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Tikhonov regularization

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Journal Article

Robust estimation of structural orientation parameters and 2D/3D local anisotropic Tikhonov regularization Available to Purchase

Ali Gholami, Silvia Gazzola
Journal: Geophysics
Published: 03 October 2024
Geophysics (2024) 89 (6): V521–V536.
DOI: https://doi.org/10.1190/geo2023-0632.1
... inverse problems. Specifically, our approach adaptively integrates recovered information about structural orientation, enhancing the effectiveness of anisotropic Tikhonov regularization in recovering geophysical parameters. The paper also discusses the automatic tuning of algorithmic parameters...
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View PDF for article title, Robust estimation of structural orientation parameters and 2D&#x2F;3D local anisotropic <span class="search-highlight">Tikhonov</span> <span class="search-highlight">regularization</span>
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Book Chapter

Generalized Tikhonov Regularization Available to Purchase

Author(s)
Herman Jaramillo, Andreas Rüger
Book: Machine Learning for Science and Engineering Volume I: Fundamentals
Series: Course Notes Series
Publisher: Society of Exploration Geophysicists
Published: 30 March 2023
DOI: 10.1190/1.9781560803898.appa
EISBN: 9781560803898
View PDF for content titled, Generalized <span class="search-highlight">Tikhonov</span> <span class="search-highlight">Regularization</span>
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AI of Figure 1 calculated using (a) Tikhonov regularization and (b) TV. (c) AI at the location of trace 105 using Tikhonov and TV and (d) Tikhonov followed by TV regularization.

AI of Figure  1 calculated using (a) Tikhonov regularization and (b) TV. (... Available to Purchase

Published: 22 November 2021
Figure 2. AI of Figure  1 calculated using (a) Tikhonov regularization and (b) TV. (c) AI at the location of trace 105 using Tikhonov and TV and (d) Tikhonov followed by TV regularization.
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Tikhonov regularization L‐curves for the tomography at different periods. Solid dots are the optimal Tikhonov regularization parameters. The color version of this figure is available only in the electronic edition.

Tikhonov regularization L‐curves for the tomography at different periods. S... Available to Purchase

Published: 08 December 2020
Figure 9. Tikhonov regularization L‐curves for the tomography at different periods. Solid dots are the optimal Tikhonov regularization parameters. The color version of this figure is available only in the electronic edition.
Image
Tikhonov regularization L‐curves for joint inversion of receiver functions and surface‐wave dispersions at different stations. Solid dots are the optimal Tikhonov regularization parameters. The color version of this figure is available only in the electronic edition.

Tikhonov regularization L‐curves for joint inversion of receiver functions ... Available to Purchase

Published: 08 December 2020
Figure 13. Tikhonov regularization L‐curves for joint inversion of receiver functions and surface‐wave dispersions at different stations. Solid dots are the optimal Tikhonov regularization parameters. The color version of this figure is available only in the electronic edition.
Image
Tikhonov regularization by 3T projection. Corresponding to any regularization parameter in Tikhonov regularization, there is an equivalent 3T projection. The set of increasing regularization values follows the magenta regularization paths on the 3T Explorer. The red and green dots correspond to specific low and medium regularization values. In this figure, paths are for S-domain target reflectivities.

Tikhonov regularization by 3T projection. Corresponding to any regularizati... Available to Purchase

Published: 02 August 2018
Figure 6. Tikhonov regularization by 3T projection. Corresponding to any regularization parameter in Tikhonov regularization, there is an equivalent 3T projection. The set of increasing regularization values follows the magenta regularization paths on the 3T Explorer. The red and green dots
Journal Article

Blind inversion of multidimensional seismic data using sequential Tikhonov and total variation regularizations Available to Purchase

