A027 Uncertainties in Local Anisotropy Estimation from Multi-offset VSP Data

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1 A07 Uncertinties in Locl Anisotropy Estimtion from Multi-offset VSP Dt M. Asghrzdeh* (Curtin University), A. Bon (Curtin University), R. Pevzner (Curtin University), M. Urosevic (Curtin University) & B. Gurevich (Curtin University) SUMMARY We hve untified the errors ssocited with VTI prmeter estimtion using multi-offset VSP dt. Two common methods, P-wve slownesses only nd slowness-polriztion re investigted. Estimtion errors re expressed in terms of the mgnitude of the erth nisotropy, uncertinties relted to first brek pickings nd mximum vilble source offset. For homogeneous overburden, P-wve slownesses techniue cn be used to estimte VTI prmeters. We demonstrte tht estimtion errors of using only P-wve slownesses re significntly decresed s longer source offsets re included in the inversion lgorithm. Lrger offsets involve P-wves which propgte ner horizontl t the receiver level nd enhnce the method's efficiency. An exmple synthetic VSP is presented next where P-wve slownesses techniue successfully recovers VTI model prmeters. In cse of heterogeneous overburden, P-wve slowness-polriztion techniue seems to be solution s there is no need to compute P-wve horizontl slownesses. However, we demonstrte tht the errors of VTI prmeter estimtion using this techniue re smll only where the nisotropy is very wek (below 5%) nd they re not improved by incresing the offset. Furthermore, wve interference effect on polriztions mkes the method imprcticl even on noise free synthetic dt. 7 th EAGE Conference & Exhibition incorporting SPE EUROPEC 01 Copenhgen, Denmrk, -7 June 01

2 Introduction We estimte VTI prmeters from multi-offset VSP dt. We use two methods: P-wve slowness techniue, nd P-wve slowness - polriztion techniue. The ccurcy of the methods is dependent on vilbility of dt from lrge offsets (this trnsltes to higher ngles of wve propgtion t the receiver loction), errors in estimting slownesses nd polriztions (P-wve s first rrivl picking nd wve interferences effect on polriztions), nd mgnitude of the nisotropy itself. The im of this pper is to clrify the influence of ech of these fctors on the ccurcy of the nisotropy estimtion. VTI prmeter estimtion - P-wve slownesses techniue Miller nd Spencer (199) derived phse dispersion reltion for P or SV wves from Kelvin- Christoffel eution in terms of the horizontl slowness ( p = px ), the verticl slowness ( = pz ) nd four of the five density normlized elstic coefficients of the VTI medium,, 1, nd : A = p + ( + ( 1 + A ) p + ) + ( ) + 1 = 0 (1) Where n independent mesurement of density exists, dispersion reltion cn be inverted for given set of slownesses to estimte the elstic stiffnesses of the VTI medium nd hence VTI nisotropy prmeters δ nd ε s defined by Thomsen (1986). To untify the errors of P-wve slownesses techniue, we generted synthetic slownesses of P-wve using Kelvin-Christoffel eution over rnge of nisotropy vlues common in sedimentry bsins (Tsvnkin, 001). Since mesurements re lwys erroneous, we dd 1% error to the slowness vector. Then, we use the horizontl nd verticl components of this vector in the inversion lgorithm. To untify the effect of offset rnge, we inspect vrious rnges for mximum P-wve propgtion ngle with verticl xis. The inversion lgorithm uses eution 1 s forwrd model nd minimizes lest sure objective function to estimte the Thomsen (1986) δ nd ε nisotropy prmeters. Figure 1 shows errors in estimting the Thomsen nisotropy prmeters where P-wve phse ngle rnges from -0 o to 0 o in subfigures A, B, nd C; -5 o to 5 o in subfigures D, E, nd F; -80 o to 80 o in subfigures G, H, nd I. A totl number of 100 reliztions is generted nd verged to produce ech grid point on the error mps. Figures 1C, 1F nd 1I show three exmple-reliztions for the model prmetersδ = 0. 1 ndε = t vrious P-wve mximum propgtion ngles. In ll the cses, P-wve verticl velocity, S-wve verticl velocity, medium density nd nisotropy prmeter γ re 000 m / s, 1500 m / s, 000 kg / m nd 0.07, respectively. VTI prmeter estimtion - P-wve slownesses techniue, Synthetic Wlkwy VSP exmple Figure displys the geometry of the erth model where wlkwy VSP survey ws cuired using finite difference wve propgtion lgorithm. The geometry nd lyer properties (tble 1) re tken from the Nylor field, Otwy Bsin in Victori, Austrli. Bsed on the other studies in the Nylor field, constnt VTI nisotropy δ = 0. 1 ndε = is defined for ll the intervls below lyer number. The VSP survey comprises of 01 source positions t every 0 meters intervl on the surfce nd distributed symmetriclly on both sides of the well. 01 three-component receivers re positioned from the surfce down to km depth t every 10 meters. Both verticl nd horizontl components of the wve-field re recorded t ech receiver loction. P-wve verticl slowness,, is clculted in shot domin s the grdient of the recorded P-wve first rrivls. As there is not ny rry of horizontlly positioned receivers in the well, lterl homogeneity ssumption nd Snell s lw (horizontl slowness, p is conserved with depth long ech ry) llow us to estimte p t the surfce nd trnsfer it to the receiver level. Therefore, the estimtes of the horizontl slowness, p, re mde in the receiver domin s the grdient of the recorded P-wve first rrivls. Figure demonstrtes n 7 th EAGE Conference & Exhibition incorporting SPE EUROPEC 01 Copenhgen, Denmrk, -7 June 01

