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A frequency-approximated approach to Kirchhoff migration

Mark E. Vardy and Timothy J. Henstock
A frequency-approximated approach to Kirchhoff migration
Geophysics (December 2010) 75 (6): S211-S218


The integral solution of the wave equation has long been one of the most popular methods for imaging (Kirchhoff migration) and inverting (Kirchhoff inversion) seismic data. For efficiency, this process is commonly formulated as a time-domain operation on each trace, applying antialiasing through high-cut filtering of the operator or pre-/postmigration dip filtering. Migration in the time domain, however, does not allow for velocity dispersion; standard antialiasing methods assume a flat reflector and tend to overfilter the data. We have recast the Kirchhoff integral in the frequency domain, enabling robust antialias filtering through appropriate dip limiting of each frequency and implicit accommodation of true dispersion. Full frequency decomposition of the input seismogram can be approximated by band-pass filtering (or correlation with band-limited source sweeps for Chirp/Vibroseisdata) into a few narrow-band traces that cumulatively retain the full source bandwidth. From prior knowledge of the source waveform, we have defined suitable bandwidths to describe broadband (3.0 octaves) data using just six frequency bands. Kirchhoff migration of these narrow-band traces using coefficients determined at their central frequencies significantly improves the preservation of higher frequencies and cancellation of steeply dipping aliased energy over traditional time-domain antialiasing methods. If, however, two bands per octave cease to be a robust approach, our frequency-approximated approach provides the processor with ultimate control over the frequency decimation, balancing increased resolution afforded by more bands against computing cost, whereas the number of frequency bands is few enough to permit detailed control over frequency-dependent antialias filtering parameters.

ISSN: 0016-8033
EISSN: 1942-2156
Coden: GPYSA7
Serial Title: Geophysics
Serial Volume: 75
Serial Issue: 6
Title: A frequency-approximated approach to Kirchhoff migration
Affiliation: University of Southampton, School of Ocean and Earth Science, Southampton, United Kingdom
Pages: S211-S218
Published: 201012
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
References: 37
Accession Number: 2011-036561
Categories: Applied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Illustration Description: illus. incl. 2 tables
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: 201121
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