Annual Report 2000 - WIT

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116 Versteeg, R., and Grau, G., 1990, Practical aspects of seismic data inversion, the Marmousi experince: 52th Mtg., Eur. Assoc. Expl Geophys., Proc. 1990 EAEG Workshop, 1–194. Vidale, J. E., 1990, Finite-difference calculation of traveltimes in three dimensions: Geophysics, 55, 521–526. Vinje, V., Iversen, E., and Gjøystdal, H., 1993, Traveltime and amplitude estimation using wavefront construction: Geophysics, 58, 1157–1166. Vinje, V., Iversen, E., Åstebøl, K., and Gjøystdal, H., 1996a, Estimation of multivalued arrivals in 3D models using wavefront construction–Part I: Geophys. Prosp., 44, 819–842. Vinje, V., Iversen, E., Åstebøl, K., and Gjøystdal, H., 1996b, Part II: Tracing and interpolation: Geophys. Prosp., 44, 843–858.
Wave Inversion Technology, <strong>Report</strong> No. 4, pages 117-129 Poisson's ratio analysis and reflection tomography E. Menyoli and D. Gajewski 1 keywords: Poisson's ratio, velocity ratio, converted waves, tomography, residual curvature ABSTRACT Depth imaging of multi-component dataset provides a tool for estimating elastic parameters ( &gf E determining shear wave velocities and velocity ratio in a postmigrated domain after doing Poisson's ratio analysis (PRA). Raypaths are traced through an initial Poisson's ratio funtion and are used in combination with depth deviations in the postmigrated domain to compute Poisson's ratio perturbations. The perturbations are added to the initial Poisson's ratio function to obtain the updated Poisson's ratio. The traveltime of the CRP rays to and from the reflection point and the horizontal components of the slowness are used to constrain the raypath when parameters of the reference Poisson's ratio function are perturbed. The Poisson's ratio model is corrected by an iterative optimization technique that minimizes discrepancies in raypath. The optimization scheme is a conjugate-gradient method, where the gradient operator linearly relates perturbations in Poisson's ratio to changes in reflector positions. This includes a tomographic approach in estimating Poisson's ratios. Having the correct Poisson's ratio the shear velocity model is directly computed. We assume here that the depth model is known from previous P-wave velocity/depth analysis implying also that the wave conversion occured at the same interface as the P-wave reflection. The methodology described here has been applied to a 2D synthetic dataset but is also applicable in a 3D isotropic medium. &)h , " and &gf0i0&(h ) in complex media. This paper, introduces a method of INTRODUCTION The Poisson's ratio of sediments and rocks has been of special interest in seismology and oil-exploration. It can be determined from the ratio of compressional wave velocity &jf to shear wave velocity &)h . The presence of gas in the pore space of a rock layer causes a remarkable drop in the &gf0i0&(h ratio which leads to a decrease in the Poisson's ratio. Therefore an analysis of Poisson's ratio is vital as hydrocarbon 1 email: menyoli@dkrz.de 117
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Wave Inversion Technology WIT Annua
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Wave Inversion Technology WIT Wave
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Copyright c 2000 by Karlsruhe Unive
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i TABLE OF CONTENTS Reviews: WIT Re
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Wave Inversion Technology, Report N
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3 theory. It relates properties of
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Imaging 5
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8 two hypothetical eigenwave experi
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7 ¢¥£§¦©¨ ; < calculate sear
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7 7 searches ¡ HNJOL for ¢IHNJML
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14 Trace no. 1000 1500 2000 0.5 1.0
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16 CDP number 3100 3000 2900 2800 2
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18 REFERENCES Höcht, G., de Bazela
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20 INVERSION BY MEANS OF CRS ATTRIB
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22 For synthetic data, it is easy t
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— J J J J J J G J - J J G
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31 Dürbaum, H., 1954, Zur Bestimmu
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0 0 ˜ ” Z ˜ ” Z 4 4
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39 strategy by combining global and
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41 elled data is presented in Figur
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43 0.2 Distance [m] 1000 1500 2000
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45 In Figure 10 we have the optimiz
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47 Gelchinsky, B., 1989, Homeomorph
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§ ¢ ø ø for a paraxial ray, ref
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54 As stated in Hubral and Krey, 19
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§ ó § 56 sequence. We made tes
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58 precision of the modeled input d
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60 Cohen, J., Hagin, F., and Bleist
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Page 77 and 78: £ 65 The details of the theory inv
Page 79 and 80: 67 of the figure. On both sides, a
Page 81 and 82: 69 (a) (b) Depth (m) 600 800 Depth
Page 83 and 84: 71 Langenberg, K., 1986, Applied in
Page 85 and 86: È Û Ñ¿ = ¨ Í Ñ>* = ¿ + ð
Page 87 and 88: Wave Inversion Technology, Report N
Page 89 and 90: g ý g [ ^ â g [ g g g g g â h [
Page 91 and 92: g § » ¹ [ƒŽ g 79 We now subst
Page 93 and 94: ê 81 ing was realized by an implem
Page 95 and 96: ˆ 83 -0.05 -0.1 Amplitude -0.15 -0
Page 97: 85 on a second-order approximation.