Saber Jahanjooy, Mohammad Ali Riahi, Hamed Ghanbarnejad Moghanloo
Journal: Geophysics
Published: 22 November 2021
Geophysics (2022) 87 (1): R53–R61.
DOI: https://doi.org/10.1190/geo2020-0692.1
...Figure 2. AI of Figure  1 calculated using (a) Tikhonov regularization and (b) TV. (c) AI at the location of trace 105 using Tikhonov and TV and (d) Tikhonov followed by TV regularization. ...
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View PDF for article title, Blind inversion of multidimensional seismic data using sequential <span class="search-highlight">Tikhonov</span> and total variation <span class="search-highlight">regularizations</span>
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Journal Article

An adaptive iterative method for downward continuation of potential-field data from a horizontal plane Available to Purchase

Xiaoniu Zeng, Xihai Li, Juan Su, Daizhi Liu, Hongxing Zou
Journal: Geophysics
Published: 09 July 2013
Geophysics (2013) 78 (4): J43–J52.
DOI: https://doi.org/10.1190/geo2012-0404.1
...Xiaoniu Zeng; Xihai Li; Juan Su; Daizhi Liu; Hongxing Zou ABSTRACT We have developed an improved adaptive iterative method based on the nonstationary iterative Tikhonov regularization method for performing a downward continuation of the potential-field data from a horizontal plane. Our method uses...
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“L-curve” for selecting Tikhonov’s regularization parameter.

“L-curve” for selecting Tikhonov’s regularization parameter. Available to Purchase

Published: 04 December 2013
Figure 7. “L-curve” for selecting Tikhonov’s regularization parameter.
Image
Time-lapse Tikhonov-regularized inversion of the 1994 and 2001 Sleipner data set vintages. (a) Inverted baseline acoustic impedance model. (b) Inverted monitor acoustic impedance model. (c) The difference between (a) and (b). The red rectangles indicate the locations of the closeups shown in Figure 8.

Time-lapse Tikhonov-regularized inversion of the 1994 and 2001 Sleipner dat... Available to Purchase

Published: 01 July 2023
Figure 6. Time-lapse Tikhonov-regularized inversion of the 1994 and 2001 Sleipner data set vintages. (a) Inverted baseline acoustic impedance model. (b) Inverted monitor acoustic impedance model. (c) The difference between (a) and (b). The red rectangles indicate the locations of the closeups
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Time-lapse Tikhonov-regularized inversion and 4D JIS results at the well location compared to the impedance well log and the well-derived initial velocity model.

Time-lapse Tikhonov-regularized inversion and 4D JIS results at the well lo... Available to Purchase

Published: 01 July 2023
Figure 9. Time-lapse Tikhonov-regularized inversion and 4D JIS results at the well location compared to the impedance well log and the well-derived initial velocity model.
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Matrix inverted in Tikhonov's regularization applied to nonstationary line fitting (a) and the distribution of its eigenvalues (b). The regularization parameter ϵ=0.1 corresponds to mild smoothing. The condition number is κ≈888888.

Matrix inverted in Tikhonov's regularization applied to nonstationary line ... Available to Purchase

Published: 29 December 2008
Figure 4. Matrix inverted in Tikhonov's regularization applied to nonstationary line fitting (a) and the distribution of its eigenvalues (b). The regularization parameter ϵ = 0.1 corresponds to mild smoothing. The condition number is κ ≈ 888888 .
Image
Matrix inverted in Tikhonov's regularization applied to nonstationary line fitting (a) and the distribution of its eigenvalues (b). The regularization parameter ϵ = 10 corresponds to strong smoothing. The condition number is κ≈14073. Eigenvalues are poorly clustered.

