Annual Report 2000 - WIT
Annual Report 2000 - WIT Annual Report 2000 - WIT
68 Reflection Coefficient (a) 0.1 0.05 0 -1000 0 1000 Distance (m) Relative Error (%) (b) 30 0 -30 -60 -1000 0 1000 Distance (m) Figure 5: (a) Amplitudes along the reflector from demodeling (solid line) and Kirchhoff migration (dashed line) in comparison to reflection coefficients (bold line). (b) Relative errors. Depth (m) 0 200 400 600 800 -2000 -1000 0 1000 2000 Distance (m) Figure 6: Model II: A trough structure below a homogeneous overburden. migrated reflector image as Kirchhoff migration. The principal drawback of demodeling is noted when comparing the amplitudes along the reflector (Figure 8). Because of the presence of the diffractions, the amplitudes on flanks of the trough are not correctly recovered. In the range between -500 m and 500 m (except a small region around the origin), the error strongly fluctuates and exceeds 50%. Further investigations on how to distinguish reflections from diffractions and how to separate conflicting events in the picking process are envisaged to improve demodeling amplitudes in caustic regions.
69 (a) (b) Depth (m) 600 800 Depth (m) 600 800 1000 -1000 0 1000 Distance (m) 1000 -1000 0 1000 Distance (m) Figure 7: (a) Kirchhoff depth migrated section, (b) Kirchhoff demodeled section, of noise-free common-offset data for Model II. Reflection Coefficient 0.1 0.05 (a) Relative Error (%) 0 -1000 0 1000 Distance (m) 50 0 -50 (b) -100 -1000 0 1000 Distance (m) Figure 8: (a) Amplitudes along the reflector from demodeling (solid line) and Kirchhoff migration (dashed line) in comparison to reflection coefficients (bold line). (b) Relative errors. CONCLUSIONS We have presented a numerical analysis of a new migration method based on the Kirchhoff-Helmholtz integral. Since the process under investigation represents an (asymptotic) inverse to Kirchhoff modeling, we have termed it Kirchhoff demodeling. The demodeling integral is completely analogous to the modeling integral in the sense that it does exactly the same procedure along the reflection traveltime surface that the modeling integral does along the reflector.
- 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 47 and 48: Wave Inversion Technology, Report N
- 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 75 and 76: Wave Inversion Technology, Report N
- Page 77 and 78: £ 65 The details of the theory inv
- Page 79: 67 of the figure. On both sides, a
- 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
- 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
68<br />
Reflection Coefficient<br />
(a)<br />
0.1<br />
0.05<br />
0<br />
-1000 0 1000<br />
Distance (m)<br />
Relative Error (%)<br />
(b)<br />
30<br />
0<br />
-30<br />
-60<br />
-1000 0 1000<br />
Distance (m)<br />
Figure 5: (a) Amplitudes along the reflector from demodeling (solid line) and Kirchhoff<br />
migration (dashed line) in comparison to reflection coefficients (bold line). (b)<br />
Relative errors.<br />
Depth (m)<br />
0<br />
200<br />
400<br />
600<br />
800<br />
-<strong>2000</strong> -1000 0 1000 <strong>2000</strong><br />
Distance (m)<br />
Figure 6: Model II: A trough structure below a homogeneous overburden.<br />
migrated reflector image as Kirchhoff migration. The principal drawback of demodeling<br />
is noted when comparing the amplitudes along the reflector (Figure 8). Because of<br />
the presence of the diffractions, the amplitudes on flanks of the trough are not correctly<br />
recovered. In the range between -500 m and 500 m (except a small region around the<br />
origin), the error strongly fluctuates and exceeds 50%. Further investigations on how<br />
to distinguish reflections from diffractions and how to separate conflicting events in the<br />
picking process are envisaged to improve demodeling amplitudes in caustic regions.
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