Annual Report 2000 - WIT

More documents

Recommendations

Info

v G ° Ã £§¦©¨ G ¬ Ã £§¦©¨ G ¾ Ã £§¦©¨ G ¿ Ã £§¦©¨ ' ' ' ' Ã Ã Ã Ã £ £ £ £ 0 ' 0 0 0 Ã Ã v v Ã Ã £ £ Ã ' ' £ ' Ã Ã · · & Ã · v Ã Ã £ & Ã 28 is formulated in such a way that the influence of the curved surface can be clearly recognized. THEORY According to (Schleicher et al., 1993), the hyperbolic traveltime approximation for a ray from ¢£ to ¢¤£ and from ¢¤£ to ¤:£ both on a curved surface, in the vicinity of a normal (zero-offset) ray from ¢Œ¤ to ¢ and from ¢ to ¢Œ¤ (Figure A-1) is given by (1) ›© ©¤ª«t¬®¯°Ÿ'(¬®¯# with (2) ±²¬®¯°QV¬®¯#Œ© ³ ©¥¦t§k |WŒ1©¨' c"µ$‡·¹¸ & ›´ (3) »5')Wº Wº²(» ¼ > This formula is valid for a 2D laterally inhomogeneus medium. is the velocity at the ZO location , is zero-offset (two-way) traveltime. and are the coordinates » & ¢ˆ¤ of ©½ the source Wº and receiver measured along the tangent to the curved surface ¢£ at ¤:£ . ¢Œ¤ The components °(|¬ |¾V|¿ of the so-called ÁÀÂ surface-to-surface propagator matrix for the two-way normal ray (see Appendix) are given by (4) £3¦©¨ ·…¸ 4 & (5) ,f. ¸ 4 · ,/. · Ã · 4 & (6) ,/. Ã £3¦6¨ ,/. ¸ ¸ · £3¦©¨ (7) £3¦©¨ ,f. where · ¸ is the angle of incidence of the normal ray (emerging on the curved measurement surface ¢Œ¤ at ) with the normal of the tangent to the curved surface at . Let us define Ã · as the surface curvature at the point ¢Œ¤ . £3¦6¨ and Ã £ are ¢Œ¤ the curvatures of the NIP-wave and the N-wave observed ¢Œ¤ at , respectively (Hubral, 1983; Jäger et al., 2001). · ¸ 4
· · v 0 B 0 £ & Ä Ã & v Ä Ã Ä 4 Ã £ · & · Ä Ã Ã £ Ã Ã · > Ã > ' > Ã Ã Ã £ 29 Inserting eqs. (2), (4), and (5) into eq. (1) we obtain © ,/. '(,/. ¥|¦P§ ` © ¸ c"µ$“· & (8) ·¹Å)v ¸ · ¸ · © ,/. '(,/. Ã Ã £3¦6¨ Here are wanted parameters that help solve a variety of stacking and ¸ inversion problems (Hubral, 1999). They can be obtained by modifying the presently existing 2D CRS stack formula (Jäger et al., 2001) that is obtained from eq. ÆB (8) by sub- . In the following, we discuss 3 particular reductions of formula (8) which are of practical relevance. stituting Ã · ¸ · ¸ · ·CÅ £§¦©¨ Particular cases Common-mid-point (CMP) gather For this case, v , the equation (8) reduces to © (9) This expression is commonly written as (Shah, 1973) Ç Pˆ‹ ,f. '(,f. 8¥¨ £§¦©¨ ¸ · ¸ · ·…Å (10) Ç tWŒŸ È where the normal moveout (NMO) velocity & £§8:9 is now given by 8¥¨ & £§8:9 & (11) For Ã · £§8:9 & this reduces to Shah's formula. For a 1-D model with a planar surface, £§¦©¨ ¸ ¸ · ©E Ã ,f. '(,f. =B TB straight normal ray and incidence ¸ angle g 8 · , where É g 8 · is the familiar root-mean-square velocity. É Common - shot gather For this case, , equation (8) reduces to »‡‹Wº²( this expression reduces to ÉW£§8:9 & 4 © & ¸ · ¸ · ¸ · i ·¹Å (12) ,/. Ç 1 ˆ ,/. ©Ê c"µ$“·…¸ ,f. £3¦6¨ where according to eq. (A-9) and (Hubral, 1983), is demonstrated that £3¦©¨ , with Ã Ã being the wavefront curvature of the reflected wave at ¢Œ¤ . ½ Ã ½
Page 1 and 2: Wave Inversion Technology WIT Annua
Page 3: Wave Inversion Technology WIT Wave
Page 7: Copyright c 2000 by Karlsruhe Unive
Page 11 and 12: i TABLE OF CONTENTS Reviews: WIT Re
Page 13 and 14: Wave Inversion Technology, Report N
Page 15 and 16: 3 theory. It relates properties of
Page 17: Imaging 5
Page 20 and 21: 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: Wave Inversion Technology, Report N
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 72 and 73: 60 Cohen, J., Hagin, F., and Bleist
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,
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 128 and 129:
116 Versteeg, R., and Grau, G., 199
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
Page 146 and 147:
Å éÙó ó ».-.‹œì/-jì¨‹
Page 148 and 149:
136 TRIGGERING FRONTS IN HETEROGENE
Page 150 and 151:
Ö ˆ Ö “P£'ˆ é ˆ ó,Lˆ¨
