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True-amplitude Kirchhoff migration: analytical and geometrical considerations
Thomas Hertweck
ISBN 978-3-8325-0512-7
163 pages, year of publication: 2004
price: 40.50 €
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.
