Generalized seismic wavelets
File(s)
Published version
Author(s)
Wang, Y
Type
Journal Article
Abstract
The Ricker wavelet, which is often employed in seismic analysis, has a symmetrical form.
Seismic wavelets observed from field data, however, are commonly asymmetric with respect
to the time variation. In order to better represent seismic signals, asymmetrical wavelets are
defined systematically as fractional derivatives of a Gaussian function in which the Ricker
wavelet becomes just a special case with the integer derivative of order 2. The fractional
value and a reference frequency are two key parameters in the generalization. Frequency
characteristics, such as the central frequency, the bandwidth, the mean frequency and the
deviation, may be expressed analytically in closed forms. In practice, once the statistical
properties (the mean frequency and deviation) are numerically evaluated from the discrete
Fourier spectra of seismic data, these analytical expressions can be used to uniquely determine
the fractional value and the reference frequency, and subsequently to derive various frequency
quantities needed for the wavelet analysis. It is demonstrated that field seismic signals, recorded
at various depths in a vertical borehole, can be closely approximated by generalized wavelets,
defined in terms of fractional values and reference frequencies.
Seismic wavelets observed from field data, however, are commonly asymmetric with respect
to the time variation. In order to better represent seismic signals, asymmetrical wavelets are
defined systematically as fractional derivatives of a Gaussian function in which the Ricker
wavelet becomes just a special case with the integer derivative of order 2. The fractional
value and a reference frequency are two key parameters in the generalization. Frequency
characteristics, such as the central frequency, the bandwidth, the mean frequency and the
deviation, may be expressed analytically in closed forms. In practice, once the statistical
properties (the mean frequency and deviation) are numerically evaluated from the discrete
Fourier spectra of seismic data, these analytical expressions can be used to uniquely determine
the fractional value and the reference frequency, and subsequently to derive various frequency
quantities needed for the wavelet analysis. It is demonstrated that field seismic signals, recorded
at various depths in a vertical borehole, can be closely approximated by generalized wavelets,
defined in terms of fractional values and reference frequencies.
Date Issued
2015-11-01
Date Acceptance
2015-08-14
Citation
GEOPHYSICAL JOURNAL INTERNATIONAL, 2015, 203 (2), pp.1172-1178
ISSN
0956-540X
Publisher
OXFORD UNIV PRESS
Start Page
1172
End Page
1178
Journal / Book Title
GEOPHYSICAL JOURNAL INTERNATIONAL
Volume
203
Issue
2
Copyright Statement
© The Author 2015. Published by Oxford University Press on behalf of The Royal Astronomical Society.
Identifier
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Subjects
Science & Technology
Physical Sciences
Geochemistry & Geophysics
Time-series analysis
Numerical solutions
Computational seismology
Wave propagation
LAMBERT W FUNCTION
SERIES
Publication Status
Published