CRS-based minimum-aperture Kirchhoff migration in the time domain

Miriam Eva Tanja Spinner
2007
A key element in the seismic imaging sequence is migration, the transformation of the preprocessed seismic data into a structural image of the subsurface which resembles the distribution of geological interfaces. Thus, the primary aim of migration is to reverse the effects of wave propagation. So-called true-amplitude migration schemes additionally appropriately compensate for the dynamic effects of the wave propagation. This allows to recover reflection amplitudes which can be directly related
more » ... be directly related to the angle-dependent reflection coefficients at the interfaces. The latter can finally be inverted for physical properties which characterise the adjacent rock formations. Migration requires a solution of the elastodynamic wave equation which is usually employed to describe the wave propagation in the Earth. Various approaches for this task have been proposed. In this thesis, I consider the Kirchhoff migration which is based on an integral solution of the wave equation. An additional weighting factor ensures that the migrated output is true-amplitude. The evident output domain of migration is the depth domain in which the migrated image resembles the actual geological structures. However, in this domain the solution of the wave equation requires a model of the velocity distribution in depth. Errors in the estimated model lead to poorly focussed and mispositioned images and additionally bias the migrated amplitudes. Time migration has been introduced as an approximate alternative requiring only smooth models of integral velocities. As time migration shows a strongly reduced sensitivity to model errors, it is well suited for studies on reflection amplitudes. The time-migrated image is still defined in the time domain, thus requiring a subsequent time-to-depth conversion for interpretation. Kirchhoff migration can be realised in terms of a so-called diffraction stack based on Huygens' principle. From a theoretical point of view, such a diffraction stack requires an integration over an infinite aperture. Of course, this is infeasible due to the always finite acquisition area. Therefore, an optimum finite aperture has to be defined which guarantees optimal resolution in the image, physically sound amplitudes, and the highest possible signal-to-noise ratio at the same time. This optimum aperture corresponds to the minimum aperture given by the size of the first projected Fresnel zone. It is centred around the stationary point where the migration operator is tangent to the actual reflection event. The usually employed smooth migration velocity models obtained by means of stacking velocities or by migration velocity analysis are not sufficient to calculate these properties prior to migration. Thus, minimum-aperture migration cannot be addressed by conventional migration schemes. In this thesis, a generalisation of stacking velocity analysis called Common-Reflection-Surface stack method is utilised to obtain information beyond stacking velocity. Based on a spatial stacking operator, the Common-Reflection-Surface stack provides a whole set of stacking parameters which characterise the kinematics of the reflection events. These so-called kinematic wavefield attributes cannot only be utilised in the migration velocity model building but also to estimate the location of the stationary i Abstract point and the size of the projected Fresnel zone. This allows a direct application of (true-amplitude) minimum-aperture migration. In this thesis, the theoretical background as well as the practical application of minimum-aperture Kirchhoff migration in the time domain is discussed for the 2.5D and 3D case. I demonstrate the potential of the method for synthetic as well as real datasets. The time-domain approach allows an efficient and stable implementation of the minimum-aperture estimation due to the considered analytic migration operators. The main observation is an overall improved quality of the migrated images, reduced imaging artifacts, and a higher signal-to-noise ratio. Amplitudes extracted from the migrated images show less scattering and better defined AVO/AVA responses compared to the conventional approach. ii
doi:10.5445/ir/1000007099 fatcat:7ovwebw5ivalvdt3wmd7w5osbq