Signal leakage in f-x deconvolution algorithms

Gülünay, Necati

doi:10.1190/geo2017-0007.1

Cited by 42 publications

(12 citation statements)

References 27 publications

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“…The optimum filter

\overset{f}{true}

can be obtained in a least‐squares sense by minimizing the innovation energy

J = ∥ ε {false∥}_{2}^{2} = ∥ d - Xf {false∥}_{2}^{2},

known to be

\tilde{boldf} = {({boldX}^{H} X)}^{- 1} false(X^{H} boldd false),

where the superscript ‘ H ’ denotes the transpose‐conjugate of a matrix. For a more algorithmic‐oriented description, the reader is referred to Gülünay () for exact definitions of forward prediction filters.…”

Section: Theorymentioning

confidence: 99%

“…However, due to distortion in amplitudes caused by random noise K linear events cannot be accurately predicted by AR models of order K . Therefore, one should favour larger prediction filters since they are known to perform better in terms of signal preservation (Gülünay ).…”

Section: Theorymentioning

confidence: 99%

“…where the superscript ' H ' denotes the transpose-conjugate of a matrix. For a more algorithmic-oriented description, the reader is referred to Gülünay (2017) for exact definitions of forward prediction filters. The enhanced complex exponentials can then be obtained by convolving the optimum forward and backward filters with the data and finally averaging its overlapping results (Naghizadeh and Sacchi 2012;Gülünay 2017).…”

Section: T H E O R Y F − X Prediction Via Autoregressive Modelsmentioning

confidence: 99%

“…For a more algorithmic-oriented description, the reader is referred to Gülünay (2017) for exact definitions of forward prediction filters. The enhanced complex exponentials can then be obtained by convolving the optimum forward and backward filters with the data and finally averaging its overlapping results (Naghizadeh and Sacchi 2012;Gülünay 2017). The combination of forward and backward prediction is of great interest as it reduces possible errors produced by the individual application of forward (or backward) prediction, such as incomplete prediction of traces along a given direction.…”

Section: T H E O R Y F − X Prediction Via Autoregressive Modelsmentioning

confidence: 99%

“…For sections with more linear events, say K, the filter length should be no less than K if a proper prediction is to be achieved. However, due to distortion in amplitudes caused by random noise K linear events cannot be accurately predicted by AR models of order K. Therefore, one should favour larger prediction filters since they are known to perform better in terms of signal preservation (Gülünay 2017).…”

Section: T H E O R Y F − X Prediction Via Autoregressive Modelsmentioning

confidence: 99%

See 4 more Smart Citations

Widely linear denoising of multicomponent seismic data

Bahia

Sacchi

2019

Geophysical Prospecting

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Seismic data processing is a challenging task, especially when dealing with vector‐valued datasets. These data are characterized by correlated components, where different levels of uncorrelated random noise corrupt each one of the components. Mitigating such noise while preserving the signal of interest is a primary goal in the seismic‐processing workflow. The frequency‐space deconvolution is a well‐known linear prediction technique, which is commonly used for random noise suppression. This paper represents vector‐field seismic data through quaternion arrays and shows how to mitigate random noise by proposing the extension of the frequency‐space deconvolution to its hypercomplex version, the quaternion frequency‐space deconvolution. It also shows how a widely linear prediction model exploits the correlation between data components of improper signals. The widely linear scheme, named widely‐linear quaternion frequency‐space deconvolution, produces longer prediction filters, which have enhanced signal preservation capabilities shown through synthetic and field vector‐valued data examples.

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“…The optimum filter