradient nhan dugc tir phuang trinh gan dung ciia Shuey khong cho phep chung ta tinh toan 1 each djnh lugng eae tham so dja chan.
Buac t i i p theo trong phan tich AVO se la phan tich djnh lugng de xac djnh eae tham s i noi tren sir dung bien dp cua tai lieu dja chan truae khi cpng (phan tieh AVO ngugc).
Phan tieh AVO djnh lugng g I m 2 buac chinh:
Mo phong AVO thuan va phan tich AVO ngugc.
Buac thif n h l t dugc t i i n hanh b i n g each xay dyng mo hinh van t i e va mat dp sau do mo phong tai lieu sir dung phuang trinh Zoeppritz hoae phuang trinh song (xem phIn 3).
Buac thir hai bao g I m viec cap nhat mo hinh d l tao ra sy phu hgp han giira s i lieu mo phong va s i lieu thyc dja (Hinh 3).
3. SLP dung bien do dja chan trong phan tich AVO
Ca sa toan hpe eua phuang phap phan tieh AVO tren thyc te dugc xay dyng sir dung bien dp tuang d i i dual dang he s i phan xa hoae bien dp phan xa da duge hieu chinh theo bien dp cua song tai. Tuy nhien, viec ap dung phan tich AVO lai dugc tien hanh tren tai lieu dia c h i n thu no sir dung bien dp ciia mach dja c h i n (bien dp tuyet doi). O i l u nay dan den 1 cau hoi kha quan trpng: Lam sao ehung ta CO t h i nhan duge bien dp tuang d i i trong phan tich AVO khi chung ta chi c6 tai lieu dja chan vai bien dp tuyet d i i ?
Vi du trong bai bao [9] ciia minh. Smith &
Gidlow v i l t :
a (3 (8) Trong 66 a = Vp va /5 = Fv
- - - ' - ^ s m ^ e , + - t a n - e va fi =
8 2 a ' 2 = - 4 - ! ^ sin
a ' (9)
Hinh 3. Sir dung phan tich AVO dinh iwang di tinh toan van tdc sdng doc, sdng ngang va mat do. Cac dwang cong mau den la md hinh trwac khi phan tich AVO ngwac. Mau dd la md hinh sau khi da cap nhat sir dung phan tich AVO ngwac. Mach dia chin md phdng (mau xanh) sau khi phan tich AVO ngwac phii hap kha tot vai vai mach dia chin thwc dia
Ca hai phuang trinh (8) va (9) deu khong co thir nguyen;
chung bao g I m bien dp tuang d i i . Tuy nhien, Smith & Gidlow t i i p tuc va viet " n l u bien dp that ciia tu'ng mach dia c h i n la a,, thi sai so binh phuang trung binh..."
se la:
-i^:
Aa Ap (10)Tiep theo do 2 ong dua ra k i t qua phan tich h I i qui binh phuang nho nhlt cho a va b:
AV
V
I«,c,
(11)Trong do V dai dien cho a va DAU KHi-so 12/2010 31
T H A M DO - K H A I T H A C D A U KHi
p. C, la cac trpng s i khong co thu' nguyen bai vl ehiing chi bao gom tong va tich so ciia cac b i l n khong thu' nguyen A. va B.. Do do cac gia tri a- hien nhien cung la cac dai lugng khong co thir nguyen, hoae da dugc hieu ehinh theo bien dp song tai.
Cae gia trj bien dp tuyet doi ciia mach dja chan CO the duge viet dual dang Ka^, trong do K la hang s i hieu ehinh dugc gia thilt la khong bilt. Do do phuang trinh (11) se thanh:
^';r=i(^«.)c,
(12)Trong do Ka- la cac gia trj bien dp ciia mach dja chan. Phuang trinh (8) liie do tra thanh:
KR,,{Q,)=A, K Aa
+ B. K Ap
(13) Vai cac dai lugng trong ngoac dugc tinh toan sir dung phan tieh h I i qui.
Phuang trinh (13) eho thIy, d l tinh toan dugc bien dp tuang d i i tu' bien dp dja c h i n , chiing ta d n phai xac djnh dugc gia trj ciia K. N l u khong xac djnh dugc K thi chi phan tich AVO djnh tinh mai CO the dugc t i i n hanh con phan tich AVO djnh lugng thi khong t h i . Phan tich AVO ngugc sir dung bien dp dja c h i n khong dugc hieu chinh theo cac he so phan xa se eho k i t qua khong chinh xac v l eae tham so van t i e song dpc, song ngang va mat dp.
