Snd Ordrs of Rprints at rprints@bnthamscinc.nt Th Opn Acoustics Journal 23 6 - Opn Accss Rsarch Progrss in Acoustical Application to Ptrolum Logging and Sismic Exploration Lin Fa * Li Wang Yuan Zhao 2 Lin Liu Yajuan Zhng Nan Zhao 2 Mishan Zhao 2 and Guohui Li School of Elctronic Enginring Xi an Univrsity of Post and Tlcommunications Xi an Shaanxi 72 China 2 Th Jams Frank Institut and Dpartmnt of Chmistry Th Univrsity of Chicago Chicago Illinois 6637 USA Abstract: This papr is concrnd with an improvd ntwork modl in acoustical application to ptrolum logging and sismic xploration. Utilizing acoustic-lctric analogu w rport in this papr a nwly dvlopd acoustic-logging ntwork modl. Important rlationships amongst various physical factors ar stablishd i.. driving-voltag signal lctric-acoustic convrsion of sourc-transducr acoustic-lctric convrsion of rcivr-transducr th physical and gomtrical proprtis of propagation mdia as wll as th masurd logging signal. Tchnically a driving-voltag convolution with lctric-acoustic impuls rspons is usd to substitut for som traditionally assumd acoustic-sourc functions on acoustic logging.g. Tsang wavlt Rickr wavlt Gaussian impuls wavlt tc. With an improvd undrstanding of th anisotropic ffcts on rflction/rfraction btwn two diffrnt anisotropic rock slabs th nw ntwork modl can b usd to dtrmin th various proprtis of signal propagation in acoustic-logging including propagation spd phas factor signal amplitud and fruncy information. In turn it provids input for analysis of amplitud variations with offst (AVO). Corrsponding to th improvd ntwork modl with availabl logging and sismic xploration data a nw algorithm for analysis of amplitud variation has bn dvlopd to xplor nw oil rsrvoirs or gas filds. Kywords: Acoustic-logging transducr rflction/rfraction invrsion oil rsrvoir sismic xploration sismic signal and data analysis.. INTRODUCTION Rflction and rfraction of plan wavs at th intrfac btwn two mdia ar amongst th most fundamntal procsss in wav propagation. Thy form th basis for sismic forward modling and sismic amplitud variations with offst (AVO) data analysis. Th proprtis of plan wavs at th intrfac of diffrnt mdia hav bn invstigatd xtnsivly and rportd lswhr such as th uality dtction of concrt structurs as rportd by Laros tc []. Ths studis wr aimd primarily at achiving an improvd undrstanding of th physical proprtis and gomtric structur of th propagation mdia. Nglcting th impacts of lctric-acoustic and acousticlctric convrsions of transducr on acoustic-logging signals traditional acoustic logging mthods usually adopt som assumd mathmatical functions such as Tsang wavlt Gaussian puls wavlt tc. to dscrib an acoustic sourc [2-4]. Ths approachs hav advancd thortical guidanc significantly to many applications. Tchnically thy simplifid physical and mathmatical analyss and providd rasonabl rsults in many cass of ptrolum *Addrss corrspondnc to this author at th School of Elctronic Enginring Xi an Univrsity of Post and Tlcommunications Xi an Shaanxi 72 China; Tl: 86-29-8866264; E-mail: fa_yy@yahoo.com.cn logging and sismic xploration. Nvrthlss it must b notd that this traditional simplification without propr justification can lad to significant rror in many practical applications. Th lctric-acoustic and acoustic-lctric convrsions could caus transmission dlay and amplitud/fruncy variation of a masurd signal. It is xactly du to this rason that traditional logging mthods ar far from prfct in practical work on ptrolum logging and sismic xploration. Indd for accurat analysis in practical applications of ptrolum logging an improvd ntwork modl nds to b stablishd. Drawing on analogy btwn acoustic logging procss and signal transmission w hav stablishd a nw ntwork modl which is mor favorabl and accurat for analysis of acoustic-logging transmission. It should b notd that th majority of oilfilds in China as wll as in many parts of th world hav ntrd into th mid- or lat-stag of xploitation. It bcoms much mor challnging to rais th oil and natural gas yild for th xisting rsrvoirs or vn to stabiliz th production. Thrfor prcis mthods to discovr nw oil and gas rsrvoirs ar urgntly ndd spcially for thin-layr oilgas rsrvoirs. Building on a rgional gological modl and applying logging data from svral oil-wlls in th China rgion w rport in this papr a nwly dvlopd algorithm in constructions of th so calld sismic wavlt dictionary. 874-8376/3 23 Bntham Opn
