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Karhunen-Loeve method

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Journal Article
Published: 01 May 2024
Russ. Geol. Geophys. (2024) 65 (5): 650–662.
... ; Naghizadeh and Sacchi, 2018 ), and KarhunenLoeve transform ( Verma et al., 2016 ). All these methods succeed in removing coherent interference and affecting the reflection signals to varying degrees, but have not become widespread among specialists involved in practical data processing. Currently...
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Journal Article
Published: 01 February 2025
Jour. Geol. Soc. India (2025) 101 (2): 251–261.
...Chao Yue; Jianping Wang; Zitao Wang ABSTRACT This paper proposes a parameter compression method using the Karhunen-Loève Transform (K-L) to reduce the computational burden of parameter inversion in groundwater models. Two spatial distributions of hydraulic conductivity (K) were generated using...
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Journal Article
Journal: Geophysics
Published: 21 January 2022
Geophysics (2022) 87 (2): A19–A24.
... , 2008 ), and other approaches. Each technique has advantages and disadvantages and is discussed. Development of the ground-roll suppression methods that do not harm the reflection energy remains relevant. Here, I address the Karhunen-Loeve (KL) transform technique, which is well known and has many...
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Journal Article
Published: 13 July 2021
Bulletin of the Seismological Society of America (2021) 111 (6): 3332–3340.
... the range of relevant earthquake scenarios. This Gaussian random process is discretized using the KarhunenLoeve expansion, which leads to multivariate PC expansions of uncertain hazard curves. The hazard fractiles can be reconstructed during an efficient postprocessing phase that includes the effects...
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Series: Society of Exploration Geophysicists Open File
Published: 01 January 1996
EISBN: 9781560801894
...) in a paper on model-based transform (MBT) processing. A second example, using marine seismic data, is presented by Hinds and Durrheim (1993). These authors used a Karhunen-Loeve (K-L) based multiple attenuation scheme (Jones, 1985; Jones and Levy, 1987) to create an output seismic section. The latter...
Journal Article
Journal: Interpretation
Published: 03 August 2015
Interpretation (2015) 3 (4): SAE19–SAE28.
... interpreted on high-quality 3D seismic data are used to constrain the time window for 41 horizon-based attribute extractions. Next, we used the joint rough sets and Karhunen-Loève transform (K-L transform) selection method to choose the optimal number and the type of seismic attributes that exhibit a high...
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Journal Article
Published: 14 July 2020
Bulletin of the Seismological Society of America (2020) 110 (4): 1982–1995.
... magnitude earthquakes available for development and refinement of early warning procedures; thus, simulated data are a valuable supplement. We demonstrate the advantage of using the KarhunenLoève expansion method for generating stochastic scenario rupture models, as it allows the user to build in desired...
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Journal Article
Journal: Geophysics
Published: 12 July 2017
Geophysics (2017) 82 (5): D265–D277.
... signal is almost entirely obscured by the directly arriving P-, S-, and Stoneley wave modes. Effective extraction of these reflection signals from the full acoustic waveforms is therefore a critical data-processing step. We have examined the use of the Karhunen-Loève (KL) transform, combined with a band...
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Journal Article
Journal: Geophysics
Published: 16 November 2006
Geophysics (2007) 72 (1): V1–V11.
... is then decomposed into orthogonal components with the Karhunen-Loeve (KL) method, also known as the Orthogonal Decomposition Theorem or Principal Component Analysis (PCA) ( Karhunen, 1947 ; Loeve, 1955 ; Golub and Van Loan, 1983 ; Riesz and Nagy, 1955 ; Aster et al., 2005 ). This approach has proven to be very...
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Journal Article
Published: 01 September 2016
Journal of Environmental and Engineering Geophysics (2016) 21 (3): 91–97.
... the quality of seismic images will improve the results of subsequent processing and interpretation. The quality of seismic images can be improved by methods such as f - k filtering, coherency stacks, median filtering, the KarhunenLoève (K-L) transform, singular value decomposition (SVD) ( Bekara and van...
