Annual Report 2000 - WIT
Annual Report 2000 - WIT Annual Report 2000 - WIT
70 By our numerical analysis, we have confirmed that demodeling can indeed be used for migration purposes. In all our experiments, demodeling correctly positioned the reflector in depth. Concerning amplitudes, demodeling presents positive as well as negative properties. Positively is to be noted that, under ideal circumstances, demodeling recovers the reflection coefficients along the reflecting interface with very small errors. Boundary zones can be kept smaller than in Kirchhoff migration. Random noise does not affect demodeling amplitudes any more than it does Kirchhoff migration. Off the reflector, the noise level is reduced by demodeling. As a negative quality of demodeling, its bad amplitude recovery in the presence of caustics is to be cited. From an implementational point of view, we want to stress the following differences between Kirchhoff migration and demodeling. Because of the structure of the underlying integrals, demodeling is much faster than Kirchhoff migration, even when applied with full true-amplitude weights. We remind that the demodeling process is analogous to that of Kirchhoff modeling and, thus, needs comparable computing time. Like Kirchhoff migration, demodeling is a target-oriented migration method. However, contrary to Kirchhoff migration, where a target zone needs to be specified, demodeling can directly be restricted to a target reflector. As a disadvantage, we remind that demodeling requires an identification and picking of the events to be migrated. In consequence, its result may vary with the picking algorithm used. For a kinematic migration, traveltime picking is sufficient. For trueamplitude migration, amplitude picking is also necessary. This should, however, not pose a severe restriction to the applicability of the method since the identification of horizons of interest is always necessary at some stage of the seismic processing sequence. In conclusion, the new process is not to be seen as replacement of Kirchhoff migration, but as an alternative and complementary procedure. Possible applications include the fast true-amplitude migration of an identified event to determine whether a promising AVO trend in the CMP section is confirmed after migration. ACKNOWLEDGEMENTS The research of this paper was supported in part by the National Research Council (CNPq – Brazil), the Sao Paulo State Research Foundation (FAPESP – Brazil), and the sponsors of the WIT Consortium. REFERENCES Bojarski, N., 1982, A survey of the near-field far-field inverse scattering inverse source integral equation: IEEE Trans. Ant. Prop., AP-30, no. 5, 975–979.
71 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. 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. 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., 1995, Dualities between reflectors and reflection-time surfaces: J. Seis. Expl., 4, no. 2, 123–150. Tygel, M., Schleicher, J., Santos, L., and Hubral, P., 2000, An asymptotic inverse to the Kirchhoff-Helmholtz integral: Inv. Probl., 16, 425–445. PUBLICATIONS The general derivation of the demodeling integral in inhomogeneous media was published in (Tygel et al., 2000). APPENDIX A 2.5-D CONSTANT VELOCITY FORMULAS In this appendix we investigate briefly the form of the Inverse Kirchhoff-Helmholtz integral (Tygel et al., 2000), Ë ¼Ó¾¾²Ô Õ7Ö ×ÙØƒÚ ¹ ÛÝÜ2Þ (A-1) »¤¼%½³¾‰¿ÁÀ µ ·5¸º¹ ¨êÄÆŇÇÉÈ »Ê¼ ¸º¹ Ë ¾+Ì ¸ ¹ Ë ¾SÍŠÎ¨Ï ¸ ½ÐÀÒÑ ¸º¹ »Ê¼ ¹
- Page 32 and 33: 20 INVERSION BY MEANS OF CRS ATTRIB
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- 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
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- 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 and 80: 67 of the figure. On both sides, a
- Page 81: 69 (a) (b) Depth (m) 600 800 Depth
- 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
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- 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
70<br />
By our numerical analysis, we have confirmed that demodeling can indeed be used<br />
for migration purposes. In all our experiments, demodeling correctly positioned the<br />
reflector in depth. Concerning amplitudes, demodeling presents positive as well as<br />
negative properties. Positively is to be noted that, under ideal circumstances, demodeling<br />
recovers the reflection coefficients along the reflecting interface with very small<br />
errors. Boundary zones can be kept smaller than in Kirchhoff migration. Random<br />
noise does not affect demodeling amplitudes any more than it does Kirchhoff migration.<br />
Off the reflector, the noise level is reduced by demodeling. As a negative quality<br />
of demodeling, its bad amplitude recovery in the presence of caustics is to be cited.<br />
From an implementational point of view, we want to stress the following differences<br />
between Kirchhoff migration and demodeling. Because of the structure of the<br />
underlying integrals, demodeling is much faster than Kirchhoff migration, even when<br />
applied with full true-amplitude weights. We remind that the demodeling process is<br />
analogous to that of Kirchhoff modeling and, thus, needs comparable computing time.<br />
Like Kirchhoff migration, demodeling is a target-oriented migration method. However,<br />
contrary to Kirchhoff migration, where a target zone needs to be specified, demodeling<br />
can directly be restricted to a target reflector.<br />
As a disadvantage, we remind that demodeling requires an identification and picking<br />
of the events to be migrated. In consequence, its result may vary with the picking<br />
algorithm used. For a kinematic migration, traveltime picking is sufficient. For trueamplitude<br />
migration, amplitude picking is also necessary. This should, however, not<br />
pose a severe restriction to the applicability of the method since the identification of<br />
horizons of interest is always necessary at some stage of the seismic processing sequence.<br />
In conclusion, the new process is not to be seen as replacement of Kirchhoff migration,<br />
but as an alternative and complementary procedure. Possible applications include<br />
the fast true-amplitude migration of an identified event to determine whether a promising<br />
AVO trend in the CMP section is confirmed after migration.<br />
ACKNOWLEDGEMENTS<br />
The research of this paper was supported in part by the National Research Council<br />
(CNPq – Brazil), the Sao Paulo State Research Foundation (FAPESP – Brazil), and<br />
the sponsors of the <strong>WIT</strong> Consortium.<br />
REFERENCES<br />
Bojarski, N., 1982, A survey of the near-field far-field inverse scattering inverse source<br />
integral equation: IEEE Trans. Ant. Prop., AP-30, no. 5, 975–979.