Complex spectral decomposition via inversion strategies

Bonar, David; Sacchi, Mauricio D.

doi:10.1190/1.3513105

Cited by 40 publications

(14 citation statements)

References 11 publications

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“…First, it includes a minimization term to reduce the number and magnitudes of retrieved atoms, yielding a sparse representation [e.g., Chen et al , ]. Second, instead of applying a deflationary approach where atoms are recognized and removed sequentially, basis pursuit identifies all atoms simultaneously by casting both steps into a single inversion problem [ Bonar and Sacchi , ; Zhang and Castagna , ; Vera Rodriguez et al , ].…”

Section: Methodsmentioning

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: Methodsmentioning

confidence: 99%

Spectral estimation-What is new? What is next?

et al. 2014

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“…Complex spectral decomposition (Bonar and Sacchi ) is a signal analysis technique, which decomposes the seismic signal into time–frequency distributions utilizing a dictionary of complex wavelets with different frequencies and phases. A seismic trace s ( t ) at time t can be regarded as the sum of convolutions of complex wavelets (Bonar et al .…”

Section: Complex Spectral Decompositionmentioning

confidence: 99%

“…After deconvolving the dictionary of complex wavelets from the seismic trace, the complex time–frequency spectrum r is obtained. Unlike the real‐valued time–frequency spectrum, the complex time–frequency spectrum is not influenced by the signal polarity and can be used to construct both the energy distribution of reflectivity and the phase information for discrete frequency (Bonar and Sacchi ; Han, Liu, and Yuan ; Liu et al . ).…”

Section: Complex Spectral Decompositionmentioning

confidence: 99%

“…The fast iterative soft thresholding algorithm introduced by Beck and Teboulle () is used to minimize the objective function J :

J = \frac{1}{2} {(‖‖, boldWr - italics)}^{2} + λ {(‖‖, r)}_{1}, λ > 0,

where on the right‐hand side of the equation the first term is the misfit between the observed and predicted data, and the second term is the L1 norm of the reflection series, used to regularize the cost function. Including this L1 norm, adjusted by the regularization parameter λ, produces a sparse solution (Bonar and Sacchi ). By applying sparsity constraints, the inverted reflectivity and wavelet phase will focus on the centre of the corresponding wavelet (Bonar et al .…”

Section: Complex Spectral Decompositionmentioning

confidence: 99%

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Feasibility of utilizing wavelet phase to map the CO₂ plume at the Ketzin pilot site, Germany

Huang

Juhlin

Han³

et al. 2016

Geophysical Prospecting

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Spectral decomposition is a powerful tool that can provide geological details dependent upon discrete frequencies. Complex spectral decomposition using inversion strategies differs from conventional spectral decomposition methods in that it produces not only frequency information but also wavelet phase information. This method was applied to a time‐lapse three‐dimensional seismic dataset in order to test the feasibility of using wavelet phase changes to detect and map injected carbon dioxide within the reservoir at the Ketzin carbon dioxide storage site, Germany. Simplified zero‐offset forward modelling was used to help verify the effectiveness of this technique and to better understand the wavelet phase response from the highly heterogeneous storage reservoir and carbon dioxide plume. Ambient noise and signal‐to‐noise ratios were calculated from the raw data to determine the extracted wavelet phase. Strong noise caused by rainfall and the assumed spatial distribution of sandstone channels in the reservoir could be correlated with phase anomalies. Qualitative and quantitative results indicate that the wavelet phase extracted by the complex spectral decomposition technique has great potential as a practical and feasible tool for carbon dioxide detection at the Ketzin pilot site.

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“…Seismic data are used to detect the distribution of subsurface hydrocarbons (Castagna et al, 2003;Castagna and Sun, 2006;Ebrom, 2004;Sinha et al, 2005;Wang, 2007;Gholami, 2012). Thus, seismic data noise attenuation methods (Bonar and Sacchi, 2010) as well as seismic data processing and interpretation are critical (Askari and Siahkoohi, 2008;Gholami, 2012). Within this context, the study of the TF components of seismic data is critical in seismic data processing and interpretation.…”

Section: Introductionmentioning

confidence: 98%

Application of sparse time-frequency decomposition to seismic data

Wang

2014

Appl. Geophys.

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The Gabor and S transforms are frequently used in time-frequency decomposition methods. Constrained by the uncertainty principle, both transforms produce low-resolution time-frequency decomposition results in the time and frequency domains. To improve the resolution of the time-frequency decomposition results, we use the instantaneous frequency distribution function (IFDF) to express the seismic signal. When the instantaneous frequencies of the nonstationary signal satisfy the requirements of the uncertainty principle, the support of IFDF is just the support of the amplitude ridges in the signal obtained using the short-time Fourier transform. Based on this feature, we propose a new iteration algorithm to achieve the sparse time-frequency decomposition of the signal. The iteration algorithm uses the support of the amplitude ridges of the residual signal obtained with the short-time Fourier transform to update the time-frequency components of the signal. The summation of the updated time-frequency components in each iteration is the result of the sparse timefrequency decomposition. Numerical examples show that the proposed method improves the resolution of the time-frequency decomposition results and the accuracy of the analysis of the nonstationary signal. We also use the proposed method to attenuate the ground roll of fi eld seismic data with good results.

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Complex spectral decomposition via inversion strategies

Cited by 40 publications

References 11 publications

Spectral estimation-What is new? What is next?

Spectral estimation-What is new? What is next?

Feasibility of utilizing wavelet phase to map the CO₂ plume at the Ketzin pilot site, Germany

Application of sparse time-frequency decomposition to seismic data

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Complex spectral decomposition via inversion strategies

Cited by 40 publications

References 11 publications

Spectral estimation-What is new? What is next?

Spectral estimation-What is new? What is next?

Feasibility of utilizing wavelet phase to map the CO2 plume at the Ketzin pilot site, Germany

Application of sparse time-frequency decomposition to seismic data

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Feasibility of utilizing wavelet phase to map the CO₂ plume at the Ketzin pilot site, Germany