Experiments on elastic wave modelling in isotropic and anisotropic media

Transcription

1 Exeriment on elatic wave modelling in iotroic and aniotroic media Fan Jiang, Yiqing Ren, and Shengwen Jin, Halliburton Landmark Software & Service Summary Recent advance in eimic data roceing with multi-comonent land and ocean-bottomnode (OBN) data have hown ome contribution from hare wave, converted wave a well a aniotroy. To get better undertanding of the elatic wave roagation in iotroic and aniotroic media, we comared the wavefield in acoutic and elatic media with and without aniotroy. The reliminary exeriment on three ynthetic model, i.e., wave/olid interface, free urface with toograhy, and near-urface low velocity layer, demontrate the comlicated wave roagation in elatic media. Introduction Recent advance in eimic data roceing with multi-comonent land and ocean-bottom-node (OBN) data have hown ome contribution from hare wave, converted wave a well a aniotroy. Proer treatment on elatic wave can avoid miinterretation of hear wave and converted wave a artifact and rovide comlimentary information over acoutic wave. It i crucially imortant to undertand and exloit elatic wave roagation in comlex media. Finite-difference cheme ha been conidered a the mot oular imlementation to model the wave roagation in elatic media. Kelly et al. (1976) decribed a imle finite-difference aroximation to the elatic wave equation to model P- and SV-wave in iotroic homogeneou media. Virieux (1986) rooed an aroach that udate tre and article velocity on a taggered grid that overcome the accuracy and tability roblem of the non-centered tandard finite-difference aroximation for P-SV wave equation. Koloff et al. (1984) introduced a eudo-ectral method to olve the iotroic elatic wave equation. Tranformation of the atial derivative into wavenumber domain by Fourier tranform rovide more accurate imulation than finite-difference. However, the eudo-ectral method require much more memory and i more comutationally exenive in 3D aniotroic elatic media. Free urface with toograhy, hear wave trilication, and water/olid interface are among the major iue of elatic wave modeling in iotroic and aniotroic media. Levander (1988) rooed an image method for free urface calculation in the velocity-tre taggered-grid finite-difference method. An alternative method i called vacuum formulation rooed by Boore (1972). Thi method aume P- and S-wave velocitie to zero but kee contant denity above the free urface. The vacuum method i eay to imlement with the ame finite difference equation ued for the interior model (Hayahi et al., 2001). Shear wave trilication are commonly oberved in crut. In aniotroic media, elatic wave modeling how the nature of hear wave trilication (Thomen and Dellinger, 2003). In exloration eimology, hear wave trilication are uually treated a artifact and need to be ecially handled in re-tack deth migration. In thi aer, everal exeriment on the elatic wave modeling in iotroic and aniotroic media demontrate the effect of wave roagation with the water/olid interface for marine data, in the reence of toograhic free urface and the low velocity layer near urface for land data. The different wave tye will alo be addreed and dicued. Numerical examle In the following examle, a higher-order taggered grid finite-difference cheme i imlemented for the imulation of wave roagation. 73 rd EAGE Conference & Exhibition incororating SPE EUROPEC 2011 Vienna, Autria, May 2011

2 Deth (km) Deth (km) Deth (km) Exeriment I: Wave roagation with a ingle diing interface between water and olid Aume the firt layer i water with velocity of 1500m/ and the econd layer i a olid with P-wave velocity of 3000m/ and S-wave velocity of 1732 m/. TTI arameter in the olid are aigned a ε=0.23, δ=0.12, and the di angle i 20. The ource i located in the center at urface. To correctly imulate the wave roagation in liquid, hear module need to et a zero if the finite-difference grid i located at liquid and olid boundary. Figure 1, and are the nahot in iotroic, VTI and TTI acoutic media. Figure 1(d), (e) and (f) are the nahot of the vertical article velocity in iotroic, VTI and TTI elatic media. Figure 1(g), (h) and (i) are the nahot for the horizontal article velocity in iotroic, VTI and TTI elatic media. The nahot of acoutic and elatic wave how identical P-wave wavefront in water layer. A exected, S-wave are reent in the elatic olid layer. In aniotroic TTI media, the wavefront i tilted by the TTI di angle. We alo notice that the S-wave i generally tronger on the horizontal comonent than that of the vertical comonent. (d) (e) (f) (g) (h) Figure 1: Comarion of the nahot with a ingle interface between water and olid layer., and are nahot in iotroic, VTI, and TTI acoutic media; (d), (e) and (f) are nahot of the vertical comonent in iotroic, VTI and TTI elatic media; (g), (h) and (i) are nahot of the horizontal comonent in iotroic, VTI and TTI elatic media. (i) 73 rd EAGE Conference & Exhibition incororating SPE EUROPEC 2011 Vienna, Autria, May 2011

