We P5 09 Q Estimation Using an Improved Frequency Shift Method

Transcription

1 1-4 June 15 IFEMA Madrid We P5 9 Estiation Using an Iproved Frequeny Shit Method F. Li (University o Oklahoa), K. Marurt (University o Oklahoa), H. Zhou (Chengdu University o Tehnology) & Y. Chen* (University o Texas) SUMMARY This paper proposes an iproved requeny shit ethod to estiate the quality ator or hydroarbon detetion. As a powerully diagnosti tool or strutural interpretation, reservoir haraterization and hydroarbon detetion, quality ator provides useul inoration in seisi proessing and interpretation. The popular ethods, like spetral ratio (SR) ethod, entral requeny shit (CFS) ethod, peak requeny shit (PFS) ethod, have their respetive liitations in ield seisi data appliation. In this paper, we derive an approxiate equation and propose an iproved entral requeny shit (ICFS) ethod by obining the quality ator, the travel tie, doinant and entral requenies o two suessive seisi signals, along the wave propagating diretion. Tests on syntheti data and statistial experients show the proposed ethod an ahieve higher auray and robustness opared with existing ethods. Appliation o ield data also shows its potential and eetiveness to estiate seisi attenuation. 77 th EAGE Conerene & Exhibition 15 IFEMA Madrid, Spain, 1-4 June 15

2 Introdution 1-4 June 15 IFEMA Madrid Seisi attenuation is a undaental ehanis o elasti waves propagating through the earth. The quantiied attenuation attribute an provide iportant inoration about the subsurae to ailitate seisi interpretation (Parra and Hakert, ). uality () ator is usually used to easured seisi attenuation. Riker (1953) pioneered a wavelet broadening tehnique to deterine attenuation. Nowadays, requeny-based ethods are oon in exploration geophysis beause o their reliability and ease o use, whih inlude the spetral ratio (SR) (White, 199), entral requeny shit (CFS) (uan and Harris, 1997), peak requeny shit (PFS) (Zhang and Ulryh, ), iproved peak requeny shit (IPFS) (Hu et al., 13), and Gabor- Morlet joint tie requeny analysis (JTFA) (Singleton et al., 6) ethods. The ost lassi approah is SR ethod, whih easures the log o the ratio between two aplitude spetra oputed as untion o requeny. But, SR ethod would be easily aeted by noise. While as opposed to SR ethod, the requeny-shit ethods, suh as CFS and PFS ethods, just use the variations o the spetra rather than the entire aplitude spetru, whih iproves the auray o the estiation. In this paper, obining CFS approah and pratial Riker spetru preondition, we derive an iproved ethod to estiate. The hypothesis o the proposed ethod satisies the basi harateristis o seisi signal, whih provides the basis o reasonable auray and robustness. Finally, we alibrate the proposed ethod or both syntheti and ield seisi data. Central Frequeny Shit Method For requeny independent intrinsi in the bandwidth o interest, a seisi signal will have its spetral aplitude A( ) odiied to A( 1 ) ater traveling tie t at requeny : A( 1 ) A( ) e, (1) where the aplitude deay or inrease aused by requeny-independent eets is ignored. CFS ethod orrelates with the hanges in the entral requeny o the seisi signal. For the reerene seisi signal A and the target seisi signal A 1, their entral requenies denoted by and 1, assuing that A ( ) is o Gaussian shape, an be quantiied by, t A, ( ) A ( ) d A () A ( ) d 1 where A is the spetru variane o A. We notie that the preonditions o CFS ethod are the Gaussian shape o the seisi spetru and the unhanged spetru variane. However, the seisi spetru is usually a non-gaussian distribution and the attenuation would ertainly hange the spetru variane. Iproved Central Frequeny Shit Method In order to better satisy ield situations, we evaluate the aplitude spetru variane by CFS approah odeled as a Riker wavelet traveling. Cobining Equation (1) and Riker wavelet deinition, we an get the aplitude spetru o the reeived signal as t A(, t) e e, (3) 3 where denotes the doinant requeny o the soure wavelet. Thus, the entral requeny o the reeived seisi aplitude spetru A(, t ) is expressed as, 3 t t A(, t) d e e d e e d. (4) 3 3 A(, t) d t 77 th EAGE Conerene & Exhibition 15 IFEMA Madrid, Spain, 1-4 June 15

3 1-4 June 15 IFEMA Madrid Ater sipliying, separating the ators and oputing the integrals, we an get an approxiate relationship as ollows 3 t t t (5) t t 1 + As our goal is to estiate ator, we derivate equation (5) to an equation about unknown paraeter. Beause that equation is a ubi equation in one variable, we an only get an approxiate solution, 1.3 t. (6) The relationship between the entral requeny, doinant requeny and ator has been established by now. Thus, we an obtain the quality ator estiation. It is an iproved CFS ethod, as we substitute Gaussian spetru to non-gaussian spetru o Riker wavelet, whih is ore oinident with the atual situation as wave propagates under the survey. In addition, we get rid o the variane estiation o the reerene spetru, whih akes alulation ore straight orward and ree ro the inauray ro ignorane o the shape dierene between reerene and reeived spetra. Figure 1 Coparison between the proposed ICFS ethod and SR, CFS ethods. (a) A noise-ree syntheti generated by a 4 Hz Riker wavelet with values o 8, 5, 4 and 3. (), (e) and (g) show syntheti traes with SNR=1,, and -1 db rando noise, respetively. (b), (d), () and (h) show the orresponding the results o estiation using SR, CFS and ICFS ethods. Note that the results applied by ICFS ethod are loser to the true values even with dereasing o SNRs. Syntheti Tests In order to hek the eetiveness and stability o our proposed iproved CFS(ICFS) ethod, we estiate values on both noise-ree and noisy syntheti data and analyze the results alulated by SR, CFS and ICFS ethods. We use a Riker wavelet with a 4 Hz doinant requeny to produe a noise-ree syntheti with values 8, 5, 4 and 3 shown in Figure 1(a). The ost diiult proble 77 th EAGE Conerene & Exhibition 15 IFEMA Madrid, Spain, 1-4 June 15

