Patrick Boston (Leeds University) and Mark Chapman (Edinburgh University)

Transcription

1 Iversio o requecy-depedet AVO data or luid properties Patric Bosto (Leeds Uiversity) ad Mar Chapma (Ediburgh Uiversity) Summary A umber o methods to estimate the requecy-depedece o relectivity have bee published recetly. Applicatio to ield data has show promise, but the iormatio cotet o the images is poorly uderstood ad o meas to quatitatively iterpret the results is available. We preset a method to quatitatively ivert requecy-depedet relectivity or luid properties. The method is model depedet, ad relies o good owledge o the relatioship betwee dispersio ad roc ad luid properties. Specializig the method to the case o gas-water mixtures, we show the potetial to estimate ractioal gas saturatio rom requecy-depedet AVO data. 74 th EAGE Coerece & Exhibitio icorporatig SPE EUROPEC 202

2 Itroductio Laboratory measuremets o the requecy-depedece o velocities (Batzle et al. 2006) demostrate that dispersio is related to luid saturatio. This suggests that velocity dispersio may be a useul tool or seismic luid characterizatio, but uortuately direct estimates o dispersio are diicult to obtai. Oe promisig strategy is based o attemptig to estimate the requecy-depedece o the relectio coeiciet (Chapma et al. 2005; Re, 2009; Iae, 2009). Wu (200), Zhag (20) ad Xu (20) produced images o the requecy-depedece o relectivity, ad oted correlatios with roc properties o iterest. Although the techique is clearly promisig, the iormatio cotet o the images is still poorly uderstood ad o method or quatitatively iterpretig the results is available. I this paper we preset a ew method or ierrig roc ad luid properties rom requecydepedet AVO data. We use a roc physics model to apply the method to the case o gaswater mixtures, where the gas saturatio is allowed to vary. The method allows us to derive attributes which measure both the low requecy relectivity ad the requecy-depedece o relectivity. We derive a roc physics template which suggests that crossplottig these attributes may allow us to separate the cases o low gas saturatio, ull water saturatio ad ull gas saturatio. This has proved problematic i the past with traditioal, requecyidepedet, AVO aalysis. Method Stadard AVO iterpretatio relies o associatig a measured seismic amplitude with the plae wave relectio coeiciet. Wilso et al. (2009) exteded this aalysis to the case where velocity dispersio was preset ad relectivity was requecy-depedet. His method ivolved the spectral decompositio ad balacig o pre-stac seismic data ad the applicatio o a liearized equatio relatig the relectio coeiciet to agle o icidece ad requecy. He showed how to ivert the pre-stac data to obtai a estimate o dispersio properties. The method produces images o requecy-depedece o relectivity which ote correlate with luid properties (Wu, 200). Clearly, it would be advatageous to be able to quatitatively relate such images to roc properties o iterest. I this paper we cosider relectios rom the iterace betwee a layer havig requecyidepedet properties ad a layer whose properties are requecy-depedet. This is to simulate the case o relectio rom the top o a reservoir which exhibits strog luid-related dispersio. Our attetio is ocussed o a particular roc property o iterest X, ad we cosider p dieret values o this property. We assume that we ow velocity ad atteuatio as a uctio o requecy i the dispersive layer, either rom use o a appropriate roc physics model or through direct measuremet i the laboratory, i which case we may calculate the relectio coeiciet as a uctio o requecy ad oset by stadard meas. Cosiderig m agles o icidece θ, requecies ad p roc properties we arrage our computed relectio coeiciets i a matrix R o the ollowig orm: 74 th EAGE Coerece & Exhibitio icorporatig SPE EUROPEC 202

