Generalized S Transform and Seismic Response Analysis of Thin Interbedss Surrounding Regions by Gps

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.

Amplitude spectrum compensation and phase spectrum correction of seismic data based on the generalized S transform

“…Based on the characteristics of the seismic signal, Gao et al (2003) proposed the basic wavelet of the S transform…”

“…Nonetheless, owing to the fixed form of the basic wavelet function, the S transform is not without problems in practical applications. To overcome this limitation, the generalized S transform (GST) was proposed (McFadden, 1999;Gao et al, 2003).…”

S-Transform and Its Application in the Spectrum Analysis of Seismic Signal

“…Generalized S transform overcome the default[2] [3]. The generalized S transform discussed in [2] is adapted to analyze signal in the paper. As in Fig.4, signal is composed of 10Hz,50Hz,80Hz and 90Hz components, its length is 256ms, sampling interval is 1/256ms.…”

The Synchrosqueezing Algorithm Based on Generalized S-transform for High-Precision Time-Frequency Analysis

“…Nevertheless, the fixed changing trend of the basic wavelet in ST limits its practical application. Therefore, many researchers have proposed a variety of forms of generalized S transform (GST) on the basis of ST by introducing variable window parameters to improve the flexibility and adaptability of the wavelet window [4][5][6][7][8][9]. The method based on Empirical Mode Decomposition (EMD) [10] or its extended algorithms (e.g., ensemble empirical mode decomposition (EEMD), complete ensemble empirical mode decomposition (CEEMD)) are other time-frequency transforms, which have also been applied in seismic data and have achieved excellent time-frequency resolution (e.g., [11][12][13][14]).…”

“…The generalized S-transform (GST) introduced by Gao et al [6] overcomes the dilemma of the fixed wavelet in ST by introducing four undetermined parameters (amplitude, energy decay rate, energy delay time, and video rate) to construct the basic wavelet adaptive to the non-stationary signal characteristics in practical application. Due to having no restriction of the time window length, GST can obtain real time-frequency spectra with excellent time-frequency resolution, which provides more possibility and higher accuracy for the detailed information extraction of complicated non-stationary signals than ST.…”