Research Progress in Acoustical Application to Petroleum Logging and Seismic Exploration


 Samuel Arnold
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1 Snd Ordrs of Rprints at Th Opn Acoustics Journal 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 acousticlctric analogu w rport in this papr a nwly dvlopd acousticlogging ntwork modl. Important rlationships amongst various physical factors ar stablishd i.. drivingvoltag signal lctricacoustic convrsion of sourctransducr acousticlctric convrsion of rcivrtransducr th physical and gomtrical proprtis of propagation mdia as wll as th masurd logging signal. Tchnically a drivingvoltag convolution with lctricacoustic impuls rspons is usd to substitut for som traditionally assumd acousticsourc 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 acousticlogging 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: Acousticlogging 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 lctricacoustic and acousticlctric convrsions of transducr on acousticlogging signals traditional acoustic logging mthods usually adopt som assumd mathmatical functions such as Tsang wavlt Gaussian puls wavlt tc. to dscrib an acoustic sourc [24]. 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: ; 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 lctricacoustic and acousticlctric 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 acousticlogging 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 latstag 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 thinlayr oilgas rsrvoirs. Building on a rgional gological modl and applying logging data from svral oilwlls in th China rgion w rport in this papr a nwly dvlopd algorithm in constructions of th so calld sismic wavlt dictionary /3 23 Bntham Opn
2 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 oilgas rsrvoirs.g. th thinlayr oilgas rsrvoirs [7]. 2. ACOUSTICLOGGING AND SEISMIC EXPLORATION 2.. Rlationship Btwn Radiatd AcousticSignal and DrivingVoltag Signal Lt s considr th rlationship btwn drivingvoltag signal and acousticsignal radiatd by th sourctransducr as wll as that of acousticsignal and lctricsignal convrtd from th rcivrtransducr. For th radiatd acousticsignal and drivingvoltag signal lt s considr a sphrical thinshll transducr with acousticlctric and lctricacoustic 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 acousticlctric impuls rsponss can b obtaind. Th lctricacoustic and acousticlctric 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 sourctransducr and rcivrtransducr. Th drivingvoltag convolution function with th lctricacoustic 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 lctricacoustic and acousticlctric convrsion. Th transducr is composd of th pizolctric matrial PZT7A [] 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 thinshll transducr as shown in Tabl. From Es. ()(2) th calculatd lctricacoustic and acousticlctric convrsions in tim and fruncydomains 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 sourctransducr. 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 rcivrtransducr. C 3 m N : 2.2. AcousticLogging 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 fluidfilld cylindrical borhol and it is mbddd in an infinitly larg mdium. T and R ar th sourctransducr and rcivrtransducr 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 lctricacoustic and acousticlctric convrsion. Nvrthlss non of th traditional acousticlogging mthods has vr put that into considration. Th traditional acousticlogging modls simply nglct th transmission tim dlay causd by both th lctricacoustic convrsion and th acousticlctric 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 acousticlogging 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
3 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 AcousticImpdanc of CouplingMdium 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) 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 drivingcircuit Drivingvoltag signal Voltag signal of lctrictrminals of T Acousticprssur signal radiatd by T Acousticprssur 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 Mchanicallctrical 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 Acousticimpdanc of coupling mdium around transducr modl taks a full considration on th ffct of lctricacoustic and acousticlctric 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 acousticlogging as shown in Fig. (6). In this modl th drivingvoltag 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 lctricacoustic convrsion of T th physical and gomtrical proprtis of th propagation mdia (borhol mud or th formation around borhol) and acousticlctric convrsion of R on th drivingvoltag signal u (). t W may