Theory. d are sparse and unrecorded datasets respectively.

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1 An approach for qai-contino time-lape eimic monitoring with pare ata Aeyemi Arognmati* an Jerry M. Harri, Stanfor Univerity, California, USA Smmary An approach for qai-contino, geophyical time-lape monitoring with pare eimic ata i propoe. Thi approach take avantage of the mall change in the eimic property of a geological reervoir that are expecte to occr in a mall time interval. The goal of thi approach i to obtain high temporal an patial reoltion in recontrcte, time-lape geophyical image ing comparable reorce that wol have provie high patial bt low temporal reoltion image with conventional approache. Thi i one by acqiring patially pare ata at mall time interval. In thi cae, a patially pare ataet refer to that ataet which i a mall fraction (a little a 5%) of what wol be acqire to recontrct a high patial reoltion tomographic image of the brface. The high patial reoltion obtaine by the propoe approach occr becae nrecore ata are preicte from ftre an pat ata. With high temporal an patial reoltion, early etection of important reervoir change i more likely to occr. Introction Geophyical imaging ha playe a large part in brface monitoring project, epecially in petrolem reervoir monitoring project (e.g., Harri et al., 1995; Rickett an Lmley, 2001). Thi i primarily e to the kin of eimic change that occr in the reervoir rock propertie (Wynn, 2003). In aition, eimic ata analyi i a well evelope an nertoo bject (Yilmaz, 1987; Yilmaz, 2001). Seimic ignal are able to penetrate eep into the earth an can be e in virtally any geologic etting (Wynn, 2003). The e of eimic tomography in timelape monitoring take avantage of the change in a eimic property of the reervoir rock ring the time interval ner conieration. For example, a reervoir velocity moel can be qantitatively recontrcte from either eimic reflection or tranmiion traveltime ing tomography. Conier a time-lape eimic monitoring ty eigne to lat for everal ecae a might be the cae in whole-life monitoring of a petrolem reervoir or for a CO 2 torage ite. The conventional approach to monitoring i to acqire a large amont of eimic ata ch that a high patial reoltion image of the brface can be obtaine each time a ataet i acqire. The time interval between cceive ata acqiition campaign are often o large that there are large change in the cceive eimic ata acqire. The time interval are ally of the orer of year (e.g., Mathien et al., 1995; Lanrø et al., 1999; Art et al., 2004). Sch a trategy work very well for ome time-lape project bt for other application ch a monitoring CO 2 torage, the late ientification of a reervoir leak by a year col have ire coneqence. In other wor, ome time-lape monitoring trategie are more effective when the change in cceive time-lape ataet are mall. In ch cae, temporal reoltion i a important a patial reoltion, an ometime, more important. If reorce are to be kept comparable, two cenario are poible acqiring ata ch that the monitoring provie either high patial reoltion an low temporal reoltion image, or low patial reoltion an high temporal reoltion. In the econ cenario, low patial reoltion relt becae a mall amont of ata i acqire each time, an high temporal reoltion relt becae ata are acqire more freqently. The traitional approach to inverting pare ata i to rece the nmber of moel parameter olve. Becae only a fraction of the ata that will normally be e to get a high reoltion image i e, the relting eimic image ha a lower patial reoltion. We propoe to etimate nrecore ata (Harri et al., 2004; 2007; 2008), an then recontrct geophyical moel withot recing the nmber of moel parameter olve, thereby maintaining the high patial reoltion. Althogh the iea poe here i omewhat imilar to the recently evelope concept of compreive ampling (Canè an Romberg, 2007) in the ene that pare ata are acqire an e in etimating nrecore ata, we eal here with ataet that are even more pare than what wol be acqire a compreive ampling. Alo, we take avantage of the large portion of the ata pace available in the ene baeline ata. Theory Let the ene time-lape ata be compoe of a recore pare part an an nrecore part. i.e. = S + (I - S) (1) = + (2) where S i the ata ampling operator that elect which ata are recore from the ene ataet, an an are pare an nrecore ataet repectively. SEG Hoton 2009 International Expoition an Annal Meeting 3899 Downloae 01 Dec 2011 to Reitribtion bject to SEG licene or copyright; ee Term of Ue at

