Vector reconstruction of multicomponent seismic data

Stanton, Aaron; Sacchi, Mauricio D.

doi:10.1190/geo2012-0448.1

Cited by 34 publications

(7 citation statements)

References 30 publications

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“…One can represent quaternions in different ways to that of its Cartesian form in equation such as its Cayley–Dickson form, which is given by

q = (a + b i) + (c + d i) j .

Such representation allows one to accommodate, for instance, the Fourier transforms of multivariate post‐stack seismic data (such as PP‐ and PS‐wave datasets) similarly to the approach presented in Stanton and Sacchi (). Although one would be preserving conjugate symmetry properties of the Fourier transform of real‐valued signals, there is no guarantee that previous processing steps have preserved vector fidelity in post‐stack datasets.…”

Section: Discussionmentioning

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%

“…Thanks to the recent developments in quaternion-based signal processing, one can now process vector-valued data following an approach that is not only physically consistent but also offers the possibility of making the most of the additional useful information acquired by multicomponent sensors. In applied seismology, for instance, examples of vector-signal processing through the noncommutative algebra of quaternions include velocity analysis (Grandi, Mazzotti and Stucchi 2007), deconvolution (Menanno and Mazzotti 2012), reconstruction (Stanton and Sacchi 2013) and wavefield separation (Sajeva and Menanno 2017). Other applications of quaternions in the geophysical literature include time-lapse analysis (Witten and Shragge 2006) and anisotropic inversion of cross-dipole sonic logs (Zeng, Yue and Li 2018).…”

Section: Introductionmentioning

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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“…One can represent quaternions in different ways to that of its Cartesian form in equation such as its Cayley–Dickson form, which is given by

q = (a + b i) + (c + d i) j .

Section: Discussionmentioning

confidence: 99%

Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Widely linear denoising of multicomponent seismic data

Bahia

Sacchi

2019

Geophysical Prospecting

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“…Quaternion algebra has been used in various scientific fields, ranging from theo-retical physics [15] to robotics and computer graphics [16]. In seismic processing, it has been used to perform various tasks, such as wavefield separation [1], polarisation studies [17], multi-component velocity analysis [18], multi-component deconvolution [19], vector interpolation of multi-component data [20], and reorientation of vector-sensors [21]. To our knowledge, Le Bihan and Mars [1] were the first to introduce quaternion algebra to seismic data processing, proposing a method to separate wavefields in multi-component multi-channel seismic acquisitions based on an extension to the quaternion field of Singular Value Decomposition (QSVD) [22].…”

Section: Introductionmentioning

confidence: 99%

Characterisation and extraction of a Rayleigh-wave mode in vertically heterogeneous media using quaternion SVD

Sajeva

Menanno

2017

Signal Processing

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We propose a method that identifies a mode of Rayleigh waves and separates it from body waves and from other modes, using quaternions to represent multi-component data. Being well known the abilities of quaternions to handle rotations in space, we use previous results derived from Le Bihan and Mars (2004) to prove that a Rayleigh-wave mode recorded by an array of vector-sensors can be approximated by a sum of trace-by-trace rotating time signals. Our method decomposes the signal into narrow-frequency bands, which undergo both a velocity correction and a polarisation correction. The aim of these corrections is to reduce the mode of interest to a quasi-monochromatic wave packet with infinite apparent velocity and quasi-circular polarisation. Once written in quaternion notation, we refer to this wave packet as quaternion brick. Based on theoretical considerations, we prove that this quaternion brick maps into the first quaternion eigenimage of the quaternion singular value decomposition. We apply this method to synthetic datasets derived from two vertically heterogeneous models to extract the fundamental mode and we prove that it is correctly separated from either a higher mode of propagation or body waves with negligible residual. Results are presented in both time-offset and frequency-phase slowness domains

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“…There exist different interpolation methods that use the properties of various transforms. These include the Fourier transform (Zwartjes and Sacchi, 2007), curvelet transform (Hennenfent andHerrmann, 2006, 2008), Radon transform (Trad et al, 2002,Kabir andVerschuur (1995)), and frequency-wavenumber transform (Stanton and Sacchi, 2013). In our recent publication (Alfaraj et al, 2017), we have interpolated each component of randomly subsampled multicomponent ocean bottom seismic data independently and then decomposed the interpolated components into up-and down-going S-waves.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of S-waves from low-cost randomized and simultaneous acquisition by joint sparse inversion

Alfaraj

Herrmann

Kumar

2017

SEG Technical Program Expanded Abstracts 2017

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Spatial Nyquist sampling rate, which is proportional to the apparent subsurface velocity, is the key deciding cost factor for conventional seismic acquisition. Due to the lower shear wave velocity compared with compressional waves, finer spatial sampling is required to properly record the earlier, which increases the acquisition costs. This is one of the reasons why shear waves are usually not considered in practice. To avoid having the Nyquist criterion as the deciding cost factor and to utilize multicomponent data to its available full extent, we propose acquiring randomly undersampled ocean bottom seismic data. Each component can then be interpolated separately, followed by elastic decomposition to recover up-and down-going S-waves. Instead, we jointly interpolate and decompose the recorded multicomponent data by solving one sparsity promoting optimization problem. This way we ensure that the relative amplitudes of the multicomponent data is preserved. We compare two sparsifying transforms: the curvelet transform and the frequency-wavenumber transform. Another key cost deciding factor for seismic acquisition is the efficiency of acquiring data. This calls for simultaneous acquisition, which requires a source separation step. Similarly, instead of taking a two-step approach, we perform a sparsity-promoting joint source separation decomposition. Results on economically and efficiently acquired synthetic data of both joint methods show their ability of reconstructing accurate up-and down-going S-waves.

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Vector reconstruction of multicomponent seismic data

Cited by 34 publications

References 30 publications

Widely linear denoising of multicomponent seismic data

Widely linear denoising of multicomponent seismic data

Characterisation and extraction of a Rayleigh-wave mode in vertically heterogeneous media using quaternion SVD

Reconstruction of S-waves from low-cost randomized and simultaneous acquisition by joint sparse inversion

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