SUMMARY. surface, and the requirement on the accuracy of such estimate is yet to be studied.

Transcription

1 Dt-driven deep locl imging using both surfce nd borehole seismic dt Yi Liu, Norwegin University of Science nd Technology; Joost vn der Neut, Delft University of Technology; Børge Arntsen, Norwegin University of Science nd Technology; Kees Wpenr, Delft University of Technology SUMMARY Seismic interferometrysi is proven dt-driven redtuming method to crete virtul sources for better illumintion of the trget re. It requires physicl receiver t the position of the creted virtul source. With the development of the itertive Mrchenko method, one cn now use surfce dt lone to crete virtul source in the subsurfce, but n estimte of the direct wvefield from those virtul source positions to the surfce is needed, which mens n dequtely ccurte smooth velocity model is nevertherless necessry. We show tht when borehole dt from horizontl well is vilble, one cn combine the principles of SI nd the Mrchenko method to formulte severl inversion-bsed redtuming schemes, such tht no prior smooth velocity model is needed t ll nd tht the ect forms of retrieving the reflection responses from bove nd from below cn lso be obtined. Furthermore, the internl multiples re ccounted for using these ect forms. No surrounding cquisition geometry is required or multi-component well dt is needed. We demonstrte the proposed schemes using synthetic gs cloud emple. We then show the retrieved responses nd the migrted imges using only locl velocity model. The results show tht given the sme velocity uncertinty, these responses tht re redtumed by dt produce better positioned imge ner the well thn surfce seismic imge. The proposed schemes cn be beneficil for deep boreholes nd comple res with big velocity uncertinties. INTRODUCTION Different types of borehole seismic dt Schuster et l., 2004; Bkulin nd Clvert, 2006; Vsconcelos nd Snieder, 2008b; Poletto et l., 2010 hve been used to crete virtul source dt by pplying seismic interferometry SI Wpenr nd Fokkem, 2006; Curtis et l., Compred to other redtuming methods, SI does not require ny velocity informtion nd the physicl receivers re turned into virtul source or vice vers. Known pproches to SI re crosscorreltion CC Snieder, 2004, deconvolution DC Vsconcelos nd Snieder, 2008, multidimensionl deconvolution MDD vn der Neut et l., 2011 nd crosscoherence CH Nkt et l., Comprehensive nd systemtic comprisons mong different pproches cn be found in Wpenr et l. 2011, Snieder et l. 2009, nd Gletti nd Curtis Tking step beyond SI, the itertive Mrchenko method Broggini et l., 2012; Wpenr et l., 201 hs been developed to crete virtul sources in the subsurfce from surfce seismic dt lone, which mens the presence of physicl receivers t depth is no longer needed. Vrious pplictions tht use the Mrchenko method for imging re suggested by Wpenr et l However, the scheme does require n estimte of the direct wvefield from the virtul source positions to the surfce, nd the requirement on the ccurcy of such estimte is yet to be studied. We show tht when the dt from horizontl borehole is vilble, the direct wvefield cn be obtined directly from the borehole dt, thus mking the whole Mrchenko imging scheme completely independent of ny trveltime estimtion errors. Further, by combining the principles of SI nd the properties of the focusing functions in the Mrchenko method, the ect formultions of retrieving the reflection responses from bove nd from below the well cn be obtined. The internl multiples cn lso be properly ccounted for. Compred to the scheme for imging from below by Polinnikov 2011, whose pproch is bsed on source-receiver interferometry SRI Curtis nd Hllidy, 2010, our scheme is n inversion-bsed scheme under one-sided illumintion nd cn ccount for internl multiples. These schemes lso do not require multicomponent borehole dt, both for imging from bove Meht et l., 2007 nd from below vn der Neut nd Wpenr, 2015, but the surfce relted