2 Qai-contino time-lape eimic monitoring From (1) an (2), we ee that = S ; = (I - S) (3) In thi notation, each vector contain all previoly meare an ftre meare ata. Or goal i to etimate the nrecore ataet,. Here, ɶ i the moel (nrecore ata) etimate from ata. The fitting goal for etimating i Having a time interval of two year between the baeline image an the monitor image i atifactory for ome monitoring project. However, if potentially angero coneqence col occr from an abnormality in the reervoir, it will be neceary to monitor the reervoir with a finer ampling in time. Alo, if reorce neceary for ata acqiition are limite, a more efficient time-lape monitoring trategy i neee. Thi, cenario illtrate the nee for a qai-contino monitoring trategy ing pare ata. A 0 (4) where the operator, A i the moel contraint operator, or etimation operator. If we ame the etimate ata ɶ i approximately the ene ata, eqation (4) can be rewritten a which give Aɶ 0 (5) A + Aɶ 0 (6) The etimate nrecore ata, ɶ i then obtaine ing (6), an minimizing the objective fnction Φ= A +A ɶ 2 (7) Time-lape Fiel Monitoring Example The fiel ata example preente here are crowell ata from the McElroy fiel in Wet Texa. The ataet were acqire to monitor velocity change in the reervoir in repone to CO 2 injection (Harri et al., 1995; Lazarato an Marion, 1997) between 1993 an The well are over 3000ft eep an are eparate by approximately 600ft. Figre 1 how common-hot gather ata from the rvey. Firt arrival eimic traveltime were picke from the ata. The larget traveltime ifference occr at the epth correponing to the location of the reervoir between 2750 an 3150 ft. Uing thee traveltime, velocity moel were recontrcte ing the tomography coe, FAST (Zelt an Barton, 1998). Figre 2 how the recontrcte velocity moel an the ifference between them when the complete ataet in both cae are e. The mot obvio ifference in the velocity moel i the ignificant rop in the p-wave velocity between 1993 an 1995, relting from the injection of CO 2 into the reervoir. Figre 1: Common-orce gather from the 1993 an the 1995 rvey at the McElroy fiel in Wet Texa. The re line inicate firt arrival. SEG Hoton 2009 International Expoition an Annal Meeting 3900 Downloae 01 Dec 2011 to Reitribtion bject to SEG licene or copyright; ee Term of Ue at

3 Qai-contino time-lape eimic monitoring Figre 3: Recontrcte contrat moel from the ecimate 1995 fiel ataet. Time-lape Synthetic Monitoring Example Figre 2: Recontrcte velocity moel from the baeline (1993) an monitor (1995) rvey, an the ifference between both moel. To tet the efficiency of the approach preente in thi paper on fiel ata, we e the complete ataet from the 1993 rvey an 1% of the ataet from the 1995 rvey to etimate the icare ata from the 1995 ataet. Here, the A operator in eqation (7) wa the firt orer erivative operator. The velocity moel were then recontrcte from the etimate ata. Figre 3 how the relting contrat moel. We obtaine a goo comparion between the tre contrat moel an the contrat moel from the recontrcte ataet. In orer to tet thi approach of qai-contino monitoring, we create a erie of 70 two-imenional p- wave velocity moel from the baeline moel recontrcte ing the 1993 ataet, an a et of imlate fli flow moel converte to velocity moel. The converion wa one ing a Gamann fli btittion moel. Thee moel are intene to imlate CO 2 injection into the reervoir over a perio of 32 month. We incle a fractre in the moel which allowe injecte CO 2 to flow ot of the reervoir. Leakage occrre after the injecte CO 2 reache the fractre zone approximately 10 month after the tart of injection. Uing the finite ifferencing eikonal olver cheme given by Hole an Zelt (1995), we calclate ene firt arrival eimic traveltime recore in a crowell ata acqiition geometry for all 70 ynthetic velocity moel. Gaian noie with a tanar eviation that we conier to be the picking error of the fiel ata wa then ae to the ynthetic ataet. To imlate pare ata, we rece the ata ize to 10%, 5%, 2%, an 1% of the original ize for a given ataet in time. The rection wa one ch that the total ata volme in each ampling cenario wa contant. From thee pare yntheize ataet, we etimate the ene ataet ing the metho ecribe in the previo SEG Hoton 2009 International Expoition an Annal Meeting 3901 Downloae 01 Dec 2011 to Reitribtion bject to SEG licene or copyright; ee Term of Ue at

