Annual Report 2000 - WIT

Wave Inversion Technology, Report No. 4, pages 99-109
AVO curves from prestack depth migrated images
based on the Unified Approach Theory
Alexander Goertz, Matthias Riede and Thomas Hertweck 1
keywords: True Amplitude Kirchhoff Depth Migration and Demigration, AVO,
Reflectivity
ABSTRACT
The unified approach theory establishes a method to convert seismic data from the
time to the depth domain and vice versa without loss of amplitude information. In
this contribution, we present an application of the unified approach theory for trueamplitude
depth imaging. By using a weighted Kirchhoff-type diffraction stack that
correctly accounts for geometrical spreading effects in the propagating wavefield, we
are able to yield amplitude-versus-offset (AVO) curves of high precision in the depth
domain. By comparing the results with analytical values calculated with Zoeppritz'
equations, we show the correct treatment of amplitudes for the inverse (migration)
process as well as for the forward (demigration) process. A synthetic example of a
steeply dipping fault shows how fine-scaled variations of in-situ properties (as, e.g.,
hydraulic properties) can be detected in complex environments.
INTRODUCTION
We present a method to obtain highly accurate information about the offset-dependent
reflectivity in the depth domain. This is an application of the Unified Approach theory
(Hubral et al., 1996),(Tygel et al., 1996) which establishes a pair of integrals to
perform transformations from time to depth and vice versa. Both of these stacking operations
can be performed as a true-amplitude process in terms of the correct treatment
of geometrical spreading effects, i.e., the transformation of these effects from the input
configuration to those of the output configuration. We show that the method is capable
of retrieving the correct amplitudes in the depth domain as well as in the time domain.
By cascading migration and demigration for different configurations, arbitrary seismic
image transformations can be performed. The accuracy of the results is tested by
comparing the migrated and demigrated amplitudes with analytical AVO-curves calculated
by means of Zoeppritz' equations (Zoeppritz, 1919). In order to apply the correct
1 email: Alexander.Goertz@gpi.uni-karlsruhe.de
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