Constrained least-squares spectral analysis: application to seismic data

Puryear, Charles; Castagna, John P.; Portniaguine, Oleg; Cobos, C.

doi:10.1190/segam2012-0822.1

Cited by 15 publications

(13 citation statements)

References 5 publications

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“…Hence, there is a need for algorithms that can handle both narrowband and broadband t–f representations depending on the actual underlying signal characteristics. In a similar way as the synchrosqueezing transform is combining the continuous wavelet transform, instantaneous frequencies, and reassignment in a single method, mixing algorithms [e.g., Puryear et al , ] or dictionaries [e.g., Rubinstein et al , ] might be alternatives to address these important challenges.…”

Section: Discussionmentioning

confidence: 99%

Spectral estimation-What is new? What is next?

et al. 2014

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Spectral estimation, and corresponding time-frequency representation for nonstationary signals, is a cornerstone in geophysical signal processing and interpretation. The last 10-15 years have seen the development of many new high-resolution decompositions that are often fundamentally different from Fourier and wavelet transforms. These conventional techniques, like the short-time Fourier transform and the continuous wavelet transform, show some limitations in terms of resolution (localization) due to the trade-off between time and frequency localizations and smearing due to the finite size of the time series of their template. Well-known techniques, like autoregressive methods and basis pursuit, and recently developed techniques, such as empirical mode decomposition and the synchrosqueezing transform, can achieve higher time-frequency localization due to reduced spectral smearing and leakage. We first review the theory of various established and novel techniques, pointing out their assumptions, adaptability, and expected time-frequency localization. We illustrate their performances on a provided collection of benchmark signals, including a laughing voice, a volcano tremor, a microseismic event, and a global earthquake, with the intention to provide a fair comparison of the pros and cons of each method. Finally, their outcomes are discussed and possible avenues for improvements are proposed.

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Section: Discussionmentioning

confidence: 99%

Spectral estimation-What is new? What is next?

et al. 2014

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“…TPAS can be used for revealing faults and channels and highlighting the seismic events (Marfurt, Kirlin and Farmer ; Luo, Saleh and Marhoon ; Liu and Marfurt ; Puryear et al . ). Thus, TPAS is a good seismic characterisation method that can be a supplement or alternative of the time–frequency spectrum, which mainly reflects the amplitude and phase changes with respect to the time and frequency.…”

Section: Introductionmentioning

confidence: 97%

Time‐phase amplitude spectra based on a modified short‐time Fourier transform

Zhang

2017

Geophysical Prospecting

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A B S T R A C TThe short-time Fourier transform allows calculation of the amplitude and initial phase distribution of the real signal as functions of time and frequency, whereas the wavelet transform allows calculation of the amplitude and instantaneous phase distribution of the real signal as functions of time and scale. However, for a complete description of the non-stationary signal, we should obtain not only the amplitude, initial phase, and instantaneous phase distribution as functions of time and frequency simultaneously with high precision but also the amplitude distribution as a function of time and phase referred to as the time-phase amplitude spectrum. In this paper, the time-phase amplitude spectrum is presented based on the high-precision time-frequency amplitude spectrum and initial and instantaneous phase spectra that are generated simultaneously by the proposed modified short-time Fourier transform. To minimise the effect of noise on the high-precision time-frequency amplitude spectrum, initial and instantaneous phase spectra, and time-phase amplitude spectrum, the modified short-time Fourier transform is applied to the real signal reconstructed by the peak high-precision time-frequency amplitude spectrum and the high-precision time-frequency instantaneous phase spectrum at that location to obtain the stable high-precision time-frequency amplitude spectrum, initial and instantaneous phase spectra, and stable time-phase amplitude spectrum. Compared with the short-time Fourier transform and wavelet transform, the time-frequency amplitude spectrum and initial and instantaneous phase spectra obtained by the modified short-time Fourier transform have higher precision than those obtained by the shorttime Fourier transform and wavelet transform. Analysis of synthetic data shows that the modified short-time Fourier transform can be used not only for the calculation of the high-precision time-frequency amplitude spectrum, initial and instantaneous phase spectra, and time-phase amplitude spectrum but also for signal reconstruction, stable high-precision time-frequency amplitude spectrum, initial and instantaneous phase spectra, and stable time-phase amplitude spectrum. Analysis of real seismic data applications demonstrates that the stable time-phase amplitude spectrum reveals seismic events with high sensitivity and is well-matched for seismic data processing and interpretation.

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“…Later, Puryear et al . () using iteratively reweighted least‐squares regularization developed constrained least square spectral algorithm. The method has superior resolution compared to CWT and STFT and was applied for mapping stratigraphic features.…”

Section: Introductionmentioning

confidence: 99%

Time‐frequency decomposition of seismic signals via quantum swarm evolutionary matching pursuit

Semnani

Wang

Ostadhassan

et al. 2019

Geophysical Prospecting

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Matching pursuit belongs to the category of spectral decomposition approaches that use a pre‐defined discrete wavelet dictionary in order to decompose a signal adaptively. Although disengaged from windowing issues, matching point demands high computational costs as extraction of all local structure of signal requires a large size dictionary. Thus in order to find the best match wavelet, it is required to search the whole space. To reduce the computational cost of greedy matching pursuit, two artificial intelligence methods, (1) quantum inspired evolutionary algorithm and (2) particle swarm optimization, are introduced for two successive steps: (a) initial estimation and (b) optimization of wavelet parameters. We call this algorithm quantum swarm evolutionary matching pursuit. Quantum swarm evolutionary matching pursuit starts with a small colony of population at which each individual, is potentially a transformed form of a time‐frequency atom. To attain maximum pursuit of the potential candidate wavelets with the residual, the colony members are adjusted in an evolutionary way. In addition, the quantum computing concepts such as quantum bit, quantum gate, and superposition of states are introduced into the method. The algorithm parameters such as social and cognitive learning factors, population size and global migration period are optimized using seismic signals. In applying matching pursuit to geophysical data, typically complex trace attributes are used for initial estimation of wavelet parameters, however, in this study it was shown that using complex trace attributes are sensitive to noisy data and would have lower rate of convergence. The algorithm performance over noisy signals, using non‐orthogonal dictionaries are investigated and compared with other methods such as orthogonal matching pursuit. The results illustrate that quantum swarm evolutionary matching pursuit has the least sensitivity to noise and higher rate of convergence. Finally, the algorithm is applied to both modelled seismograms and real data for detection of low frequency anomalies to validate the findings.

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Constrained least-squares spectral analysis: application to seismic data

Cited by 15 publications

References 5 publications

Spectral estimation-What is new? What is next?

Spectral estimation-What is new? What is next?

Time‐phase amplitude spectra based on a modified short‐time Fourier transform

Time‐frequency decomposition of seismic signals via quantum swarm evolutionary matching pursuit

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