Viee xac djnh gia trj cua Kdoi hoi chung ta phai t i i n hanh mo phong tai lieu dja c h i n vai nhiiu khoang each thu no khac nhau sir dung tai lieu sonic luang eye. T i i p theo, bien dp RMS (root mean square) dugc tinh toan cho moi mach dia c h i n mo phong va hieu chinh vai mach dia c h i n thyc dja tuang irng.
Co 2 phuang phap de mo phong tai lieu dja c h i n vai nhiiu khoang each thu no khac nhau:
Thuat toan sir dung phuang trinh Zoeppritz va thuat toan sii' dung phuang trinh song.
- Thuat toan sir dung p h u a n g trinh Zoeppritz xac djnh goe tai eiia song tai cac ranh giai phan xa b i n g phuang phap ve d u a n g truyen song
(ray tracing). TO' cac gia trj goc tai nay va dac tinh thach hpe phia tren va phia d u a l ranh giai phan xa, bien dp phan xa d u g c tinh toan sir dung he p h u a n g trinh Zeoppritz. Thuat toan nay chi ehinh xac cho song phang tren tu'ng ranh giai phan xa rieng le. Tren t h y c t l song d u d u g c t r u y i n tai nhieu mat phan xa va tao ra hang loat cac song phan xa n h i i u l i n va song c h u y i n doi giua cac ranh giai nay. Cac song nay co the gay anh h u a n g d i n tin hieu phan xa va lam thay doi chung. Do do thuat toan nay ehi CO the mo phong tin hieu phan xa va co the cho k i t qua khong chinh xac, dac biet la d i i vai mo hinh phan lap mong co dp t u a n g phan v l tra khang am hpe lan.
- Thuat toan sir dung phuang trinh song co the khac phuc d u g c nhuge d i l m eiia phuang phap tren bang each mo phong d i n g thai t i t ea eae loai song. Vai viec co the mo phong song phan xa n h i i u lan va song chuyen doi, thuat toan nay v l ly t h u y l t r I t chinh xae cho mo hinh 1 chilu (khong co sy thay doi theo c h i l u ngang). Tuy nhien, do thuat toan d u g e t i i n hanh tren m i i n f-k nen n l u mo hinh khong d u g c xay dyng chi t i l t se gay ra cae song gia tao. Do do viec thyc hien thuat toan nay tren 1 so mo hinh co t h i ton nhiiu thai gian may tinh.
Ket luan
Trong bai bao nay chung toi da giai thieu tong quan v l p h u a n g phap phan tich AVO cOng n h u thao luan v l each sir dung bien dp dja c h i n truae khi cpng trong phan tieh AVO. Chung toi chia phan tich AVO thanh 2 loai chinh: Phan tich AVO djnh tinh va djnh l u g n g . Trong khi phan tich AVO djnh tinh co the d u g e tien hanh su' dung bien dp dja ehan tuyet doi thi dp ehinh xac ciia phan tich AVO dinh l u g n g lai phu thupc r I t n h i i u vao viec hieu chinh bien dp tai lieu dja c h i n theo cac he so phan xa. T r u a e khi t i i n hanh phan tieh AVO n g u g c , tai lieu dja chan thyc dja n h l t t h i l t phai d u g c hieu chinh sir dung hang s i hieu chinh K d u g c tinh toan b i n g p h u a n g phap mo phong va doi chieu vai tai lieu thuc dia.
3 2 DAU KHi - S6 12/2010
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Tai lieu tham l<hao
1. Ostrander, W. J., 1984. Plane-wave reflection coefficients for gas sands at non-normal angles of incidence. Geophysics, 49, 1637 - 1648.
2. Shuey, R.T., 1985. A simplification of the Zoeppritz equations. Geophysics, 50, 609 - 614.
3. A k i , K., a n d R i c h a r d s , P. G., 1 9 8 0 . Quantitative Seismology: Theory and Methods. San Francisco: W. H. Freeman and Co.
4. Verm, R., and Hilterman, F., 1995. Lithology color-coded seismic sections: The calibration of AVO crossplotting to rock properties. The Leading Edge, 14, 847.
5. Rutherford, S. R., and Williams, R. H., 1989.
Amplitude-versus-offset variations in gas sands.
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