Quaternionic rank-reduction methods for vector-field seismic data processing

Bahia, Breno; Sacchi, Mauricio D.

doi:10.1016/j.dsp.2019.02.001

Cited by 15 publications

(4 citation statements)

References 22 publications

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“…Canales ), could lead to better results ,but this was not the focus of this paper. Also, one should bear in mind that all of the components are assumed to contain signal since noise‐only components can degrade the final results of the quaternion components (Bahia and Sacchi ). In such cases, one is likely to be dealing with uncorrelated components which will yield vanishing off‐diagonal terms in the augmented covariance matrix (equation ).…”

Section: Discussionmentioning

confidence: 99%

“…The advent of the QFT allows signal‐processing techniques performed in the frequency domain, such as the FXDECON, to be generalized to quaternion‐defined datasets (Ell and Sangwine ; Ortolani et al . ; Bahia and Sacchi ). However, since quaternion algebra is non‐commutative, the QFT is not uniquely defined and requires the definition of a side for the transformation.…”

Section: Theorymentioning

confidence: 97%

“…In this view, an excellent example to be given is that of the QFT, but detailed explanations on the topic can be found elsewhere in literature such as Ell et al (2014). The advent of the QFT allows signal-processing techniques performed in the frequency domain, such as the FXDECON, to be generalized to quaternion-defined datasets (Ell and Sangwine 2007;Ortolani et al 2017;Bahia and Sacchi 2019). However, since quaternion algebra is noncommutative, the QFT is not uniquely defined and requires the definition of a side for the transformation.…”

Section: Quaternion Fourier Transformmentioning

confidence: 99%

“…This preferential association, however, is application‐dependent, and it can be defined accordingly to the practitioner's preference. In the case of applied seismology, both the definitions of specific side and eigenaxis have no clear implication on the processing steps (Stanton and Sacchi ; Bahia and Sacchi ).…”

Section: Theorymentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

Section: Theorymentioning

confidence: 97%