Time–frequency domain local spectral analysis of seismic signals with multiple windows
File(s)
Published version
Author(s)
Wang, Yanghua
Type
Journal Article
Abstract
For a non-stationary seismic signal, time–frequency analysis methods often include a time window function that serves as a weighting function and by which the signal is multiplied to form a segment. The time window function often has the highest weighting coefficient for the central sample of the signal segment. For the rest of the segment, there is no adequate representation in the frequency spectrum. Here I propose to use multiple orthogonal window functions to properly represent the local spectral property in the time–frequency plane and recover the information lost due to time-windowing before applying the Fourier transform. First, I propose to construct multiple window functions directly using a stack of Gaussian functions. The weighted average spectrum of the multiple window functions has a flat passband, which is better than the conventional multiple windows. Taking advantage of the linearity of the Fourier transform, we can apply each window to the analytic signal to generate the instantaneous autocorrelation accordingly and form an averaged instantaneous autocorrelation by a weighted sum before performing the Fourier transform to generate the Wigner–Ville distribution (WVD). This multi-window WVD method successfully represents the local spectrum of the non-stationary seismic signal in the time–frequency plane.
Date Issued
2022-09-07
Date Acceptance
2022-07-26
Citation
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2022, 478 (2265), pp.1-19
ISSN
1364-5021
Publisher
The Royal Society
Start Page
1
End Page
19
Journal / Book Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume
478
Issue
2265
Copyright Statement
© 2022 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
License URL
Identifier
https://royalsocietypublishing.org/doi/10.1098/rspa.2022.0251
Subjects
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status
Published
Article Number
ARTN 20220251
Date Publish Online
2022-09-07