considr T as an lctricacoustic filtr th propagation mdia as an acoustic filtr and R as an acousticlctric 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 acousticlctric convrsion of R Tsang wavlt may b usd for th acousticprssur 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 4 Th Opn Acoustics Journal 23 Volum 6 Fa t al. EAIRWF EAIRAS Ngativ Phas Tim (s) * khz Fruncy (Hz) * 4 Fig. (2). Elctricacoustic convrsion of sourctransducr: lctricacoustic impuls rspons; amplitud spctrum. EAIRWF stands for th magnitud of th lctricacoustic impuls rspons wavform and EAIRAS is that of th corrsponding amplitud spctrum. NAWF NAAS 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 Positiv Phas AEIRAS Tim (s) * khz Fruncy (Hz) * 4 Fig. (3). Acousticlctric convrsion of rcivrtransducr: acousticlctric impuls rspons; amplitud spctrum. AEIRWF stands for th magnitud of acousticlctric impuls rspons wavform and EAIRAS is that of th corrsponding amplitud spctrum. AEIRWF AEIRAS Positiv Phas Tim (s) * khz Fruncy (Hz) * 4 Fig. (4). Drivingvoltag signal: th wavform; amplitud spctrum. NEWF stands for th magnitud of th normalizd drivingvoltag 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 acousticlogging systm: T and R ar rspctivly th sourctransducr and rcivrtransducr 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 acousticlogging 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 Pwav and v sv is th acoustic spd of SVwav 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 acousticlogging signal wavlt th transmission dlay causd by th acousticlctric convrsion of R can b up to
5 ( t ( Progrss of Application Rsarch on Acoustics Th Opn Acoustics Journal 23 Volum 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 a=.6w p t(s) x 3 a=.6w p f (Hz) 4 x (c) us t(s) 3 x (d) KHz f (Hz) 4 x.596 () us t(s) 3 x (f) KHz f (Hz) 4 x Fig. (8). Acousticlctric convrsion of rcivrtransducr 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 acousticlogging signal is small th cmnt bond uality of th casdwll is dfind as good; othrwis th cmnt bond uality is considrd as poor. Now if th impact of acousticlctric convrsion of R on th hadwav amplitud is not proprly considrd th bad cmntation uality may b misjudgd as a good cmntation uality and vic vrsa [4] Addition and Multiplication ALTNs For an array acousticsourc (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 acousticsourc ALTN modl with a singl rcivr is rciprocal to that of a singl sourc with an array acousticrcivr (AAR). E. (4) may b usd to adjust th xcitation tim dlay of an array acousticsourc ALTN modl with a singl rcivr. It is asy s that th hadwav amplitud of acousticlogging signal linarly incrass with rspct to th numbr of transducr lmnts in th AAS. Similarly to adjust th shifting tim of acousticlogging signals rcivd by ach rciving lmnts in ALTN with a singl sourctransducr th hadwav amplitud of acousticlogging 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 Pwav 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 hadwav 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 acousticbam 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 acousticlogging signal.
6 6 Th Opn Acoustics Journal 23 Volum 6 Fa t al () (2) 3 two diffrnt mdia. Applying acousticscattring thory and adopting mdium acousticabsorption tchnology th outrshll of drillcollar may b proprly dsignd with som ruird spcifications. By doing so th outrshll nsurs that acoustic signal mittd by th sourctransducr would pass fully through th windows on outrshll of ALTWD as wll as on drill collars. Du to th acousticscattring and acousticabsorption th drillcollar innrwall nsurs that th acoustic signal raching th drillcollar is scattrd and attnuatd. This will nsur th acoustic logging signals com from th formation around th borhol rathr than from drillcollar Rcivrtransducr Outrshll of logging tool Drill collar Formation around th borhol Fig. (9). Acousticbam 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 Acoustic Signal Propagation in DrillCollar 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 acoustictransducrs 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 drillcollar is usually mad of stl and th outrshll of ALTWD is a stlgroovs casing. Th ALTWD is placd in drill collar and th outrshll 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 drillcollar and on th outrshll of ALTWD. Ths windows ar locatd in th vicinity of sourc transducrs and rcivr transducrs. Th acoustic signal radiatd by th sourctransducr in ALTWD can pass through th pip layrs via th windows and thn rach th formation around th borhol. Th acousticsignal coming from th formation can b collctd by rcivrtransducrs in ALTWD. On of th tchnical