multiples re ssumed to hve been removed from both surfce nd borehole dtsets. We strt by introducing some of the properties of the focusing functions Wpenr et l., Then we use them to derive the equtions for retrieving the reflection responses from bove nd from below, nd suggest some pproimtions s lterntives for situtions in which the focusing functions cnnot be obtined. In totl, we illustrte four schemes for imging from bove nd two for imging from below. We show the results using synthetic gs cloud model. THEORY The focusing functions The two focusing functions f 1 ± i,t nd f 2 ± 0,t hve been studied in detil in Wpenr et l Here we will just show briefly some results. f 1 ± 0 i,t describes wvefield tht focuses t position i t depth level i nd is recorded t position 0 t surfce level 0, while f 2 ± i 0,t describes wvefield tht focuses t position 0 nd is recorded t position i. The superscripts + nd denote downgoing nd upgoing, respectively. The two focusing functions re mutully relted vi f i = f 2 i 0 ; 1 f 1 0 i = f 2 + i 0, 2 where the focusing functions re now represented in the frequency domin, indicted by the bove the ngulr frequency vrible ω is omitted, nd the superscript denotes the comple conjugte. Due of the cuslity rguments for the one-wy Green s function G i 0,t, G+ i 0,t nd the focusing function f 2 + i 0,t Wpenr et l., 2014, the following reltions pply, for t < t d i, 0, where t d is the direct

2 Dt-driven imging bove nd below horizontl well rrivl time from 0 to i, t f1 0 i,t = R 0 0,t t f i,t dt d 0 ; t f i, t = R 0 0,t t f1 0 i, t dt d 0 ; 4 nd for t t d i, 0, G i 0,t = t R 0 0,t t f i,t dt d 0 ; G + i 0,t t = R 0 0,t t f1 0 i, t dt d 0 + f i, t. 6 Here R 0 0,t cn be viewed s the reflection response tht one could obtin from surfce seismic dt fter surfce relted multiple removl SRME. This is to be distinguished from R i i in Imging from bove, nd R i i in Imging from below. The time window indicted by t d i, 0 cn for emple be found by the direct rrivls from borehole dt. In ddition, the strting pproimtion to the focusing functions written in the frequency domin is 5 f 1,0 + 0 i = f 2,0 i 0 = Ĝ d i 0, 7 where the subscript 0 indictes tht the Ĝ d i 0 is the initil estimte, the direct rrivl of the Green s function obtined from borehole dt with time gte. Imge from bove To imge from bove, the ide is to retrieve the reflection response coming from the reflectors below the borehole level i, s if the medium bove is reflection-free. Such reflection response R i i cn be found by the stndrd redtuming method of SI by MDD Wpenr nd vn der Neut, 2010 Ĝ i 0 = R i iĝ + i 0 d i. 8 Here we tret Ĝ i 0 nd Ĝ+ i 0 s if they come from borehole dt, not s solutions of the Mrchenko method using only surfce reflection dt. This scheme requires up-down decomposition using multi-component dt. Solving Eq. 8 by MDD, the retrieved R i i does not contin ny dowgoing reflections coming from bove. When such seprtion is not vilble, one option is to replce the downgoing Ĝ + i 0 with the direct rrivls in the borehole dt nd use the remining events s the upgoing Ĝ i 0 Bkulin nd Clvert, 2006, such s Ĝ i 0 Ĝ d i 0 R i iĝ d i 0 d i. 9 Here the retrieved R i i will contin some spurious events relted to this wvefield seprtion pproimtion. Now, to utilize the surfce reflection response R 0 0 s in the Mrchenko method, we substitute Eq. 5 nd 6 into Eq. 8 nd cn get [ W R 0 0 f i d 0 = R i i { W [ R 0 0 f 1 } 0 i d 0 + f i d i. 10 Here n opertor W is introduced to represent the opertion of inverse Fourier trnsforming the dt, pplying time window which psses dt only for t t d i, 0, nd Fourier trnsforming the result bck to the frequency domin. Such retrieved R i i does not contin ny spurious events relted to the internl multiples from the overburden. To mke similr choice s for Eq. 9, we cn lso write nother version of it by using Eq. 5, 7 on the left-hnd side of Eq. 8 nd replce Ĝ + i 0 with the direct rrivls in the borehole dt G d i 0 on the right-hnd