3 exmple of plotting P-wve versus p for the receiver locted t depth 150 m (circles). Eution 1 is then fitted to these dt points (red curve) nd δ nd ε re estimted. Figure shows the results of the inversion over lrge depth intervl of the model. A B C D E F G H I Figure 1 Left nd middle columns re error mps ssocited with the inversion of synthetic P-wve slownesses. Right column, is n exmple of P-wve synthetic slownesses generted t point with δ ndε eul to -0.1 nd 0.08, respectively. VTI prmeter estimtion - P-wve slowness - polriztion techniue Where there is lterl heterogeneity in the overburden, horizontl slowness mesured on the surfce cnnot be trnsferred to the receiver level. Grechk nd Mteev (007) propose n eution for VTI nisotropy prmeter estimtion which reltes P-wve verticl slowness, to the ngle between the P- wve s polriztion vector, ψ nd the verticl xis: ( ψ ) cosψ (1 + δ vsp sin ψ + ηvsp sin ψ ) VP0 () 7 th EAGE Conference & Exhibition incorporting SPE EUROPEC 01 Copenhgen, Denmrk, -7 June 01

Where δ VSP = ( f 0 1) δ, η = ( f VSP 0 1) η, re newly defined nisotropy prmeters for VSP ε δ f 0 = 1 V S 0 V nd η = is Alkhlifh-Tsvnkin (1995) nellipticity coefficient. P0 1+ δ pplictions, ( ) 1.

4 Where δ VSP = ( f 0 1) δ, η = ( f VSP 0 1) η, re newly defined nisotropy prmeters for VSP ε δ f 0 = 1 V S 0 V nd η = is Alkhlifh-Tsvnkin (1995) nellipticity coefficient. P0 1+ δ pplictions, ( ) 1.5 x 10- vs. p vs. p Receiver depth (m) =150 P-wve verticl slowness, (s/m) P-wve horizontl slowness, p(s/m) Figure Geometry of the erth model used to generte synthetic wlkwy VSP. Anisotropy strts from lyer number four nd remins constnt with depth. Figure Verticl component of the slowness vector plotted versus the horizontl component for the receiver locted t the depth 150 m. Vp 0 (m/s) Vs 0 (m/s) ρ (kg/m^) Tble 1 properties of the geologicl model displyed on figure. Anisotropy strts from lyer number nd remins constnt with depth ( δ = 0. 1 ndε = ). Depth (m) Figure Estimted Thomsen nisotropy prmetersδ nd ε (solid curves) versus the vlues used to build the model δ = 0. 1 ndε = (dotted curve). Similr to the previous method, we produced error mps of VTI nisotropy prmeter estimtion using eution. In order to study the ccurcy of the eution, we did not dd ny errors to the dt generted by Kelvin-Christoffel eution. Figure 5 shows the bsolute vlues of the errors in estimting the Thomsen nisotropy prmeters δ nd ε using Grechk nd Mteev (007) 7 th EAGE Conference & Exhibition incorporting SPE EUROPEC 01 Copenhgen, Denmrk, -7 June 01

5 pproximtion given by eution. P nd S wve verticl velocities, density nd nisotropy prmeterγ re the sme s before. Figure 5 Absolute errors ssocited with the inversion of synthetic P- wve s slowness nd polriztion using eution s forwrd model. Results nd conclusions We studied the ccurcy of the two most common VTI prmeter estimtion techniues bsed on P- o wve mesurements. For moderte offset rnges (orθ MAX = ± 5 ), estimtion errors bsed on only P- wve s slownesses re stisfctory (0.5-% for δ in figure 1D nd 1-8% for ε in figure 1E) nd for 0 longer offsets (orθ MAX 5 ) re very good (lmost zero in figure 1G nd 1H). Therefore, if the ssumption of lterl homogeneity is vlid, P-wve slownesses techniue is robust method for VTI prmeter estimtion. On the other hnd, VTI nisotropy estimtion using P-wve s slownesspolriztion techniue s introduced by Grechk nd Mteev s (007) fils beyond wek nisotropies s smll s 5%, nd does not improve by involving longer offsets (figure 5). Furthermore, the effect of wve interference on P-wve polriztion mkes the method imprcticl even on noise free synthetic dt. Tking into ccount this interference effect for nisotropy estimtion techniues tht rely on polriztion mesurements is prt of our future reserch. References Alkhlifh, T. nd Tsvnkin I. [1995] Velocity nlysis for trnsversely isotropic medi. Geophysics 60(5), Grechk, V. nd Mteev, A. [007] Inversion of P-wve VSP dt for locl nisotropy, Theory nd cse study. Geophysics 7(), D69-D79. Miller, D. nd Spencer, C. [199] An exct inversion for nisotropic moduli from phse slowness dt. Journl of Geophysicl Reserch 99, Thomsen, L. [1986] Wek elstic nisotropy. Geophysics 51(10), Tsvnkin, I. [001] Seismic Signtures nd Anlysis of Reflection Dt in Anisotropic Medi - Hndbook of Geophysicl Explortion. Elsevier Science. London 7 th EAGE Conference & Exhibition incorporting SPE EUROPEC 01 Copenhgen, Denmrk, -7 June 01

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION DOI:.38/NMAT343 Hybrid Elstic olids Yun Li, Ying Wu, Ping heng, Zho-Qing Zhng* Deprtment of Physics, Hong Kong University of cience nd Technology Cler Wter By, Kowloon, Hong Kong, Chin E-mil: phzzhng@ust.hk