2 Th Opn Acoustics Journal 23 Volum 6 Fa t al. It is wll known that lastic anisotropy is ubiuitous in Earth s intrior [5]. Th ffcts of th rock anisotropy on th rflction cofficint ar usually calculatd using th masurd rock anisotropy paramtrs such as ths paramtrs as rportd by Thomson [6]. Th rsults of calculations may b usd in amplitud variations with offst (AVO) analysis for rflction/rfraction cofficints. Th rflction cofficints of rock formations insid th arth may b obtaind by matching rgional sismic data with th constructd sismic wavlt dictionary i.. sismic wavlts constructd by using logging data. Th amplitud and phas of th rfction cofficints may b usd to locat th oil-gas rsrvoirs.g. th thin-layr oil-gas rsrvoirs [7]. 2. ACOUSTIC-LOGGING AND SEISMIC EXPLORATION 2.. Rlationship Btwn Radiatd Acoustic-Signal and Driving-Voltag Signal Lt s considr th rlationship btwn driving-voltag signal and acoustic-signal radiatd by th sourc-transducr as wll as that of acoustic-signal and lctric-signal convrtd from th rcivr-transducr. For th radiatd acoustic-signal and driving-voltag signal lt s considr a sphrical thin-shll transducr with acoustic-lctric and lctric-acoustic uivalnc. Th circuits of th transducr ar stablishd as shown in Fig. (a b). For ths two uivalnt circuits by solving pizolctric and particl movmnt uations th lctricacoustic and acoustic-lctric impuls rsponss can b obtaind. Th lctric-acoustic and acoustic-lctric impuls rspons functions may b writtn as [8-] h ()= t K t + K 2 t cos( t ) () h 3 ()= t K 3 3 t + K 4 3 t cos( 3 t 3 ). (2) In Es. ()-(2) K K 2 K 3 and K 4 ar constants; and ar th damping cofficints for th dirct currnt and altrnat currnt of h (); t 3 and 3 ar thos for th dirct currnt and altrnat currnt of h 3 (); t and 3 ar th phas shifts; and 3 ar th cntr fruncis of th sourc-transducr and rcivr-transducr. Th driving-voltag convolution function with th lctric-acoustic impuls rspons from th transducr may b usd to substitut for th traditionally assumd acousticsourc functions such as Tsang wavlt Gaussian puls wavlt tc which maks th acoustic logging forward modl to b much closr to th actual acoustic logging. Now lt s construct a systm with th following conditions and do a practical calculation for lctric-acoustic and acoustic-lctric convrsion. Th transducr is composd of th pizolctric matrial PZT-7A [] th coupling mdium around th transducr is th transformr oil and th output impdanc of th driving circuit is takn to b 5. W also us th physical and gomtrical paramtrs of th thin-shll transducr as shown in Tabl. From Es. ()-(2) th calculatd lctric-acoustic and acoustic-lctric convrsions in tim- and fruncy-domains of th transducr ar prsntd in Figs. (2 3). Th various symbol notations usd in ths figurs and throughout th papr ar dfind in Tabl 2. A gatd sin voltag signal as shown in Fig. (4) is usd to xcit th sourc-transducr. Acoustic signal radiatd by th sourc transducr is as shown in Fig. (5). u(t) (t) R u (t) C m 3r R 2 3m C m 3 : N Fig. (). Two uivalnt circuits of th transducrs: th sourctransducr; th rcivr-transducr. C 3 m N : 2.2. Acoustic-Logging Transmission Ntwork Modl Now lt s considr th gomtrical configuration of an acoustic logging as shown in Fig. (6). A logging tool is placd in a fluid-filld cylindrical borhol and it is mbddd in an infinitly larg mdium. T and R ar th sourc-transducr and rcivr-transducr rspctivly with a