side, then Eq. 8 becomes [ W Ĝ d i 0 R 0 0d 0 R i iĝ d i 0 d i. 11 The retrieved response by this scheme will contin spurious events relted to internl multiples, but much simpler to implement in prctice. One more dditionl choice without much impliction is to join Eq. 9 nd 11 nd solve with MDD, which reds in mtri forms s, [ U1 αu 2 [ D1 = R αd 1 12 where U 1 nd U 2 correspond to the left-hnd sides of Eq. 9 nd 11, nd D 1 to the right-hnd sides. Here α is user-defined frequency dependent sclr weight. Inverting this joint scheme might be better thn inverting single scheme Eq. 9 or 11. First of ll, both problems my hve different frequency content nd signl-to-noise rtios; second, the borehole dt my hve higher propgtion ngles tht could help to imge structures tht could not be found in the surfce dt; third, the dt could be incomplete, so merging them could help. Imge from below The concept of imging from below mens to retrieve the reflection response coming from the reflectors bove the borehole level i, s if the medium underneth is reflection-free. Such reflection response R i i is found to be relted to the focusing function f 2 i 0 vi Wpenr et l., 2014 f 2 + i 0 = R i i f 2 i 0 d i. 1 Now by using Eq. 2, nd Eq., Eq. 1 cn be rewritten s { [ } W f i R 0 0d = R i i f 2 i 0 d i. 14

3 Dt-driven imging bove nd below horizontl well Here the opertor W is defined to represent the opertion of inverse Fourier trnsforming the dt, pplying time window which psses dt only for t < t d i, 0, nd Fourier trnsforming the result bck to the frequency domin. f i needs to be clculted from the Mrchenko method with the input of R 0 0 nd the direct rrivls Ĝ d i 0. Similr to the cse from bove, simple pproimtion to the bove eqution is { [ W Ĝ d i 0 R } 0 0d R i iĝ d i 0 d i, 15 where we used Eq. 7 for substitution. A correltion-bsed pproimte solution to this eqution is closely relted to the method by Polinnikov 2011, whose derivtion is bsed on SRI, but we solve it here by inversion insted. We see now tht becuse of the substitution of Eq. 7, solving Eq. 15 either by MDD or by CC results in some spurious events in the retrieved R i i, nd those spurious events relted to the upgoing internl multiples cn be removed by using Eq. 14. However, when the internl multiples re not strong, Eq. 15 offers simple but sufficient lterntive. Net, we show some synthetic results. SYNTHETIC EXAMPLE We illustrte the schemes using synthetic coustic model. The model is 5 by 5.5 km with grid smpling of 2.5 m, shown in Fig. 1. Both the borehole dt nd the surfce dt re modeled using finite difference method Thorbecke nd Drgnov, 2011 without free surfce. The borehole dt hve 201 sources t the surfce nd 81 receivers t.7 km depth. The surfce dt hve 201 sources nd receivers t the surfce. To imge from bove, four schemes Eq. 9, 11, 10 nd 12 re tested, nd the retrieved virtul reflection responses in red re compred with the reference response in blue in Fig. 2. The reference response is modeled with homogeneous overburden. The reference source position is 1 = 2500, = 700 indicted by the green dot in Fig. 1, nd the receiver positions re from 1 = 1500 to 1 = 500 t the sme depth. For the first scheme Eq. 9, only the borehole dt re used; for the second scheme Eq. 11, the surfce reflection responses re used to redtum the direct rrivls from the borehole dt; for the third schemeeq. 10, the input is the sme s for the second scheme, but n itertive Mrchenko method Wpenr et l., 2014 is used to find the focusing functions, where the trveltime nd the initil focusing functions time-gted direct rrivls re tken directly from the borehole dt; for the fourth scheme Eq. 12, scheme one nd two re joined nd the focusing functions re not computed. Fig. 4 shows the corresponding migrted imges. By compring the trces in Fig. 2, it is observed tht pnel hs the most spurious events, but minly for the lter rrivls ll events fter 1 s re dded n etr sclr gin, wheres these downgoing events re lmost completely