3 Deth (km) Deth (km) Exeriment II: Wave roagation with a toograhic free urface (d) Figure 2: Comarion of the nahot with the reence of toograhic free urface. Toograhic free urface model;, and (d) are nahot in iotroic, VTI and TTI elatic media. In thi model, V=2000m/,V=1000m/, ε=0.2, δ=-0.1. TTI di angle i 30 in (d). Toograhic free urface can make wave roagation more comlicated eecially for land data. To tet the effect of free urface with toograhy, we generate a half urface model with contant aniotroic elatic arameter. In the model, P- and S-wave velocitie are 2000m/ and 1000m/, reectively. ε=0.2 and δ=-0.1. The TTI tilted di angle i 30. An exloive ource i hown in Figure 2. A vacuum method i alied to addre the variation of toograhy. In Figure 2, and (d) are the nahot of the vertical comonent in iotroic, VTI and TTI elatic media. The converted wave S to P and P to S are generated by free urface. In aniotroic elatic media, S-wave trilication exit after S-wave are reflected from the free urface. Exeriment III: Modified 3D SEG overthrut model with near-urface low velocity layer To imulate the near-urface wave roagation, a 3D SEG overthrut model wa modified by adding a low velocity layer with random denity variation on to of the model a hown in Figure 3. The P- wave velocity in the layer i 1229m/. S-wave velocity wa et a half of the P-wave velocity. The near-urface low velocity layer diturb the wave roagation and generate comlicated wave mode uch a Rayleigh wave. The (x,y) grid acing i 25m by 25m. The deth interval i 12.5m. Ricker wavelet with dominant frequency of 12.5Hz wa ued in the numerical imulation. Figure 4, and are the nahot of acoutic wave, vertical comonent of elatic wave, and horizontal comonent of elatic wave. The wave mode on the elatic horizontal comonent are very different from the elatic vertical comonent. Figure 4(d), (e) and (f) are the correonding hot gather of acoutic wave, vertical comonent of elatic wave and horizontal comonent of elatic wave. Due to a near-urface low velocity layer, Rayleigh wave ha trong dierion near urface a hown in Figure 4(e) and (f). The amlitude of Rayleigh wave decreae exonentially with the increaing roagation time. 73 rd EAGE Conference & Exhibition incororating SPE EUROPEC 2011 Vienna, Autria, May 2011

4 Deth (km) Figure 3: A modified 3D SEG overthrut model with a near-urface low velocity layer with random denity variation. Velocity model of the 3D SEG overthrut model; A cro ection with random denity variation in the low velocity layer. (Courtey of Chritof Stork). Concluion Wave roagation in elatic media generate more wave mode than that in acoutic media. The wavefront of P- and S-wave in TTI media are tilted by the TTI di angle. S-wave trilication are reent on the modeling reult in aniotroic elatic media. Free urface reflection make the wave roagation more comlicated. Near-urface low velocity layer generate Rayleigh wave with trong dierion. Acknowledgement We would like to thank Chritof Stork for the helful dicuion and comment on the elatic wave modelling. 73 rd EAGE Conference & Exhibition incororating SPE EUROPEC 2011 Vienna, Autria, May 2011

5 Deth (km) Time () (d) (e) (f) Figure 4: Comarion of acoutic and elatic wavefield in a modified 3D overthrut model with a near-urface low velocity layer., and are nahot for acoutic wave, vertical and horizontal comonent of elatic wave; (d), (e) and (f) are hot gather for acoutic wave, vertical and horizontal comonent of elatic wave. Reference Boore, D. M., 1972, Finite difference method for eimic wave roagation in heterogeneou material, in Method in Comutational Phyic, B.A. Bolt, Academic, New York, Vol. 11. Hayahi, K., D. R., Burn, and M. N. Tokoz, 2001, Dicountinuou-grid finite difference eimic modeling including urface toograhy: Bull. Sei. Soc. Am., 91, Kelly, K.R., R.W. Ward, S., Treitel, and R.M. Alford, 1976, Synthetic eimogram: a finite difference aroach: Geohyic, 41, Koloff, D., M., Rehef, and D., Loewenthal, 1984, Elatic wave calculation by the Fourier method: Bull. Sei. Soc. Am., 74, Levander, A. R., 1988, Fourth-order finite-difference P-SV eimogram: Geohyic, Thomen, L., and J., Dellinger, 2003, On hear-wave trilication in tranverely iotroic media: Journal of Alied Geohyic, 54, Virieux, J., 1986, P-SV wave roagation in heterogeneou media: Velocity-tre finite-difference method: Geohyic, 51, rd EAGE Conference & Exhibition incororating SPE EUROPEC 2011 Vienna, Autria, May 2011