distanc L from T to R. Elctric driving signal xcits T to mit acoustic signal which propagats to R via th borhol mud or th formations surrounding th borhol. Thn th acoustic signal is convrtd into lctric signal by R and rcordd by th logging tool [2]. It is notd that th transducr impact on amplitud and fruncy of a logging signal can b significant mainly contributd by lctric-acoustic and acoustic-lctric convrsion. Nvrthlss non of th traditional acousticlogging mthods has vr put that into considration. Th traditional acoustic-logging modls simply nglct th transmission tim dlay causd by both th lctric-acoustic convrsion and th acoustic-lctric convrsion. In our improvd modl th actual travl tim of an acousticlogging signal in mdia is obtaind from th propagation tim masurd by a traditional logging dvic minus all pics of transmission tim dlay. Basd on signal transmission thory a modl acousticlogging transmission ntwork (ALTN) may b stablishd to analyz th total acoustic-logging procss shown in Fig. (7). Surpassing traditional acoustic logging modls an ALTN 3 m C m R r R m m r x(t) P R3r C 3 u 3 (t) R3
Progrss of Application Rsarch on Acoustics Th Opn Acoustics Journal 23 Volum 6 3 Tabl. Physical and Gomtrical Paramtrs of Transducr and Acoustic Impdanc of th Coupling Mdium: in th Tabl is th Dnsity of Transducr Matrial; d 3 T E E 33 s 2 and s ar th Pizolctric Dilctric and Strain Constants Rspctivly; Z m is th Acoustic-Impdanc of Coupling-Mdium Around th Transducr; r b and l t ar th Avrag Radius and th Shll Thicknss of th Transducr 3 (kg / m 3 ) d 3 2 (m /V ) T 33 9 (F / m) s E 2 2 (m 2 / N ) s E 2 (m 2 / N ) Z m 6 (kg / m 2 s) r b (cm) l t (cm) 7.6-6 3.763-3.2.7.225 8.8 Tabl 2. Dfinitions of Symbols Shown in Fig. () Symbol Dscription Exprssion R u(t) u (t) x(t) p(t) u 3(t) R 3 C 2 Output rsistanc of driving-circuit Driving-voltag signal Voltag signal of lctric-trminals of T Acoustic-prssur signal radiatd by T Acoustic-prssur signal arrivingat position whr R is locatd Elctrical output signal of R Load rsistanc of R Paralll capacity C i Clampd capacitanc of transducr C i = 4r 2 b 33 ( k 2 3 ) l t N Mchanical-lctrical convrsion cofficint of transducr N i = 4r b d 3 S c m i Mass of transducr m i = 4r b 2 l t p C im Elastic stiffnss of transducr matrial C im = (s + s 2 )8l t m ir Radiation mass of transducr m ir = 4 m r b 3 ( + k m 2 r b 2 ) R ir Radiation rsistanc of transducr R ir = 4k m 2 m m r b 4 ( + k m 2 r b 2 ) R im Friction forc rsistanc R m =.8r b 2 m v m Z m Acoustic-impdanc of coupling mdium around transducr modl taks a full considration on th ffct of lctricacoustic and acoustic-lctric convrsion of a logging signal including transmission tim dlay causd by th transducrs. Thrfor an ALTN modl yilds mor accurat masurmnt on propagation spd signal amplitud and fruncy information of logging signals. Th ALTN modl in Fig. (7) can b usd to dscrib th gomtrical configuration of acoustic-logging as shown in Fig. (6). In this modl th driving-voltag signal u () t and th masurd logging signal wavlt u 3 (t) ar dfind as th input and output rspctivly. Th masurd signal u 3 (t) is a summry contribution from svral factors including lctric-acoustic convrsion of T th physical and gomtrical proprtis of th propagation mdia (borhol mud or th formation around borhol) and acoustic-lctric convrsion of R on th driving-voltag signal u (). t W may considr T as an lctric-acoustic filtr th propagation mdia as an acoustic filtr and R as an acoustic-lctric filtr. W also dfin x(t) as th acoustic signal radiatd by T and p(t z ) as th acoustic signal wavlt propagating to R via th borhol fluid and th formation nar th borhol. To mphasiz th transmission tim dlay causd by th acoustic-lctric convrsion of R Tsang wavlt may b usd for th acoustic-prssur signal radiatd by T which taks th form x(t) = 4t t sin( t)h(t). (3) Th paramtr is a damping cofficint and is th cntr fruncy of th wavlt.