removed in pnel c. This is becuse the up-down wvefields re properly decomposed by the focusing functions. If the correct focusing functions re difficult to find, one cn use the fourth scheme. This joint scheme could reserve higher propgtion ngles nd lso helps to merge two dtsets with different signl-to-noise rtios. To imge from below, two schemes Eq. 15 nd 14 re tested, nd the retrieved virtul reflection responses in red re compred with the reference response in blue in Fig.. Here the reference response is modeled with homogeneous underburden. An etr sclr gin is dded on ll events fter s. In the trce comprison, one cn see tht the second scheme using the focusing functions results in better mtch in terms of the mplitude nd less spurious events. Nevertheless, the first scheme recovers the min reflectors phse well nd cn be more esily implemented in prctice. To show tht these schemes re prticulrly suitble when there is uncertinty in the velocity model, smooth velocity model is tried for migrtion. The comprison is shown in Fig. 6. In pnel, the imge from bove nd from below re put together to form locl imge. The retrieved responses in Fig. 2 d nd Fig. b re used for these locl imges. By comprison, we see tht the locl imge re much more resilient to velocity uncertinties in the model. Also, it is noticed tht the sme reflector is mpped to different positions in the two imges, so further ppliction of these imging results could be to eploit this sensitivity to velocity errors to form better constrined inversion scheme for velocities. CONCLUSIONS We present severl inversion-bsed schemes for deep locl imging bove nd below horizontl well. The redtuming schemes re completely dt-driven, mening no estimte of direct wvefield or velocity model is needed. For imging, only locl velocity model is needed. The methods etend previous pproches to include surfce dt, nd offer ccurte methods for retrieving the reflection responses tht do not require surrounding source boundries. Furthermore, internl multiples cn be properly ccounted for using single-component borehole dt nd surfce dt. The synthetic emple shows promising results for more robust deep imging in the presence of velocity uncertinties. The etension to include nonhorizontl boreholes, nd surfce relted multiples remins to be studied. ACKNOWLEDGEMENTS The uthors cknowledge the Reserch Council of Norwy, ConocoPhillips, Det norske oljeselskp, Sttoil, Tlismn, TO- TAL nd Wintershll for finncing the work through the reserch centre DrillWell. In ddition, the ROSE consortium t NTNU is cknowledged. We lso thnk Jn Thorbecke t TU Delft for the help on the Mrchenko method.

4 Dt-driven imging bove nd below horizontl well b d 1 c Figure 1: P-wve velocity model nd dtsets geometries. The strs denote sources nd the tringles denote receivers. The green dot indictes the position of the reference shot. b Figure 4: Migrted imges from bove using the retrieved responses from the counterprt in Fig. 2. A true locl velocity model of the trget zone is used. d b c Figure 5: Migrted imges from below using the retrieved responses s shown in Fig.. A true locl velocity model of the imged zone is used. Figure 2: Reflection responses from bove. Trce comprison between the retrieved responses in red nd the reference responses in blue, using Eq. 9, b Eq. 11, c Eq. 10 nd d Eq. 12. The reference source position is 1 = 2500, = 700, nd the receivers re t the sme depth s the source. 1 1 b Figure : Reflection responses from below. Trce comprison between the retrieved responses red nd the reference responses blue, using Eq. 15, b Eq. 14. The reference source position is 1 = 2500, = 700, nd the receivers re t the sme depth s the source. Figure 6: Migrtion imges with smooth velocity model. The bckground indictes the true model. Locl imge using the retrieved reflectivity s in Fig. 2 d nd b. The polrity of the imge from below is chnged to be consistent with the surfce imge. b Stndrd seismic imge, obtined from dt t the surfce.

