- Page 1: Wave Inversion Technology WIT Annua
- Page 6: with contributions from the WIT Gro
- Page 10: Preface The third WIT (Wave-Inversi
- Page 13 and 14: ii Vanelle C. and Gajewski D., Thre
- Page 15 and 16: 2 Müller and Shapiro extended the
- Page 17 and 18: 4 age data. Numerical results obtai
- Page 20 and 21: Wave Inversion Technology, Report N
- Page 22 and 23: 9 t " ; t = ;() N R N ; R ! S R x
- Page 24 and 25: 11 1987), h B ( ~ M I )= 2 6 4 rT (
- Page 26 and 27: 13 200 (a) Time (ms) 250 300 350 40
- Page 28 and 29: 15 reflector, we can conceive its i
- Page 30 and 31: Wave Inversion Technology, Report N
- Page 32 and 33: 19 0 X1 X2 X3 X4 Depth (m) 500 1000
- Page 34 and 35: 21 1 0 0.9 -0.05 0.8 -0.1 0.7 -0.15
- Page 36 and 37: 23 Interestingly enough, things do
- Page 38 and 39: 25 1 0 0.9 -0.05 0.8 -0.1 0.7 -0.15
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- Page 42 and 43: 29 and x G = x m + h ; x o . The co
- Page 44 and 45: 31 SENSIBILITY ANALYSIS The most im
- Page 46 and 47: 33 CONCLUSIONS By using derivatives
- Page 48 and 49: 35 T 5 = T 6 = @ @ o = T 5 + T 6 (1
- Page 50: 37 0.8 Common−Offset Section (100
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40 INVERSION OF THE WAVEFIELD ATTRI
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42 X 0 α ~ α V 0 γ i (x ,z ) i i
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44 0 1 2 v = 1.5km/s 0 v = 4.5km/s
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46 second interface are slightly sc
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48 CONCLUSION We presented an inver
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50 .
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Wave Inversion Technology, Report N
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55 time in respect to the start tim
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57 Figure 3: The same as Figure 2,
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59 By analogy with (2) we will look
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61 CONCLUSIONS We have developed a
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Wave Inversion Technology, Report N
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65 will show later how the process
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67 and develops a series solution o
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69 For the 3-D case the results are
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71 0.3 0.2 relative fluctuations of
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73 It is now possible to describe s
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75 Pulse propagation in random medi
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77 Pulse propagation in random medi
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Wave Inversion Technology, Report N
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81 The standard staggered grid A st
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83 EXPERIMENTAL SETUP As described
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85 0 0.04 0.08 0.12 0.16 depth (m)
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87 to the 2D-model (SH-waves). The
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89 The first step to use this theor
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91 ACKNOWLEDGMENTS We wish to thank
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Modeling 93
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96 are so small that the resulting
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98 zero. In other words, he sought
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100 We simulated a common-shot expe
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102 Relative error (%) 60 40 20 0
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104
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106 for the isotropic elastic case.
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108 of body forces, and with a Gree
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110 THE STATIONARY-PHASE APPROXIMAT
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112 Note that for each preassigned
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114
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116 3 s s s s x r r x s ~x 3
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118 Claim two The second claim to b
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120 Figure 2: Local Cartesian, ray
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122 Here, q and q denote the in-p
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124 Hubral, P., Schleicher, J., and
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126 and Gajewski, 1996; Vinje et al
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128 Figure 2: Wavefronts computed w
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130 source rays wavefront Figure 6:
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132 ACKNOWLEDGEMENTS This work was
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134 and Lecomte, 1992; Qin et al.,
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136 which is another form of snell'
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138 NUMERICAL TESTS The figures bel
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140 SUMMARY The following give the
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142
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144 on, e.g., the wavefront or refl
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146 Hubral et al. (1992) do a simil
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148 Depth [km] 0.2 0.4 0.6 0.8 0.2
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150 0.2 0.4 0.6 0.8 Y-Offset [km] 0
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152 and assume a linear relationshi
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154 the transformation ^Q = ^R T s
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156 rock have been generated by Joh
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158 Those latter coefficients descr
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160 (9) by explicit difference oper
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162 a series of large-amplitude sho
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164 CONCLUSIONS We have presented t
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166
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168 is slower than computing the fu
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170 Figure 1 shows the original 3D
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172 Figure 3: Snapshot of the elast
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174
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176 COMPUTING THE EFFECTIVE MEDIUM
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178 Vp [ km/s ] 4 3.8 3.6 3.4 3.2 3
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180 Figure 3: Time history of fluid
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182
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184 as salt body). To use full wave
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186 teristic change in subsurface p
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188
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190 CHEBYSHEV METHOD We use a Cheby
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192 x P 1 f (x) r P 4 P 2 f (x) r+1
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194 EXAMPLE In order to demonstrate
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196 CONCLUSION We developed a metho
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198
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200 The use of multi-parametric tra
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202 depending on the original and c
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204 (1999), the first part consists
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206 0 0.7 1 0.6 Zero offset travelt
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208 5 x 10−4 0 First reflector N
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210 Müller, T., 1999, The common r
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212 with respect to the physical pr
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214 The problem under consideration
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216 0 B @ TI mudshale =0:034, =0:
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218 exact velocities for the horizo
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220 ACCURACY OF SECTORIAL APPROXIMA
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222 Sayers, C. M., 1994, P-wave pro
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224 The forward model used for the
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226 0.2 (a) 0.1 Amp(n) 0 −0.1 −
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228 1 1 P(x,t) 0.5 P(x,t) 0.5 0 0 1
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230 KALMAN - WIENER The integral eq
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232 (2) Definition of the state vec
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234 0.2 0.15 0.1 0.05 Amp(n) 0 −0
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236 0 0 0 100 100 100 200 200 200 3
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238 Mendel, J., Nashi, N., and Chan
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240 One of the first methods which
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242 a limited time range while the
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244 Offset (km) 0.5 1.5 2.5 Figure
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246 where u 0 j is the conjugate tr
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248 CONCLUSION Coherency analysis o
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250 Montgomery, D. C., and Runger,
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252
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254 2. 3. 4. Macromodel determinati
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256 Research students: Ingo Koglin
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258 João Luis Martins Migration an
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260
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262 Elf Exploration UK plc 30 Bucki
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264 PGS Seres AS P.O. Box 354 Stran
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266 Robert Essenreiter received his
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268 L.W.B. Leite Professor of Geoph
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270 Melanie Pohl is dealing with wa
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272 The first two years of this tim
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274 scientist in Karlsruhe and at C