4 1-4 June 15 IFEMA Madrid is the stability in evaluating ator when the data is ontainated by noise. Thereore, we also reate syntheti traes added by dierent noise levels with SNR=1,, and -1 db shown in Figure 1(), 1(e) and 1(g). We an observe ro the results that there are notieable dierenes between three ethods. For SR ethod, auray and stability o estiation highly depends on the SNR o original data. When SNR is below 1 db, ICFS ethod perors ore robustly, and the results alulated by ICFS are loser to the true values than those o the other two ethods. In addition, For the attenuated layer with real value 3, we arry out 1 independent experients in dierent situation o SNR=1, and -1dB. The statistial analysis shown in Table 1 deonstrates that the ean value applied by ICFS is loser to the atual value, and the standard deviations have no obviously large lutuation even when noise level is greater than the signal (SNR=-1 db), whereas the anoaly large values o standard deviation using SR and CFS ethod iply that these two ethods have less robustness under the situation o low SNR opared to our proposed ethod. SNR(dB) SR CFS ICFS Mean SD Mean SD Mean SD Table 1 Statistial data alulated by 1 experients using SR, CFS and ICFS ethods. The atual value is 3. SD denotes the standard deviation. Field Data Appliation We applied ICFS ethod to a 3D land survey aquired in Western China, showing its value in deteting gas reservoir. Figure (a) shows a vertial seisi slie rossing three wells, wherein the wells A and B are produtive, while the well C is nonprodutive. Figure (b) shows the gas reservoir distribution, lithology and well logs (e.g. GR, RT, AC and DEN), in whih the sandstone ull o gas is painted yellow under the layer L at Well A and B, but there is no oil-gas response at well C loation. Fro estiation results in Figure 3(a) alulated by ICFS, the low values o the target layer at the loation o produtive wells A and B are highlighted by red olor, whih iplies strong absorption or attenuation in the gas-bearing sandstone, and there is no suh harateristi at the nonprodutive well C. In Figure 3(b), the estiation urves o layer L (denoted by the red urve in Figure 3(a)) deonstrate that the ost reasonable result is ro ICFS (red-dashed urve), beause the proposed ethod urve suessully distinguishes produtive Well B and dry-hole Well C, while SR (blue urve) and CFS (green urve) do not show obvious value dierene between Well B and C. Thereore, the reasonable value urve ro ICFS learly haraterizes oil/gas reservoirs by low values and nonprodutive reservoirs by high values. Conlusions This paper proposes a novel ethod or estiation based on the assuption o the non-gaussian aplitude spetru o Riker wavelet, wherein a siply eetive approxiate equation is built between doinant requeny and entroid requeny. It not only overoes the shortage o SR ethod highly depending on the SNR o seisi data, but iproves the robustness and auray opared to CFS ethod. Syntheti and ield exaples alibrate the eetiveness o the proposed ethod, and also onir the results alulated by ICFS are reliable and provide useul guides in the hydroarbon detetion and reservoir haraterization. Aknowledgents This work is inanially supported by the National Natural Siene Foundation o China (Grant No ), and Siene and Tehnology Support Progra (Grant No. 11GZ44) ro Siene and Tehnology Departent o Sihuan Provine o China. We also thank Puguang Branh o Zhongyuan Oilield o SINOPEC or providing the ield data. The last author (orresponding author) appreiates the Chinese Sholarship Counil or inanial support. 77 th EAGE Conerene & Exhibition 15 IFEMA Madrid, Spain, 1-4 June 15

5 1-4 June 15 IFEMA Madrid Figure (a) Vertial proile o seisi aplitude data that ross three joint wells. (b)the gas reservoir distribution, lithology and well logs (e.g. GR, RT, AC and DEN) through three joint wells. The red ovals denote the oparing zones under target layer L. Figure 3 (a) The estiation proile obtained by ICFS ethod. (b) Average value urves alulated by SR, CFS and ICFS ethods or target layer L within s downward tie window. Reerenes Hu, C.H., Tu, N. and Lu, W.K. [13] Seisi attenuation estiation using an iproved requeny shit ethod. IEEE Geosiene and Reote Sensing Letters, 1(5), Parra, J.O. and Hakert, C.L. [] Wave attenuation attributes as low unit indiators. The Leading Edge, 1, uan, Y. and Harris, J.M. [1997] Seisi attenuation toography using the requeny shit ethod. Geophysis, 6, Riker, N. [1953] The or and laws o propagation o seisi wavelets. Geophysis, 18, 1-4. Singleton, S., Taner, M.T. and Treitel, S. [6] estiation using Gabor-Morlet joint tie-requeny analysis tehniques. SEG Extended Abstrats, 5, White, R.E. [199] The auray o estiating ro seisi data. Geophysis, 57, Zhang, C.J. and Ulryh, T.J. [] Estiation o quality ators ro CMP reords. Geophysis, 67, th EAGE Conerene & Exhibition 15 IFEMA Madrid, Spain, 1-4 June 15