4 Qai-contino time-lape eimic monitoring ection, an then recontrcte the correponing velocity moel ing traveltime tomography. In etimating miing ata, we e zeroth, firt an econ orer erivative operator a the A operator in eqation (7). We then e the relting ataet to recontrct the ynthetic velocity moel. We preent the relt of the recontrcte velocity moel by their root mean qare (rm) error with repect to the known ynthetic moel (Figre 4). In thi cae, we e the rm error meare in the region of the moel where change are known to occr. The rm error crve of the etimate ataet how a conitent pattern. Thi implie that we can maintain an approximately eqal level of mifit in or etimate ataet an recontrcte velocity moel if we rece ata ize an ample the ata pace more freqently in time. From the plot, we ee that the rm error rece with time, inicating the impact of aitional ata on ata etimation. What i not captre by the rm error plot i that ing only 1% ata meare every two week, the leake CO2 wa etecte oon after it occrre. With the conventional trategy ch a leak might not be icovere for year. Conclion The qai-contino monitoring trategy preente prove effective for both ynthetic an fiel ataet. In the ynthetic example, the CO 2 leak which occrre in the ynthetic reervoir wa etecte early. Even thogh we ame crowell eimic acqiition geometry, ata evoltion can be applie to ata acqire ing any kin of ata acqiition geometry. We inten to contine reearch in the area of time-lape eimic monitoring with pare eimic ata ing fll eimic trace. Ftre work will involve the evelopment of techniqe that will take avantage of time epenent ata covariance in time-lape ata. The mot challenging apect of ata evoltion i eciing on the optimal ata ize that proce the eire relt, an the optimal time-lape rvey eign. The benefit of ata evoltion i the ability to ample the ata pace more freqently in time with mch le ata withot ignificantly looing patial reoltion in recontrcte velocity moel. Alo temporal reoltion i increae with increae temporal ampling. Acknowlegement Figre 4: RMS error plot of the recontrcte velocity moel ing the etimate ataet. We wol like to thank the Global Climate an Energy Project (GCEP) for pporting thi reearch; an the ponor of the Seimic Tomography Project at Stanfor Univerity for proviing the fiel ataet e an the permiion to pblih thi work. SEG Hoton 2009 International Expoition an Annal Meeting 3902 Downloae 01 Dec 2011 to Reitribtion bject to SEG licene or copyright; ee Term of Ue at

5 EDITED REFERENCES Note: Thi reference lit i a copy-eite verion of the reference lit bmitte by the athor. Reference lit for the 2009 SEG Technical Program Expane Abtract have been copy eite o that reference provie with the online metaata for each paper will achieve a high egree of linking to cite orce that appear on the Web. REFERENCES Art, R., O. Eiken, A. Chawick, P. Zweigel, L. van er Meer, an B. Zinzner, 2004, Monitoring of CO 2 injecte at Sleipner ing time-lape eimic ata: Energy, 29, Canè, E., an J. Romberg, 2007, Sparity an incoherence in compreive ampling: Invere Problem, 23, Harri, J. M., R. C. Nolen-Hoekema, R. T. Langan, M. Van Schaack, S. K. Lazarato, an J. W. Rector III, 1995, High reoltion crowell imaging of a wet Texa carbonate reervoir: Part 1 Project mmary an interpretation: Geophyic, 60, Harri, J. M., M. D. Zoback, A. R. Kovcek, F. M. Orr, Jr., 2004, Geologic torage of CO 2 : Global Climate an Energy Project 2008 Technical Report, ection , 2007, Geologic torage of CO 2 : Global Climate an Energy Project 2008 Technical Report, ection , 2008, Geologic torage of CO 2 : Global Climate an Energy Project 2008 Technical Report, ection Hole, J. A., an B. C. Zelt, 1995, 3-D finite-ifference reflection traveltime: Geophyical Jornal International, 121, Lazarato, S. K., an B. P. Marion, 1997, Crowell eimic imaging of reervoir change cae by CO 2 injection: The Leaing Ege, 16, Lanrø, M., O. A. Solheim, E. Hile, B. O. Ekren, an L. K. Strønen, 1999, The Gllfak 4D eimic ty: Petrolem Geocience, 5, Mathien, M. E., A. A. Vailio, P. Cnningham, J. Shaw, J. H. Jtice, an N. J. Ginzy, 1995, Time-lape crowell eimic tomogram interpretation: Implication for heavy oil reervoir characterization, thermal recovery proce monitoring, an tomographic imaging technology: Geophyic, 60, Rickett, J. E., an D. E. Lmley, 2001, Cro-eqalization ata proceing for time-lape eimic reervoir monitoring: A cae ty from the Glf of Mexico: Geophyic, 66, Wynn, D., 2003, Srvey of geophyical monitoring metho for monitoring CO 2 eqetration in aqifer: M.S. thei, Stanfor Univerity. Yilmaz, Ö., 1987, Seimic ata proceing: SEG. Yilmaz, Ö., 2001, Seimic ata analyi: Proceing, inverion, an interpretation of eimic: SEG. Zelt, C. A., an P. J. Barton, 1998, 3D eimic refraction tomography: A comparion of two metho applie to ata from the Faeroe Bain: Jornal of Geophyical Reearch, 103, SEG Hoton 2009 International Expoition an Annal Meeting 3903 Downloae 01 Dec 2011 to Reitribtion bject to SEG licene or copyright; ee Term of Ue at