4 Th Opn Acoustics Journal 23 Volum 6 Fa t al. EAIRWF EAIRAS.5 -.5 Ngativ Phas -.2.4.6.8 Tim (s) * -3.8.6.4.46 khz.2.5.5 2 2.5 3 3.5 Fruncy (Hz) * -4 Fig. (2). Elctric-acoustic convrsion of sourc-transducr: lctric-acoustic impuls rspons; amplitud spctrum. EAIRWF stands for th magnitud of th lctric-acoustic impuls rspons wavform and EAIRAS is that of th corrsponding amplitud spctrum. NAWF NAAS -.5.4 Fig. (5). Radiatd acoustic signal: th wavform; amplitud spctrum. NAWF is th wavform radiatd by th sourc and NAAS is th corrsponding amplitud spctrum..8 2 t(ms) f(khz) AEIRWF.5 -.5 Positiv Phas AEIRAS -..2.3.4.5.6.7.8.9 Tim (s) * -3.8.6.4.2 3. khz.5.5 2 2.5 3 3.5 Fruncy (Hz) * -4 Fig. (3). Acoustic-lctric convrsion of rcivr-transducr: acoustic-lctric impuls rspons; amplitud spctrum. AEIRWF stands for th magnitud of acoustic-lctric impuls rspons wavform and EAIRAS is that of th corrsponding amplitud spctrum. AEIRWF AEIRAS.5 -.5 Positiv Phas -..2.3.4.5.6.7.8.9 Tim (s) * -3.8.6.4.2 3. khz.5.5 2 2.5 3 3.5 Fruncy (Hz) * -4 Fig. (4). Driving-voltag signal: th wavform; amplitud spctrum. NEWF stands for th magnitud of th normalizd driving-voltag signal wavform and NEAS is that of th corrsponding amplitud spctrum; t is th abbrviation of tim and f is that of fruncy. Fig. (6). A schmatic plot of th gomtrical configuration of an acoustic-logging systm: T and R ar rspctivly th sourctransducr and rcivr-transducr with a distanc L from T to R. u(t) x(t) p(tz ) u 3 (t) h (t) h 2 (t) h 3(t) Fig. (7). A modl acoustic-logging transmission ntwork (ALTN). W hav prformd calculations of wavlt for wavform and amplitud spctrum using paramtrs listd in Tabl 3 [2 3]. For th ntris in Tabl 3 is th dnsity of propagation mdium v p is th acoustic spd of P-wav and v sv is th acoustic spd of SV-wav in mdia. Th distanc L from T to R is st to b.3224 m and th borhol radius a is at 2 cm. Th Tsang wavlt paramtrs ar = 2 4 rad / s =.6 /. Th calculatd rsults ar shown in Fig. (8). Fig. (8a b) ar th normalizd Tsang wavlt for wavform and amplitud spctrum (c d) ar thos of acoustic signal p(t z ) raching at R via th borhol fluid and th formation around th borhol and ( f) ar thos of lctric signal u 3 (t) convrtd by R. Th calculatd rsults in Fig. (8) show that for th acoustic-logging signal wavlt th transmission dlay causd by th acoustic-lctric convrsion of R can b up to
( t ( Progrss of Application Rsarch on Acoustics Th Opn Acoustics Journal 23 Volum 6 5 3.886 μs. Compard to th ngativ had wav amplitud valu of p(t z) in Fig (8c) th had wav amplitud of u 3 (t) in Fig. (8) has initially a rlativ dclin and thn changs to a positiv valu. It shows that if th ffct of acousticlctric convrsion of R on th logging signal is nglctd th masurd valu of th spd will produc a much largr rror. Tabl 3. x (t) t x (t) max max w X j ) X(jw) max ( t ) p ( t ) p max p ( j w ) p( j w ) max ( ) u ( t ) 3 u 3 max U j w ) j w ) U 3( 3 Physical Paramtrs of th Borhol Fluid and MC- Sandston Around Borhol Mdium ( kg m ) 3 v p ( ms) Borhol fluid.2 54 v s (m/s) Formation 2.6 5943 32 a=.6w p.5 -.5 -.2.4.6.8 t(s).2.4.6.8 2 x -3 a=.6w p.5.2.4.6.8.2.4.6.8 2 f (Hz) 4 x (c).5 373.897us -.5 -.2 -.4347.4.6.8.2.4.6.8 