An important task in seismic reflection imaging is to estimate subsurface structures from the prestack data. This means that the reflection events in the recorded data have to be transformed into images in the depth domain, the reflectors. A geometrically appealing approach for the corresponding process is Kirchhoff migration which is based on an integral solution of the wave equation. Applied in its original purely kinematic form, this process provides a structural image of the target region under investigation. However, Kirchhoff migration is also able to handle the amplitude-related aspects of wave propagation, thus allowing to assign physically sound amplitude values to reflector images. In such a true-amplitude migration, the geometrical spreading effects are removed from the input data during the imaging process and, thus, reflector amplitudes become basically a measure of the angle-dependent reflection coefficient. Commencing with the basics of wave propagation and ray theory, a complete description of Kirchhoff migration is presented. By relating the strict mathematical derivation of true-amplitude Kirchhoff migration to clear geometrical concepts, the gap between the originally graphical migration schemes and the nowadays available analytical descriptions based on a stationary-phase evaluation is closed. Further aspects relevant to the correct recovery of amplitudes in depth migration, such as the handling of topography and irregular geometries, are explained in a mathematical as well as in a geometrical manner. Finally, Kirchhoff migration is integrated into a seismic reflection imaging workflow based on the data-driven common-reflection-surface (CRS) stack method.

True-amplitude Kirchhoff migration: analytical and geometrical considerations

Science & Math

Hertweck, Thomas

Earth Sciences

Logos Verlag

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True-amplitude Kirchhoff migration: analytical and geometrical considerations