5 Dt-driven imging bove nd below horizontl well REFERENCES Bkulin, A., nd R. Clvert, 2006, The virtul source method: Theory nd cse study: Geophysics, 71, SI19 SI150. Broggini, F., R. Snieder, nd K. Wpenr, 2012, Focusing the wvefield inside n unknown 1d medium: Beyond seismic interferometry: Geophysics, 77, A25 A28. Curtis, A., P. Gerstoft, H. Sto, R. Snieder, nd K. Wpenr, 2006, Seismic interferometry - turning noise into signl: The Leding Edge, 25, Curtis, A., nd D. Hllidy, 2010, Source-receiver wve field interferometry: Phys. Rev. E, 81, no. 4, Gletti, E., nd A. Curtis, 2012, Generlised receiver functions nd seismic interferometry: Tectonophysics, 5255, Meht, K., A. Bkulin, J. Sheimn, R. Clvert, nd R. Snieder, 2007, Improving the virtul source method by wvefield seprtion: Geophysics, 72, V79 V86. Nkt, N., R. Snieder, T. Tsuji, K. Lrner, nd T. Mtsuok, 2011, Sher wve imging from trffic noise using seismic interferometry by cross-coherence: GEOPHYSICS, 76, SA97 SA106. Poletto, F., P. Corubolo, nd P. Comelli, 2010, Drill-bit seismic interferometry with nd without pilot signls: Geophysicl Prospecting, 58, Polinnikov, O., 2011, Retrieving reflections by sourcereceiver wvefield interferometry: Geophysics, 76, SA1 SA8. Schuster, G., J. Yu, J. Sheng, nd J. Rickett, 2004, Interferometric/dylight seismic imging: Geophysicl Journl Interntionl, 157, Snieder, R., 2004, Etrcting the green s function from the correltion of cod wves: A derivtion bsed on sttionry phse: Phys. Rev. E, 69, no. 4, Snieder, R., M. Miyzw, E. Slob, I. Vsconcelos, nd K. Wpenr, 2009, A comprison of strtegies for seismic interferometry: Surveys in Geophysics, 0, Thorbecke, J., nd D. Drgnov, 2011, Finite-difference modeling eperiments for seismic interferometry: Geophysics, 76, H1 H18. vn der Neut, J., J. Thorbecke, K. Meht, E. Slob, nd K. Wpenr, 2011, Controlled-source interferometric redtuming by crosscorreltion nd multidimensionl deconvolution in elstic medi: Geophysics, 76, SA6 SA76. vn der Neut, J., nd K. Wpenr, 2015, Point-spred functions for interferometric imging: Geophysicl Prospecting. Vsconcelos, I., nd R. Snieder, 2008, Interferometry by deconvolution: Prt 1 - Theory for coustic wves nd numericl emples: Geophysics, 7, S115 S128., 2008b, Interferometry by deconvolution: Prt 2 - Theory for elstic wves nd ppliction to drill-bit seismic imging: Geophysics, 7, S129 S141. Wpenr, K., F. Broggini, E. Slob, nd R. Snieder, 201, Three-dimensionl single-sided Mrchenko inverse scttering, dt-driven focusing, Green s function retrievl, nd their mutul reltions: Physicl Review Letters, 110, Wpenr, K., nd J. Fokkem, 2006, Green s function representtions for seismic interferometry: Geophysics, 71, SI SI46. Wpenr, K., J. Thorbecke, J. vn der Neut, F. Broggini, E. Slob, nd R. Snieder, 2014, Mrchenko imging: Geophysics, 79, WA9 WA57. Wpenr, K., nd J. vn der Neut, 2010, A representtion for Green s function retrievl by multidimensionl deconvolution: The Journl of the Acousticl Society of Americ, 128, EL66 EL71. Wpenr, K., J. vn der Neut, E. Ruigrok, D. Drgnov, J. Hunziker, E. Slob, J. Thorbecke, nd R. Snieder, 2011, Seismic interferometry by crosscorreltion nd by multidimensionl deconvolution: systemtic comprison: Geophysicl Journl Interntionl, 185,