2 t(s) -3 x (d).5.5769 KHz.5.5 2 2.5 3 f (Hz) 4 x.596 ().5 -.5 -.2 377.857 us.4.6.8.2.4.6.8 2 t(s) -3 x (f).5.6538 KHz.5.5 2 2.5 3 f (Hz) 4 x Fig. (8). Acoustic-lctric convrsion of rcivr-transducr on th masurd logging signal: (a b). th normalizd Tsang wavlt spctrum for wavform and amplitud; (c d). thos of acoustic signal p(t z ) raching at R via th borhol fluid and th formation around th borhol; ( f). thos of lctric signal u 3 (t) convrtd by R. In traditional cmnt bond uality logging if th hadwav amplitud of acoustic-logging signal is small th cmnt bond uality of th casd-wll is dfind as good; othrwis th cmnt bond uality is considrd as poor. Now if th impact of acoustic-lctric convrsion of R on th had-wav amplitud is not proprly considrd th bad cmntation uality may b misjudgd as a good cmntation uality and vic vrsa [4]. 2.3. Addition and Multiplication ALTNs For an array acoustic-sourc (AAS) in th borhol at th radiation dirctivity maximum th xcitation tim dlay t for two nighbor transmitting lmnts i.. th transducrs in ALTN modl is givn by [5 6] t = d / v (4) whr d is th intrval btwn two nighboring transmitting lmnts and v is th acoustic vlocity of P- wav in th formation around th borhol. Numrical analysis has shown that an array acoustic-sourc ALTN modl with a singl rcivr is rciprocal to that of a singl sourc with an array acoustic-rcivr (AAR). E. (4) may b usd to adjust th xcitation tim dlay of an array acoustic-sourc ALTN modl with a singl rcivr. It is asy s that th had-wav amplitud of acousticlogging signal linarly incrass with rspct to th numbr of transducr lmnts in th AAS. Similarly to adjust th shifting tim of acoustic-logging signals rcivd by ach rciving lmnts in ALTN with a singl sourc-transducr th had-wav amplitud of acoustic-logging signal incrass also roughly linarly with rspct to th numbr of transducr lmnts in th AAR. So th abov mntiond two ALTNs abid approximatly by an addition rul and ar idntifid as th addition ALTN. Assum that w hav an ALTN ntwork modl with N transducrs in AAS and M transducrs in AAR. For th ALTN with AAS and AAR P-wav vlocity around th borhol is usd to adjust th AAS xcitation tim dlay. Th acoustic signals mittd by all transmitting lmnts in AAS propagat around th borhol with th sam phas. Thn th propagating signals rach th rciving lmnts in AAR and chang into lctric signals du to th acousticlctric convrsion of th transducrs. Finally th shifting tim of ths lctric signals convrtd by ach rciving lmnts may b adjustd by solving E. (4). Th valu of th stackd had-wav amplitud incrass approximatly as a product of M and N. In this cas th ALTN modl is idntifid as a multiplication ALTN. Now lt s considr a simpl xampl with N = 4 and M = 4 i.. AAS and AAR consist of four transducrs ach. Th intrval btwn two nighboring transducrs is st to b 82 mm and th distanc from AAS to AAR is takn as 2.44 m. Th calculatd acoustic bam dirctivitis for this ALTN ar prsntd in Fig. (9). Clarly th acoustic-bam string fficincy of th multiplication ALTN is much highr than that of th addition ALTN. In ithr cas two uivalnt ALTNs ithr addition or multiplication would incras gratly th had wav amplitud for th acoustic-logging signal.