Page 100 and 101: 88 kinematic (related to traveltime
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Page 104 and 105: ° ´ ´ ã ° ¼ ´ ´ þ Ò Ò ¥
Page 106 and 107: 94 1 taper value ksi1 0 ksi2 Figure
Page 108 and 109: 96 0 1 2 3 4 5 Depth [km] CMP [km]
Page 110 and 111: 98 CONCLUSION As a generalization o
Page 112 and 113: 100 weight during the stacking proc
Page 114 and 115: 102 are not illuminated for every o
Page 116 and 117: 104 obtained from Zoeppritz' equati
Page 118 and 119: 106 PreSDM of Porous layer 0.358 re
Page 120 and 121: 108 REFERENCES Gassmann, F., 1951,
Page 122 and 123: 110 et al., 1992), Hanitzsch (1997)
Page 124 and 125: 112 consecutive wavefronts). Howeve
Page 126 and 127: 114 Numerical example We test the W
Page 130 and 131: 118 indicator. To extract elastic p
Page 132 and 133: € b b 120 S where is the position
Page 134 and 135: É É É É 122 The À constant (da
Page 136 and 137: 124 0 Distance [ m ] 1000 2000 3000
Page 138 and 139: 126 Kosloff, D., Sherwood, J., Kore
Page 140 and 141: 128
Page 142 and 143: 130 penetration distances and a pot
Page 144 and 145: and » ˆ Ö Ö is the scalar hydra
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Page 148 and 149: 136 TRIGGERING FRONTS IN HETEROGENE
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Page 154 and 155: 142 300 250 200 a) eikonal equation
Page 156 and 157: 144 Shapiro, S. A., and Müller, T.
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Page 160 and 161: 148 RESULTS Soultz-sous-Forêts Inv
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Page 164 and 165: 152 Figure 5: The cloud of events f
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Page 168 and 169: 156 straightforward. The new approa
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Page 172 and 173: 160 1982). There is also the so-cal
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Page 176 and 177: Ï u u ¬ 164 To summarize, we deri
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ã Q c ã ä 170 a=10m; std.dev.=8%
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172 Frankel, A., and Clayton, R. W.
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174 It is well-known that inhomogen
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Kneib, 1995 285-6000 superposition
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180 parameter: Hurst coefficient pa
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182 REFERENCES Bourbié, T., Coussy
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184 1999) in multiple fractured med
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j jÆÅÇ[È”u j jÎÅÇ[È”uw
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190 Davis, P. M., and Knopoff, L.,
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192 properties from the measured se
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194 discussion of these problems ca
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196 Altogether, close to 260 shotpo
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198 Time (ms) 0 2 4 6 8 10 12 14 16
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200 of groundwater. ACKNOWLEDGEMENT
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202
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204 the wavefront curvature matrix
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û ò é from ã äñ to ã î§ñ
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é 208 Table 1: Median relative err
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210 Table 2: Median relative errors
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212 CONCLUSIONS We have presented a
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214 PUBLICATIONS Previous results c
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218 weight functions from traveltim
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220 REFERENCES Bleistein, N., 1986,
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226
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228 In this paper, we present a mor
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232 Figure 3: The evolution of a WF
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234 Let us analyze next the computa
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236 CONCLUSIONS We have presented a
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238
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’ Ç r 240 traveltimes, a computa
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Ž Ž Ã Ž 242 Other two approxima
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“ Ã Æ ³ 244 0 0.5 [km] 0 0.5 1
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248 Ettrich, N., 1998, FD eikonal s
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‹ 256 transport equation. Neverth
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258 tivalued geometrical spreading
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260 .
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262
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ö ô æ º Ò x ¹ v ý ñ
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268 NUMERICAL RESULTS We constructe
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£ -š' - 272 Ô- —- Figure 6: C
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274 REFERENCES Aldridge, D. F. (199
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276
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278 3. 4. True-amplitude imaging, m
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280 Research Group Hamburg (Gajewsk
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282 Stefan Lüth Robert Patzig Refr
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284 Landmark Graphics Corp. 7409 S.
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286 TotalFinaElf Exploration UK plc
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288 as research assistant at Geoeco
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290 Ingo Koglin is a diploma studen
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292 Matthias Riede received his M.S
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294 Svetlana Soukina received her d
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296 Yonghai Zhang received the Mast
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