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Introduction

While accurate kinematics are the first requirement of a useful seismic image, its amplitude and phase behavior are nonetheless important. The amplitude and phase information can be useful in wave-equation migration velocity analysis or as direct hydrocarbon indicators. The one-way wavefield extrapolators Claerbout (1971) employed in migration produce correct traveltimes. However, their amplitude and phase characteristics can be improved.

Zhang (1993) brings theoretical insight into the problem of improving the amplitudes of downward continuation operators. Zhang et al. (2001) compare them with Kirchhoff inversion and provide formulas for amplitude-preserving shot-profile migration that are accurate in the case of constant velocity. Along the same lines, Zhang et al. (2002) give an additional term for the case of velocity varying only with depth. Zhang et al. (2003a) extend the argument to heterogeneous media. Besides that, Zhang et al. (2003b) provide a more accessible description of the basic theory of the method. In this paper, we describe implementations of this amplitude-preserving downward continuation operators in the $\omega-x$ domain (finite-difference), as well as in the mixed domain.


next up previous print clean
Next: Analytical formulation Up: Vlad et al.: Improving Previous: Vlad et al.: Improving
Stanford Exploration Project
7/8/2003