6 Th Opn Acoustics Journal 23 Volum 6 Fa t al. 8 5 2 9 6.8.6.4.2 () (2) 3 two diffrnt mdia. Applying acoustic-scattring thory and adopting mdium acoustic-absorption tchnology th outrshll of drill-collar may b proprly dsignd with som ruird spcifications. By doing so th outr-shll nsurs that acoustic signal mittd by th sourc-transducr would pass fully through th windows on outr-shll of ALTWD as wll as on drill collars. Du to th acoustic-scattring and acoustic-absorption th drill-collar innr-wall nsurs that th acoustic signal raching th drill-collar is scattrd and attnuatd. This will nsur th acoustic logging signals com from th formation around th borhol rathr than from drill-collar. 2 33 Rcivr-transducr Outr-shll of logging tool Drill collar Formation around th borhol 24 27 3 Fig. (9). Acoustic-bam string dirctivitis of addition and multiplication ALTNs: curv () is th dirctivitis of th two addition ALTNs and curv (2) is that of th multiplication ALTN. 2.4. Acoustic Signal Propagation in Drill-Collar Acoustic logging whil drilling is mainly usd for th acoustic vlocity masurmnt around horizontal wlls dviatd wlls on land and clustr wlls on offshor. Convntional logging mthod can b applid to acousticlogging tool whil drilling. Acoustic probs may b usd as ithr th gnral acoustic-transducrs or multipl acoustictransducrs. Th acuird logging data could b procssd by a propr softwar program which is writtn on th lctric circuit modul in th acoustic logging tool whil drilling (ALTWD). Th drill-collar is usually mad of stl and th outrshll of ALTWD is a stl-groovs casing. Th ALTWD is placd in drill collar and th outr-shll of ALTWD is schduld for torsion forc cratd during drilling. Baring hug torsion forc th drill collar cannot b groovd or ls it will b ruind. As shown in Fig. () thr ar small windows on th drill-collar and on th outr-shll of ALTWD. Ths windows ar locatd in th vicinity of sourc transducrs and rcivr transducrs. Th acoustic signal radiatd by th sourc-transducr in ALTWD can pass through th pip layrs via th windows and thn rach th formation around th borhol. Th acoustic-signal coming from th formation can b collctd by rcivr-transducrs in ALTWD. On of th tchnical difficultis with ALTWD is that th propagation spd of P-wav in stl is typically about 59 m/s. This spd is usually largr than that of low- or intrmdiat-vlocity formation in ALTWD. Th propagation path of acoustic signal in drill-collar is actually shortr than that of formation in ALTWD. Without a spcific dsign th acoustic signal from th drill-collar may rach rcivr-transducr unwittingly ahad of th signal from th formation around th borhol. To mak a spcific dsign w not that scattring taks plac whn acoustic-signal impings on an intrfac btwn Sourc-transducr Borhol fluid Fig. (). A schmatic plot of propagation paths of acoustic signal. 2.5. Rflction/Rfraction Btwn Two Anisotropy Rock Slabs Amplitud variations with offst (AVO) is on of th most important analyss in studis of rflction cofficint. P-wav amplitud variation with rspct to an incidnc angl is affctd by acoustic impdancs of P- and SV-wavs on both sids of th rflctor. Ostrandr [7] showd that AVO anomalis can indicat aras of Poisson s ratio chang and ar dirct hydrocarbon indicators. Howvr anisotropy has potntially significant ffcts on AVO application and tim-dpth convrsion of sismic data [8 9]. It is wll known that lastic anisotropy is so common in Earth s intrior that it is virtually impossibl to avoid it in gophysical studis. Manwhil rock anisotropy is gnrally dscribd as transvrsly isotropic and th prsnc of this kind of rock anisotropy can svrly distort th AVO analysis. In a boundary btwn two transvrsly isotropic mdia with a vrtical axis of symmtry (VTI) two 4 th ordr polynomials hav bn stablishd for calculations of rflction/rfraction angls [8] () B sin 4 (3) () + B 3 sin 2 (3) () + B 5 = (5) (2) B sin 4 (24) (2) + B 3 sin 2 (24) (2) + B 5 =. (6)