3 Followig the method o Causse et al. (2007), we perorm spectral decompositio o the matrix R, allowig us to approximate the relectio coeiciets as a series o weights, C, which are a uctio o roc properties ad requecy,ad basis uctios h which are a uctio o agle o icidece: The depedece o the weight uctios C o requecy ca ote be approximated by a liear relatioship, which allows us to carry out itercept-gradiet aalysis or the requecydepedece. I such a aalysis, the itercept will give the low requecy limit o relectivity, which should correspod to that predicted by the Gassma equatio, while the gradiet will give a measure o the requecy-depedece o relectivity. Examples R L R R L R L R L R Rθ R R R R R 2 θ 2 M M M M M M Rθ L R R L R L R L R m X... X 2... X p RX l ( θ ) C( j, X ) h ( θ ) + L+ Ci ( j, X ) hi ( θ ) We apply this method to the model cosidered by Rutherord ad Williams (989), where we itroduce dispersio ito the lower layer ollowig the techique itroduced by Chapma et al. (2006). The lower layer is cosidered to be saturated with a mixture o gas ad water, modelled as a eective luid. I such a case, it is predicted that strog dispersio ad atteuatio occurs or small values amouts o gas, with a pea value typically aroud 0% saturatio, while smaller values o atteuatio are see or the cases o ull saturatio with either water or gas. A example o the atteuatio versus gas saturatio relatio is show i Figure. Similar behaviour has bee see may times i the laboratory. Figure : Predicted values o atteuatio versus gas saturatio or the modelig. Correspodig to this Figure, we ca calculate relectio coeiciets or each value o the saturatio as a uctio o both agle o icidece ad requecy. Figure 2 shows a example o such curves. Whe we have little dispersio, the relectio coeiciets or dieret requecies overlie each other, but whe we have larger dispersio the curves are clearly separated. 74 th EAGE Coerece & Exhibitio icorporatig SPE EUROPEC 202

4 Figure 2: Relectio coeiciets as a uctio o agle o icidece or various requecies i the cases o ull gas, partial gas ad ull water saturatio. Costructig our relectio matrix ad ollowig the method described above, we id that the relectio coeiciets ca be described accurately usig oly oe basis uctio ad weight. Additioally, the variatio o the weights with requecy or each saturatio is approximately liear, allowig us to associate each saturatio with a gradiet ad itercept. Crossplottig these attributes results i Figure 3. Full gas saturatio, partial gas saturatio ad ull water saturatio are clearly separated i this crossplot. Coclusios This paper has preseted a method which i priciple ca estimate ractioal gas saturatio rom seismic data. The method is model depedet, ad relies o a good owledge o the li betwee luid saturatio ad dispersio properties. The procedure urther assumes that it is possible to estimate the requecy-depedece o the relectio coeiciet rom seismic data through the applicatio o spectral decompositio procedures. We show how to estimate both a low-requecy (or Gassma) relectivity as well as a attribute which measures the requecy-depedece o relectivity. Aalysis o a typical example reveals that crossplottig these attributes is able to separate three cases o iterest- ull gas saturatio, low gas saturatio ad ull water saturatio- whereas this was ot possible usig traditioal AVO methods. Future wor will ivolve testig this method o ield data. Reereces Batzle, M., Ha, D-H. ad Homa, R., Fluid mobility ad requecy-depedet seismic velocity Direct measuremets. Geophysics v. 7, o., pn-n9. 74 th EAGE Coerece & Exhibitio icorporatig SPE EUROPEC 202

5 Causse, E., Riede, M., va Wijgaarde, A.J., Bulad, A., Dutzer, J.F. ad Fillo, R., Amplitude aalysis with a optimal model-based liear AVO approximatio: Part I Theory. Geophysics, v. 72, o. 3, p C59-C69. Chapma, M, Liu, E. ad Li, X-Y, The iluece o abormally high reservoir atteuatio o the AVO sigature. The Leadig Edge, v. 24, o., p Chapma, M. Liu, E. ad Li, X-Y, Iae, K, Iversio o the seismic AVF/AVA sigatures o highly atteuative targets. Geophysics, v. 76, o., R-R4. Re, H.,., G. ad Hilterma, F.J., Poroelastic aalysis o amplitude-versus-requecy variatios. Geophysics, v. 74, o. 6, p N4-N48. Rutherord, S. ad Williams, P., 989. Amplitude-versus-oset variatio i gas sads. Geophyiscs, 54, Xu, D., Wag, Y-H, Ga, Q. et al., 20. Frequecy-depedet seismic relectio coeiciet or discrimiatig gas reservoirs. Joural o Geophysics ad Egieerig, v. 8, p Wilso, A., Chapma, M. ad Li, X-Y., Frequecy-depedet AVO iversio. 79 th SEG Aual Meetig, Expaded Abstracts. Wu, X-Y., Wilso, A., Chapma, M. ad Li, X-Y Frequecy depedet AVO iversio usig smoothed pseudo Wiger-Ville distributios. 72 d EAGE Coerece Barceloa Expaded Abstracts. Zhag, S, Yi, X-Y ad Zhag, G-Z, 20. Dispersio-depedet attribute ad applicatio i hydrocarbo detectio. Joural o Geophysics ad Egieerig, v. 8, 498. Figure 3: Crossplot o low-requecy-relectivity agaist requecydepedece o relectivity. 74 th EAGE Coerece & Exhibitio icorporatig SPE EUROPEC 202