Page 152 and 153:
Ö Ö Ê » Ø Ö » Ö Ê Ê Ê Ö
Page 154 and 155:
142 300 250 200 a) eikonal equation
Page 156 and 157:
144 Shapiro, S. A., and Müller, T.
Page 158 and 159:
» i » m ×]Ú ‘Œƒšj'Ÿlk hM
Page 160 and 161:
148 RESULTS Soultz-sous-Forêts Inv
Page 162 and 163:
…„ƒ 150 for the smaller ellips
Page 164 and 165:
152 Figure 5: The cloud of events f
Page 166 and 167:
…„ƒ Î Î ÎÄÈ‹•¨ Î-È
Page 168 and 169:
156 straightforward. The new approa
Page 170 and 171:
158
Page 172 and 173:
160 1982). There is also the so-cal
Page 174 and 175:
{ ³ u ´ ´ ´ ´ -y ›-^œ ´ ´
Page 176 and 177:
Ï u u ¬ 164 To summarize, we deri
Page 178 and 179:
Ý ì á ä é å¤æDçzè ä é
Page 180 and 181:
ø M ã = ã Ù ø ä Ú ã Ù ø
Page 182 and 183:
ã Q c ã ä 170 a=10m; std.dev.=8%
Page 184 and 185:
172 Frankel, A., and Clayton, R. W.
Page 186 and 187:
174 It is well-known that inhomogen
Page 188 and 189:
ã ä ä ŸSŸ S ¡S¡ ©©¨¨ æ
Page 190 and 191:
Kneib, 1995 285-6000 superposition
Page 192 and 193:
180 parameter: Hurst coefficient pa
Page 194 and 195:
182 REFERENCES Bourbié, T., Coussy
Page 196 and 197:
184 1999) in multiple fractured med
Page 198 and 199:
‹œž Ÿ¢¡¤£¦¥ƒ§©¨ ‘
Page 200 and 201:
j jÆÅÇ[È”u j jÎÅÇ[È”uw
Page 202 and 203:
190 Davis, P. M., and Knopoff, L.,
Page 204 and 205:
192 properties from the measured se
Page 206 and 207:
194 discussion of these problems ca
Page 208 and 209:
196 Altogether, close to 260 shotpo
Page 210 and 211:
198 Time (ms) 0 2 4 6 8 10 12 14 16
Page 212 and 213:
200 of groundwater. ACKNOWLEDGEMENT
Page 214 and 215:
202
Page 216 and 217:
204 the wavefront curvature matrix
Page 218 and 219:
û ò é from ã äñ to ã î§ñ
Page 220 and 221:
é 208 Table 1: Median relative err
Page 222 and 223:
210 Table 2: Median relative errors
Page 224 and 225:
212 CONCLUSIONS We have presented a
Page 226 and 227:
214 PUBLICATIONS Previous results c
Page 228 and 229:
æVU ìÿå T ü ýWYXZX[ 9\]9^\ Þ
Page 230 and 231:
218 weight functions from traveltim
Page 232 and 233:
220 REFERENCES Bleistein, N., 1986,
Page 234 and 235:
Š Ê ¦ Í ½ Í ’ » Ö ½ Ê
Page 236 and 237:
!¥”“Z• Ç ¤ É¨§ — ‘
Page 238 and 239:
226
Page 240 and 241:
228 In this paper, we present a mor
Page 242 and 243:
L • MM+,ON N N Ž ú R N N N ú
Page 244 and 245:
232 Figure 3: The evolution of a WF
Page 246 and 247:
234 Let us analyze next the computa
Page 248 and 249:
236 CONCLUSIONS We have presented a
Page 250 and 251:
238
Page 252 and 253:
’ Ç r 240 traveltimes, a computa
Page 254 and 255:
Ž Ž Ã Ž 242 Other two approxima
Page 256 and 257:
“ Ã Æ ³ 244 0 0.5 [km] 0 0.5 1
Page 258 and 259:
î r † Û(Û Ü Œ U Ú Ý Ü Û
Page 260 and 261:
248 Ettrich, N., 1998, FD eikonal s
Page 262 and 263:
ø Ð ¡ Ð÷ö Ð'ø ú Ð ¡ Ð'
Page 264 and 265:
ø ü ø ø ý Þ do ø ý Ü
Page 266 and 267:
ø ö ø ú ü ö ü ¡ ü
Page 268 and 269:
‹ 256 transport equation. Neverth
Page 270 and 271:
258 tivalued geometrical spreading
Page 272 and 273:
260 .
Page 274 and 275:
262
Page 276 and 277:
… " ¯ ü ý +- 4=° ü ü +
Page 278 and 279:
ö ô æ º Ò x ¹ v ý ñ
Page 280 and 281:
268 NUMERICAL RESULTS We constructe
Page 282 and 283:
¹ õ ' ' -š' ù ¹ ù ' ' -š
Page 284 and 285:
£ -š' - 272 Ô- —- Figure 6: C
Page 286 and 287:
274 REFERENCES Aldridge, D. F. (199
Page 288 and 289:
276
Page 290 and 291:
278 3. 4. True-amplitude imaging, m
Page 292 and 293:
280 Research Group Hamburg (Gajewsk
Page 294 and 295:
282 Stefan Lüth Robert Patzig Refr
Page 296 and 297:
284 Landmark Graphics Corp. 7409 S.
Page 298 and 299:
286 TotalFinaElf Exploration UK plc
Page 300 and 301:
288 as research assistant at Geoeco
Page 302 and 303:
290 Ingo Koglin is a diploma studen
Page 304 and 305:
292 Matthias Riede received his M.S
Page 306 and 307:
294 Svetlana Soukina received her d
Page 308:
296 Yonghai Zhang received the Mast
show all

Annual Report 2000 - WIT

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?