Progrss of Application Rsarch on Acoustics Th Opn Acoustics Journal 23 Volum 6 7 In cas of a P-wav impinging on th boundary btwn two VTI mdia th rlationship btwn displacmnt and traction across boundary in trms of th rflction/rfraction cofficints can b writtn as A R = B (7) whr A is a 4 by 4 matrix and R and B ar th 4-lmnt vctors. Th matrix lmnts of A ar givn by a = u () x a 2 = u x (2) a 3 = u z (3) a 4 = u z ( 4 ) a 2 = u z () a 22 = u z (2) a 23 = u x (3) ( 4 a 24 = u ) x a 3 = c (in) u () 3 x sin () + c () 33 u () z cos () v () ( () ) a 32 = c (r) u (2) 3 x sin (2) + C (r) 33 u (2) z cos (2) v (2) ( (2) ) a 33 = c (in) u (3) 3 z sin (3) + C (in) 33 u (3) x cos (3) v (3) ( (3) ) a 34 = - c (r) (4) u 33 x sin (4) (r) (4) +c 3 u z cos (4) v (4) ( (4) ) a 4 = c (in) (u () 44 x cos () + u () z sin () ) v () ( () ) a 42 = c (r) (u (2) 44 x cos 2 + u (2) z sin 2 ) v (2) ( (2) ) a 43 = c (in) (u (3) 44 x sin (3) + u (3) z cos (3) ) v (3) ( (3) ) a 44 = c (r) (4) (u 44 z cos (4) (4) + u x sin (4) ). v (4) ( (4) ) Th lmnts of B vctor ar givn as b = u x () b 2 = u () z b 3 = c (in) u () 3 x sin () + c (in) 33 u () z cos () and v () ( ) b 4 = c (in) (u () 44 x cos () + u () z sin () ). In all ths uations v () ( () ) mntiond abov th suprscripts {m}={ 2 3 4} dnot incidnt P-wav or SV-wav (m=) th rflctd P-wav (m=) rfractd P-wav (m=2) rflctd SV-wav (m=3) and rfractd SV-wav (m=4); {n}={in r} dnot th incidnc mdium and rfraction mdium. For th lmnts in R vctor R () is th rflction cofficint of uasi-p to uasi-p wav rflction R (2) is th rfraction cofficint of uasi-p to uasi-p wav rfraction R (3) is th rflction cofficint of uasi-p to uasi-sv wav rflction and R (4) is th rfraction cofficint of uasi-p to uasi-sv wav (m) (m) rfraction. u x and u z ar th polarization cofficints of th incidnt and mod convrsion wavs and v (m) is th (n) phas vlocity for th abov wavs. c ij is th lastic stiffnss of incidnc and rfraction mdia. W hav prformd calculations of th rflction/rfraction cofficints basd on Es. (5)-(7) using th anisotropic paramtrs of two sdimntary rocks listd in Tabl 4. Th calculatd rsults ar plottd in Fig. () and ar radily usd for AVO analysis of sismic xploration data [2]. Tabl 4. Anisotropic and Physical Paramtrs of Rocks whr and ar Vrtical Vlocity of P-Wav and SV-Wav in VTI Mdium Rspctivly; * and ar th Anisotropic Paramtrs of VTI Mdium. A-Shal Stands for Anisotropic Shal and T-Sandston Stands for Taylor Sandston Mdium Ansotropy Paramtrs (m/s) (m/s) (g / cm 3 ) * A-shal 2745 58 2.34.3 -.73.345 T-sandston 3368 829 2.5. -.27.255 2.6. Tchnology to Invrs Oil Rsrvoir by Logging and Sismic Data For various possibl gological structurs.g. thin-out top-lap down-lap tc. a sismic wavlt dictionary can b stablishd using logging data from svral oil wlls in a givn rgion. A match pursuit can b prformd for words in th dictionary with th sismic xploration data obtaind from this rgion [2 22]. Thn th rflctivity sris of undrground formation can b obtaind from th masurd sismic wavlts and from th words in th sismic wavlt dictionary. By obsrving th amplituds and phass of th obtaind rflctivity sris an oil rsrvoir may b rvald. In summary this tchnology may b classifid as two parts: cration of th sismic wavlt dictionary and softwar procssing of rflctivity sris invrsion. From th sismic wavlt dictionary th words prsntd in Fig. (2) show a gological structur of a thin-out. Thos in Fig. (3) prsnt a gological structur of an intr-bd and thos in Fig. (4) rflct a gological structur with two down-laps. In calculations of th formation rflctivity sris a softwar program is usd to scan all words in th sismiclogging dictionary with vry actual masurd sismic signal wavlt. This scan would locat th maximum corrlation cofficint. According to th shift invarianc norm th itrativ calculations ar prformd by utilizing a match pursuit algorithm. Whn th calculation is convrgd a minimal rsidual btwn th words with a maximal corrlation cofficint is obtaind. Thn th trac of actual sismic signal wavlt is rachd to locat th dsird oil-gas rsrvoirs.