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Journal Article
Journal: Geophysics
Published: 28 January 2016
Geophysics (2016) 81 (1): V79–V88.
... for lateral changes in velocity, thickness, and weathering zone topography. Using a Kuwahara algorithm, we chose the most coherent window within which we applied a structure-oriented Karhunen-Loève filter to model the coherent noise. Finally, we removed the LMO correction and subtracted the modeled ground...
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Journal Article
Journal: Geophysics
Published: 01 January 2002
Geophysics (2002) 67 (1): 177–187.
... of the multistep signal enhancement procedure based upon f − k and Karhunen-Loeve filters combined with the recursive stacking velocity analysis is displayed in Figure 9 . A second test of Karhunen-Loeve filtering was carried out, rejecting the first three to five principal components (i.e., with a lower...
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Journal Article
Journal: Geophysics
Published: 30 November 2000
Geophysics (2001) 66 (3): 932–938.
... are calculated as a smoothed average over overlapping time windows [ Kanasewich, 1981 , his equation (19.3-9)]. The SVD and the covariance-based methods have a similar approach for the solution of the eigenvalues problem. However, while the output of SVD is directly a Karhunen-Loeve transformation...
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Journal Article
Journal: Geophysics
Published: 01 January 2003
Geophysics (2003) 68 (2): 751–759.
... is in the t - x domain and is not well suited for dipping reflectors. A related family of noise-suppression methods are the Karhunen-Loeve (K-L) transforms ( Jones and Levy, 1987 ). In general these methods are either computationally expensive or require complicated modifications for them to give reasonable...
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Journal Article
Journal: Geophysics
Published: 01 April 1999
Geophysics (1999) 64 (2): 564–566.
...Xuewei Liu Abstract Ground roll is the main type of coherent noise in land seismic surveys, and is commonly much stronger in amplitude than the reflection signals. Standard methods for suppressing ground roll include 1-D high-pass filtering and 2-D f-k filtering. High-pass filtering is based...
Journal Article
Journal: Geophysics
Published: 03 January 2024
Geophysics (2024) 89 (1): WB81–WB87.
... the frequency range of 6–40 Hz, which coincides with the frequency range of surface waves. Thus, conventional frequency filtering methods were not effective in suppressing the surface waves. To address this issue, we applied the Karhunen-Loeve (KL) transform as the denoising method ( Liu, 1999 ; Verma et al...
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Journal Article
Journal: Geophysics
Published: 29 August 2017
Geophysics (2017) 82 (6): O83–O89.
... components of one analysis point from the poststack image. Then, we build the analysis window by extracting its neighboring samples through inline and crossline dips. The principal component (Karhunen-Loève) filtered traces are shown in Figure  1b . More details of the energy-ratio coherence algorithm...
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Journal Article
Journal: Geophysics
Published: 19 April 2007
Geophysics (2007) 72 (3): P33–P38.
... attributes computed in the same 100 ms window (25 samples). Figure 2. Crossplots between the amplitude attributes of Figure 1 . Attributes such as arc length and Karhunen-Loeve signal complexity lack clear and useful meaning and are useless. Average instantaneous phase is also...
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Journal Article
Journal: Geophysics
Published: 13 June 2020
Geophysics (2020) 85 (4): WA255–WA267.
...) introduce f – k filtering to reject those undesired events in seismic data. Beresford-Smith and Rango (1989) show that f – k filtering can effectively remove ground roll. Jones and Levy (1987) use the KarhunenLoève (K-L) transform to extract coherent information from...
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Journal Article
Journal: Geophysics
Published: 23 May 2005
Geophysics (2005) 70 (3): V73–V79.
.... The results were nearly indistinguishable from the NMO-dip-filter flow. DMO did not affect the reflections noticeably, but introduced some minor noise artifacts. Hence, we decided not to apply DMO in any of the following flows. The eigenvector filter is similar to the Karhunen-Loeve K-L transform (e.g...
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