difficultis with ALTWD is that th propagation spd of Pwav in stl is typically about 59 m/s. This spd is usually largr than that of low or intrmdiatvlocity formation in ALTWD. Th propagation path of acoustic signal in drillcollar is actually shortr than that of formation in ALTWD. Without a spcific dsign th acoustic signal from th drillcollar may rach rcivrtransducr unwittingly ahad of th signal from th formation around th borhol. To mak a spcific dsign w not that scattring taks plac whn acousticsignal impings on an intrfac btwn Sourctransducr Borhol fluid Fig. (). A schmatic plot of propagation paths of acoustic signal Rflction/Rfraction Btwn Two Anisotropy Rock Slabs Amplitud variations with offst (AVO) is on of th most important analyss in studis of rflction cofficint. Pwav amplitud variation with rspct to an incidnc angl is affctd by acoustic impdancs of P and SVwavs 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 timdpth 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)
7 Progrss of Application Rsarch on Acoustics Th Opn Acoustics Journal 23 Volum 6 7 In cas of a Pwav 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 4lmnt 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 Pwav or SVwav (m=) th rflctd Pwav (m=) rfractd Pwav (m=2) rflctd SVwav (m=3) and rfractd SVwav (m=4); {n}={in r} dnot th incidnc mdium and rfraction mdium. For th lmnts in R vctor R () is th rflction cofficint of uasip to uasip wav rflction R (2) is th rfraction cofficint of uasip to uasip wav rfraction R (3) is th rflction cofficint of uasip to uasisv wav rflction and R (4) is th rfraction cofficint of uasip to uasisv 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 PWav and SVWav in VTI Mdium Rspctivly; * and ar th Anisotropic Paramtrs of VTI Mdium. AShal Stands for Anisotropic Shal and TSandston Stands for Taylor Sandston Mdium Ansotropy Paramtrs (m/s) (m/s) (g / cm 3 ) * Ashal Tsandston Tchnology to Invrs Oil Rsrvoir by Logging and Sismic Data For various possibl gological structurs.g. thinout toplap downlap 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 thinout. Thos in Fig. (3) prsnt a gological structur of an intrbd and thos in Fig. (4) rflct a gological structur with two downlaps. 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 oilgas rsrvoirs.
8 8 Th Opn Acoustics Journal 23 Volum 6 Fa t al R () (2) () (2) Modulus Phas shift 2.5 R (2).5 8 (2) (2) (2) Modulus Phas shift.4 2 R (3) (3) (2) (2) Modulus (c) Phas shift R (4). (4) (2).8..2 Modulus (d) (2) 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.
9 Progrss of Application Rsarch on Acoustics Th Opn Acoustics Journal 23 Volum Sismic wavlts (or words) voltag signal with th lctricacoustic impuls rspons function was usd to substitut for som assumd acousticsourc functions. Ths assumd functions ar usually usd in traditional acousticlogging modls.g. Tsang wavlt Rickr wavlt Gaussian impuls wavlt tc. Th fourth layr Tim (s).5 Thinout Th sixth layr.5 Th first layr Th third layr Sismic wavlts (or words) Downlap 2 Tim (s).5 2 Th fifth layr Th svnth layr 2.5 Downlap Trac numbr Fig. (2). A gological structur of a thinout. Tim (s) Sismic wavlts (or words) Intrbd Trac numbr Fig. (3). A gological structur of an intrbd. 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 drivingvoltag signal lctricacoustic convrsion of sourctransducr acousticlctric convrsion of rcivrtransducr masurd logging signal and th propagation mdia. Amongst th most important physical concpts proposd in this papr ar acousticlctric analogu and a drivingvoltag convolution with lctricacoustic impuls rspons. Th lattr concpt ld to a practical and improvd ptrolum logging ALTN in which th convolution of th driving Trac numbr Fig. (4). A gological structur with two downlaps. Th anisotropic ffcts on rflction/rfraction btwn two diffrnt rockslabs 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 wavltdictionary 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 matchpursuit 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 acousticlogging ALTN transmission ntwork (ii) th tchnology of liminating acoustic signal propagation in th drillcollar 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 acousticlogging procss basd strictly on a physical mchanism. It is mor practical and much closr to th actual situation of acoustic logging than any arlir acousticlogging modls. Applications of th nw ntwork modl in analysis of acousticlogging procss lad to accurat acousticlogging information such as propagation vlocity signal amplitud wavlt phas and fruncy spctrum of acousticlogging signal in th formation. CONFLICT OF INTEREST Th authors confirm that this articl contnt has no conflicts of intrst.