8 Th Opn Acoustics Journal 23 Volum 6 Fa t al. 2 8 5 R () 6 4 2..2.4.6 (2).9. 2.2 4 6 8 () 5.2.4 (2).6.8..2 2 4 6 8 Modulus Phas shift 2.5 R (2).5 8 (2) 6 4 2.2.4.6 (2).8..2 2 4 6 8.2.4.6 (2).8..2 2 4 6 8 Modulus Phas shift.4 2 R (3).3.2. 5 (3) 5.2.4 (2).6.8..2 2 4 6 8.2.4 (2).6.8..2 2 4 6 8 Modulus (c) Phas shift.4 25.3 2.2 R (4). (4) 5.2.4.6 (2).8..2 Modulus 2 4 6 8 (d) 5.2..8 (2).5.4.2 6 8 Phas shift 4 2 Fig. (). Rflction/rfraction cofficints vrsus and (r) whn (in) *(in) and *(r) ar fixd. In th figurs () (2) (3) and (4) ar th phas of R () R (2) R (3) and R (4) rspctivly.
Progrss of Application Rsarch on Acoustics Th Opn Acoustics Journal 23 Volum 6 9.5 Sismic wavlts (or words) voltag signal with th lctric-acoustic impuls rspons function was usd to substitut for som assumd acousticsourc functions. Ths assumd functions ar usually usd in traditional acoustic-logging modls.g. Tsang wavlt Rickr wavlt Gaussian impuls wavlt tc. Th fourth layr Tim (s).5 Thin-out Th sixth layr.5 Th first layr Th third layr Sismic wavlts (or words) Down-lap 2 Tim (s).5 2 Th fifth layr Th svnth layr 2.5 Down-lap 2 2.5 3 2 3 4 5 6 Trac numbr Fig. (2). A gological structur of a thin-out. Tim (s).5.5 2 2.5 3 Sismic wavlts (or words) Intrbd 2 3 4 5 6 Trac numbr Fig. (3). A gological structur of an intr-bd. Th third layr 3. CONCLUDING REMARKS So far w hav discussd an improvd ALTN ntwork modl for acoustical application to ptrolum logging and sismic xploration. It is important to not that in studis of this nw modl w idntifid intrinsic rlationships amongst various physical uantitis such as driving-voltag signal lctric-acoustic convrsion of sourc-transducr acousticlctric convrsion of rcivr-transducr masurd logging signal and th propagation mdia. Amongst th most important physical concpts proposd in this papr ar acoustic-lctric analogu and a drivingvoltag convolution with lctric-acoustic impuls rspons. Th lattr concpt ld to a practical and improvd ptrolum logging ALTN in which th convolution of th driving- 3.5 2 3 4 5 6 Trac numbr Fig. (4). A gological structur with two down-laps. Th anisotropic ffcts on rflction/rfraction btwn two diffrnt rock-slabs ar discussd. Corrspondingly a nw fast algorithm for calculation of rflction/rfraction cofficints has bn prsntd. It provids insight into analysis of amplitud variations with offst (AVO) for xploring nw oil rsrvoirs or gas filds accuratly. Gtting into th prdiction of nw oil rsrvoirs and/or gas filds th nw algorithm lads to th construction of a sismic wavlt-dictionary which can b constructd by logging data from svral oil wlls in a givn rgion. Th rflctivity sris of th formation can b obtaind accuratly by using th match-pursuit algorithm th sismic wavlt dictionary and th masurd sismic rflction data. Within th framwork of th nwly proposd ntwork modl thr ar svral othr important issus discussd bsids th discussions abov including (i) th notation of addition and multiplication of acoustic-logging ALTN transmission ntwork (ii) th tchnology of liminating acoustic signal propagation in th drill-collar for acousticlogging whil drilling and (iii) th ffct of rock anisotropy on rflction/rfraction cofficints and its rlation to an accurat AVO analysis. In summary th nwly proposd ALTN ntwork modl dscribs th acoustic-logging procss basd strictly on a physical mchanism. It is mor practical and much closr to th actual situation of acoustic logging than any arlir acoustic-logging modls. Applications of th nw ntwork modl in analysis of acoustic-logging procss lad to accurat acoustic-logging information such as propagation vlocity signal amplitud wavlt phas and fruncy spctrum of acoustic-logging signal in th formation. CONFLICT OF INTEREST Th authors confirm that this articl contnt has no conflicts of intrst.
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