Annual Report 2000 - WIT

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60 Cohen, J., Hagin, F., and Bleistein, N., 1986, Three-dimensional Born inversion with an arbitrary reference: Geophysics, 51, no. 8, 1552–1558. Hildebrand, W., 1990, Connecting the Dots Parametrically: An Alternative to Cubic Splines: The College Mathematics Journal, 21, no. 3, 208–215. Hubral, P., and Krey, T., 1980, Interval velocities from seismic reflection traveltime measurements: Soc. Expl. Geophys. Hubral, P., Schleicher, J., and Tygel, M., 1992, Three-dimensional paraxial ray properties – Part I. Basic relations: J. Seism. Expl., 1, no. 3, 265–279. Hubral, P., 1983, Computing true amplitude reflections in a laterally inhomogeneous earth: Geophysics, 48, no. 8, 1051–1062. Langenberg, K., 1986, Applied inverse problems for acoustic, electromagnetic, and elastic wave scattering in Sabatier, P., Ed., Basic methods in Tomography and Inverse Problems:: Adam Hilger. Leite, L., 1998, Introduçao a análise espectral em geofisica: FADESP, Belém, Brasil. Martins, J., Schleicher, J., Tygel, M., and Santos, L., 1997, 2.5-d true-amplitude Kirchhoff migration and demigration: J. Seism. Expl., 6, no. 2/3, 159–180. Porter, R., 1970, Diffraction-limited scalar image formation with holograms of arbitrary shape: J. Acoust. Soc. Am., 60, no. 8, 1051–1059. Ricker, N., 1953, The form and laws of propagation of seismic wavelets: Geophysics, 18, no. 01, 10–40. Rockwell, D., 1971, Migration stack aids interpretation: Oil and Gas Journal, 69, 202– 218. Schleicher, J., Hubral, P., Tygel, M., and Jaya, M., 1997, Minimum apertures and Fresnel zones in migration and demigration: Geophysics, 62, no. 2, 183–194. Schneider, W., 1978, Integral formulation for migration in two and three dimensions: Geophysics, 43, no. 1, 49–76. Sommerfeld, A., 1964, Optics:, volume IV of Lectures on Theoretical Physics Academic Press, New York. Tygel, M., Schleicher, J., and Hubral, P., 1994, Pulse distortion in depth migration: Geophysics, 59, no. 10, 1561–1569. Tygel, M., Schleicher, J., and Hubral, P., 1995, Dualities between reflectors and reflection-time surfaces: J. Seis. Expl., 4, no. 2, 123–150.
61 Tygel, M., Müller, T., Hubral, P., and Schleicher, J., 1997, Eigenwave based multiparameter traveltime expansions: Eigenwave based multiparameter traveltime expansions:, 67th <strong>Annual</strong> Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 1770–1773. Tygel, M., Schleicher, J., Santos, L., and Hubral, P., <strong>2000</strong>, An asymptotic inverse to the Kirchhoff-Helmholtz integral: Inv. Probl., 16, 425–445. Vermeer, G., 1999, Factors affection spatial resolution: Geophysics, 64, no. 3, 942– 953.
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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
Page 22 and 23: 7 ¢¥£§¦©¨ ; < calculate sear
Page 24 and 25: 7 7 searches ¡ HNJOL for ¢IHNJML
Page 26 and 27: 14 Trace no. 1000 1500 2000 0.5 1.0
Page 28 and 29: 16 CDP number 3100 3000 2900 2800 2
Page 30 and 31: 18 REFERENCES Höcht, G., de Bazela
Page 32 and 33: 20 INVERSION BY MEANS OF CRS ATTRIB
Page 34 and 35: 22 For synthetic data, it is easy t
Page 36 and 37: — J J J J J J G J - J J G
Page 39 and 40: Wave Inversion Technology, Report N
Page 41 and 42: · · v 0 B 0 £ & Ä Ã & v
Page 43 and 44: 31 Dürbaum, H., 1954, Zur Bestimmu
Page 45 and 46: Ã Ø Ì 0 0 Ì 4 0 Ã 0 G ' 4
Page 49 and 50: 0 0 ˜ ” Z ˜ ” Z 4 4
Page 51 and 52: 39 strategy by combining global and
Page 53 and 54: 41 elled data is presented in Figur
Page 55 and 56: 43 0.2 Distance [m] 1000 1500 2000
Page 57 and 58: 45 In Figure 10 we have the optimiz
Page 59: 47 Gelchinsky, B., 1989, Homeomorph
Page 62 and 63: § ¢ ø ø for a paraxial ray, ref
Page 64 and 65: Œ § … Z ‹ Z § õ ø \ ø §
Page 66 and 67: 54 As stated in Hubral and Krey, 19
Page 68 and 69: § ó § 56 sequence. We made tes
Page 70 and 71: 58 precision of the modeled input d
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 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
Page 102 and 103: ¨ º Ý È · § À · Á · Á ¼
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,
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110 et al., 1992), Hanitzsch (1997)
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112 consecutive wavefronts). Howeve
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114 Numerical example We test the W
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116 Versteeg, R., and Grau, G., 199
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118 indicator. To extract elastic p
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€ b b 120 S where is the position
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É É É É 122 The À constant (da
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124 0 Distance [ m ] 1000 2000 3000
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126 Kosloff, D., Sherwood, J., Kore
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128
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130 penetration distances and a pot
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and » ˆ Ö Ö is the scalar hydra
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Å éÙó ó ».-.‹œì/-jì¨‹
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136 TRIGGERING FRONTS IN HETEROGENE
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Ö ˆ Ö “P£'ˆ é ˆ ó,Lˆ¨
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Ö Ö Ê » Ø Ö » Ö Ê Ê Ê Ö
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142 300 250 200 a) eikonal equation
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144 Shapiro, S. A., and Müller, T.
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» i » m ×]Ú ‘Œƒšj'Ÿlk hM
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148 RESULTS Soultz-sous-Forêts Inv
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…„ƒ 150 for the smaller ellips
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152 Figure 5: The cloud of events f
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…„ƒ Î Î ÎÄÈ‹•¨ Î-È
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156 straightforward. The new approa
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158
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160 1982). There is also the so-cal
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{ ³ u ´ ´ ´ ´ -y ›-^œ ´ ´
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Ï u u ¬ 164 To summarize, we deri
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Ý ì á ä é å¤æDçzè ä é
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ø M ã = ã Ù ø ä Ú ã Ù ø
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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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ã ä ä ŸSŸ S ¡S¡ ©©¨¨ æ
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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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‹œž Ÿ¢¡¤£¦¥ƒ§©¨ ‘
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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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æVU ìÿå T ü ýWYXZX[ 9\]9^\ Þ
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218 weight functions from traveltim
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220 REFERENCES Bleistein, N., 1986,
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Š Ê ¦ Í ½ Í ’ » Ö ½ Ê
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!¥”“Z• Ç ¤ É¨§ — ‘
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226
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228 In this paper, we present a mor
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L • MM+,ON N N Ž ú R N N N ú
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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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î r † Û(Û Ü Œ U Ú Ý Ü Û
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248 Ettrich, N., 1998, FD eikonal s
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ø Ð ¡ Ð÷ö Ð'ø ú Ð ¡ Ð'
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ø ü ø ø ý Þ do ø ý Ü
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ø ö ø ú ü ö ü ¡ ü
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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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… " ¯ ü ý +- 4=° ü ü +
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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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¹ õ ' ' -š' ù ¹ ù ' ' -š
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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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