Journal ArticleDOI
Generalized S Transform and Seismic Response Analysis of Thin Interbedss Surrounding Regions by Gps
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TLDR
In this paper, the generalized S transform (GST) is generalized with two steps, and two kinds of new transforms are obtained, which are called generalized s transform (gST) and gST2.Abstract:
S transform (ST) proposed by Stockwell et al. is the unique transform that provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum. This feature is very important for applications. However, the ST can't work well for seismic data analysis since its basic wavelet is not appropriate. In this paper, the ST is generalized with two steps, and two kinds of new transforms are obtained, which are called generalized S transform (GST). First, the basic wavelet in ST is replaced by a modulated harmonic wave with four undetermined coefficients, and then a new transform and its inverse are given, called GST1. Second, taking a linear combination of the basic wavelets in step 1 as a new basic wavelet, called GST2, and its inverse is constructed. To compare ST with GST, the ST and GST method are used to analyze several typical models of thin beds, respectively. The results show that the resolution of GST is better than that of ST. The GST method can determine accurately the location of interfaces of acoustic impedance in thin interbeds of thickness being only an eighth wavelength, while ST method can't. In this study, the effectiveness of GST method is also verified by processing results of real data.read more
Citations
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Journal ArticleDOI
A basis for efficient representation of the S-transform
TL;DR: A more efficient representation is introduced here as a orthogonal set of basis functions that localizes the spectrum and retains the advantageous phase properties of the S-transform, and can perform localized cross spectral analysis to measure phase shifts between each of multiple components of two time series.
Journal ArticleDOI
Time-Frequency Analysis of Seismic Data Using Synchrosqueezing Transform
TL;DR: The synchrosqueezing transform (SST) is a promising tool to provide a detailed time-frequency representation and its potential to seismic signal processing applications is shown.
Journal ArticleDOI
Spectral decomposition of seismic data with reassigned smoothed pseudo Wigner–Ville distribution
Xiaoyang Wu,Tianyou Liu +1 more
TL;DR: In this paper, a smoothed pseudo Wigner-Ville distribution (SPWVD) with Gauss kernel function was employed to reduce cross-term interference in time and frequency domain, then reassign values of SPWVD according to the center of gravity of the considering energy region.
Journal ArticleDOI
Seismic Time–Frequency Analysis via STFT-Based Concentration of Frequency and Time
TL;DR: Concentration in frequency and time is proposed to distinguish the different TF contents of time-dependent signals with time-varying amplitude and instantaneous frequencies and this promising TF analysis tool is introduced to seismic data processing.
Journal ArticleDOI
Self-Adaptive Generalized S-Transform and Its Application in Seismic Time–Frequency Analysis
TL;DR: This paper proposes to set the parameters of the GST adaptively using the instantaneous frequency (IF) of seismic traces, and names the proposed SAGST as the self-adaptive GST (SAGST).
References
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Journal ArticleDOI
Wavelet Transforms and their Applications to Turbulence
TL;DR: Wavelet transforms are recent mathematical techniques, based on group theory and square integrable representations, which allows one to unfold a signal, or a field, into both space and scale, and possibly directions.
Journal ArticleDOI
Localization of the complex spectrum: the S transform
TL;DR: The S transform is shown to have some desirable characteristics that are absent in the continuous wavelet transform, and provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum.
Journal Article
Localisation of the complex spectrum : The S transform
TL;DR: The S transform as discussed by the authors is an extension to the ideas of the Gabor transform and the Wavelet transform, based on a moving and scalable localising Gaussian window and is shown here to have characteristics that are superior to either of the transforms.
Book ChapterDOI
Reading and Understanding Continuous Wavelet Transforms
TL;DR: One of the aims of wavelet transforms is to provide an easily interpretable visual representation of signals that is a prerequisite for applications such as selective modifications of signals or pattern recognition.
Journal ArticleDOI
Instantaneous parameters extraction via wavelet transform
TL;DR: A novel theorem on the wavelet transform and Hilbert transform and applied to extract the instantaneous parameters of energy-limited, real signals shows advantages in both precision and antinoise performance.