10 Th Opn Acoustics Journal 23 Volum 6 Fa t al. ACKNOWLEDGEMENTS This work is supportd in part by a grant (No ) from th National Natural Scinc Foundation of China and by th Physical Scincs Division at Th Univrsity of Chicago. REFERENCES [] Laros E Rosny J Margrin L t al. Obsrvation of multipl scattring of khz vibrations in a concrt structur and application to monitoring wak changs. Physical Rv E Stat Nonlin Soft Mattr Phys 26; 73(): 669. [2] Tsang L Radr D. Numrical valuation of th transint acoustic wavform du to a point sourc in a fluidfilld bor hol. Gophysics 979; 44: [3] Gibson Jr RL Png C. Low and highfruncy radiation from sismic sourcs in casd borhols. Gophysics 994; 59: [4] Chng CH Toksöz MN. Elastic wav propagation in a fluidfilld borhol and synthtic acoustic logs. Gophysics 98; 46: [5] Crvny V. Sismic ray thory. Cambridg: Cambridg Univrsity Prss 2. [6] Thomsn L. Wak lastic anisotropy. Gophysics 986; 5: [7] Wang Y. Sismic timfruncy spctral dcomposition by matching pursuit. Gophysics 27; 72: 32. [8] Fa L Castagna JP Hovm JM. Drivation and simulation of sourc function for acousticlogging. IEEE Ultrasonics Symposium Procdings; 999 Novmbr; Lak Taho USA 999. [9] Fa L Castagna JP Hovm JM Dong DQ. An acousticlogging transmissionntwork modl. J Acoust Soc Am 22; : [] Fa L Castagna JP SuarzRivra R Sun P. An acousticlogging transmissionntwork modl (continud): Addition and multiplication ALTNs. J Acoust Soc Am 23; 3: [] Th Product Catalogu of CHANNEL Industris Inc. 839 Ward Driv Santa Barbara CA 93 USA 992 [2] Gong W. Full wavform analysis of acoustic wll logging and its multidimimnsional procssion mthods. Ph.D. thsis. China: Southast Univrsity July 988. [3] Fa L Castagna JP Hovm JM Dong D. An acousticlogging transmissionntwork modl. J Acoust Soc Am 22; : [4] Fa L Xi WY Tian Y Zhao MS MA L DONG DQ. Effcts of lctricacoustic and acousticlctric convrsions of transducrs on acousticlogging signal. Chin Sci Bull 22; 57: [5] Fa L. Application of phas control array tchniu to sonic logging. Procdings of Th ChinaJapan Joint Confrnc on Ultrasonics; 987 April Nanjing: China 987. [6] Fa L Ma HF. Dsign of a nw typ of array transmitting sonic logging. Acta Ptroli Sin 99; 2: [7] Ostrandr WJ. Plan wav rflction cofficints for gas sands at nonnormal angls of incidnc. Gophysics 984; 49: [8] Fa L Brown RL Castagna JP. Anomalous postcritical rfraction bhavior for crtain transvrsly isotropic mdia. J Acoust Soc Am 26; 2: [9] Zhao Y Zhao N Fa L Zhao M. Sismic signal and data analysis of rock mdia with vrtical anisotropy. J Mod Phys 23; 4: 8. [2] Castagna JP. Offstdpndnt rflctivity: thory and practic of AVO analysis. Oklahama Tuba USA: Socity of Exploration Gophysicists 993. [2] Mallat S Zhang Z. Matching pursuit with timfruncy dictionaris. IEEE Trans Signal Proc 993; 44(2): [22] Davis G Mallat S Avllanda M. Adaptiv grdy approximations. Constr Approximation 997; 3: Rcivd: Novmbr 5 22 Rvisd: January 6 23 Accptd: January Fa t al.; Licns Bntham Opn. This is an opn accss articl licnsd undr th trms of th Crativ Commons Attribution NonCommrcial Licns ( which prmits unrstrictd noncommrcial us distribution and rproduction in any mdium providd th work is proprly citd.
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