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The critical reflection theorem

Jacob T. Fokkema and Anton Ziolkowski
The critical reflection theorem (in Special issue on Remote sensing, Kenneth Watson (prefacer))
Geophysics (July 1987) 52 (7): 965-972


In predictive deconvolution of seismic data, it is assumed that the response of the earth is white. Any non-white components are presumed to be caused by the source wavelet or by unwanted multiples. We show that this whiteness assumption is invalid at precritical incidence.We consider plane waves incident on a layered acoustic half-space. At exactly critical incidence at any interface in the half-space, the lower layer acts similar to a rigid plate. The response of the half-space is then all-pass, or white. This result we call the critical reflection theorem. The response is also white if the waves are postcritically incident on the lower half-space. In normal data processing these postcritical components are removed by muting. Thus the whiteness assumption is normally applied to exactly that part of the data where it is invalid.The demarcation between precritical and postcritical incidence can be exploited for the purposes of deconvolution, provided the data can be decomposed into plane waves. To develop this application, we consider the response of a point source in the uppermost layer of the layered half-space, with a free surface above. The response is simply a superposition of the plane-wave responses already studied, with complications introduced by the source and receiver ghosts and by multiples in the upper layer. At postcritical incidence the earth response is white for all plane-wave components; the source spectrum may be estimated from the postcritical plane-wave components after removing the effects of ghosts and multiples in the upper layer.If the source signature is already known, the demarcation criterion can be used to separate intrinsic absorption effects from attenuation effects caused by scattering.

ISSN: 0016-8033
EISSN: 1942-2156
Coden: GPYSA7
Serial Title: Geophysics
Serial Volume: 52
Serial Issue: 7
Title: The critical reflection theorem
Title: Special issue on Remote sensing
Author(s): Fokkema, Jacob T.Ziolkowski, Anton
Author(s): Watson, Kennethprefacer
Pages: 965-972
Published: 198707
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
Accession Number: 2002-076101
Categories: Applied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2017, American Geosciences Institute. Reference includes data supplied by Society of Exploration Geophysicists, Tulsa, OK, United States
Update Code: 200223
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