Annual Report 2000 - WIT
Annual Report 2000 - WIT Annual Report 2000 - WIT
214 PUBLICATIONS Previous results concerning traveltime interpolation were published by (Gajewski and Vanelle, 1999). A paper containing these results has been submitted (Vanelle and Gajewski, 2000a)
Wave Inversion Technology, Report No. 4, pages 215-226 True-amplitude migration weights from traveltimes C. Vanelle and D. Gajewski 1 keywords: traveltimes, geometrical spreading, migration weights, amplitude preserving migration ABSTRACT 3-D amplitude preserving pre-stack migration of the Kirchhoff type is a task of high computational effort. A substantial part of this effort is spent on the calculation of proper weight functions for the diffraction stack. We propose a method to compute the migration weights directly from coarse gridded traveltime data which are in any event needed for the summation along diffraction time surfaces. The method employs second order traveltime derivatives that contain all necessary information on the weight functions. Their determination alone from traveltimes significantly reduces the requirements in computational time and particularly storage. Application of the technique shows good accordance between numerical and analytical results. INTRODUCTION Kirchhoff migration is a standard technique in seismic imaging. During the last decade its objective has changed from the conventional diffraction stack migration that produces 'only' an image of reflectors in the subsurface to a modified diffraction stack, e.g., to peform AVO analysis, lithological interpretation and reservoir characterization. In the modified diffraction stack specific weight functions are applied which countermand the effect of geometrical spreading. Following from this, amplitudes in the resulting migrated image are proportional to the reflector strength if the weight functions are chosen correctly. Three different theoretical approaches (Bleistein, 1987; Keho and Beydoun, 1988; Schleicher et al., 1993) have lead to formulations of the weight functions. As (Docherty, 1991) and (Hanitzsch, 1997) have shown these results are closely related. Since weight functions can be expressed in terms of second order spatial derivatives of traveltimes they were until now computed using dynamic ray tracing ( jCervený and de- Castro, 1993; Hanitzsch et al., 1994). Although (Schleicher et al., 1993) state that the modulus of the weight function can also be determined from traveltimes, (Hanitzsch, 1 email: vanelle@dkrz.de 215
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- Page 202 and 203: 190 Davis, P. M., and Knopoff, L.,
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214<br />
PUBLICATIONS<br />
Previous results concerning traveltime interpolation were published by (Gajewski and<br />
Vanelle, 1999). A paper containing these results has been submitted (Vanelle and<br />
Gajewski, <strong>2000</strong>a)
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