Matrix inverted in Tikhonov's regularization applied to nonstationary line ... Available to Purchase

Published: 29 December 2008
Figure 5. Matrix inverted in Tikhonov's regularization applied to nonstationary line fitting (a) and the distribution of its eigenvalues (b). The regularization parameter ϵ = 10 corresponds to strong smoothing. The condition number is κ ≈ 14073 . Eigenvalues are poorly clustered.
Journal Article

Iterative imaging method based on Tikhonov regularized downward continuation and its unmanned aerial vehicle aeromagnetic application: A case study from a Sijiaying iron deposit in eastern Hebei Province, China Available to Purchase

Wenna Zhou, Chong Zhang, Hai Tang, Qiang Li, Shuiliang Tang
Journal: Geophysics
Published: 09 October 2023
Geophysics (2023) 88 (6): B343–B354.
DOI: https://doi.org/10.1190/geo2022-0699.1
... to accomplish this goal ( Fedi and Florio, 2002 ; Pašteka et al., 2012 ; Zhang et al., 2018 ; Zhou et al., 2018 ). Tikhonov regularized downward continuation (TRDC) is a widely used stable and effective method that can calculate depth information of geologic sources without additional normalized...
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View PDF for article title, Iterative imaging method based on <span class="search-highlight">Tikhonov</span> <span class="search-highlight">regularized</span> downward continuation and its unmanned aerial vehicle aeromagnetic application: A case study from a Sijiaying iron deposit in eastern Hebei Province, China
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Image
Simultaneous FWI using Tikhonov model-difference regularization with the long-wavelength inversion of Figure 6 supplied as a prior. Note that such a multiscale approach can now resolve the short-wavelength positive-velocity changes of Figure 2. Strong Tikhonov regularization results in underestimated velocity changes within the reservoir, but correctly locates the anomalies.

Simultaneous FWI using Tikhonov model-difference regularization with the lo... Available to Purchase

Published: 07 November 2016
Figure 7. Simultaneous FWI using Tikhonov model-difference regularization with the long-wavelength inversion of Figure  6 supplied as a prior. Note that such a multiscale approach can now resolve the short-wavelength positive-velocity changes of Figure  2 . Strong Tikhonov regularization results
Journal Article

The positioning of buried pipelines from magnetic data Available to Purchase

Caifang Li, Dejun Liu, Jin Meng, Jialin Liu, Yan Zhang
Journal: Geophysics
Published: 10 November 2020
Geophysics (2020) 85 (6): J111–J120.
DOI: https://doi.org/10.1190/geo2020-0157.1
... angle of 90° marks the location of a buried pipeline, whereas the depth is the distance between the location of the 90° and its adjacent 0°. The iterative Tikhonov regularization method for downward continuation, while separating the superimposed anomalies and enhancing the horizontal resolution, also...
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View PDF for article title, The positioning of buried pipelines from magnetic data
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Journal Article

3D magnetotelluric inversion using a limited-memory quasi-Newton optimization Available to Purchase

Dmitry Avdeev, Anna Avdeeva
Journal: Geophysics
Published: 27 April 2009
Geophysics (2009) 74 (3): F45–F57.
DOI: https://doi.org/10.1190/1.3114023
...Dmitry Avdeev; Anna Avdeeva Abstract The limited-memory quasi-Newton method with simple bounds is used to develop a novel, fully 3D magnetotelluric (MT) inversion technique. This nonlinear inversion is based on iterative minimization of a classical Tikhonov regularized penalty function. However...
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View PDF for article title, 3D magnetotelluric inversion using a limited-memory quasi-Newton optimization
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The synthetic model used to test the seismic algorithm (SVD): a) Model with two seismic areas, where one is a yellow square (1,000 m/s) and the other a blue area (400 m/s); b) trajectories of the seismic rays (light blue) used in the model; c) model obtained by the algorithm (SVD) results before the Tikhonov regularization; d) model obtained after the Tikhonov regularization; e) and f) errors (%) of the cells of the synthetic model before and after the Tikhonov regularization.

The synthetic model used to test the seismic algorithm (SVD): a) Model with... Available to Purchase

Published: 01 December 2020
) results before the Tikhonov regularization; d) model obtained after the Tikhonov regularization; e) and f) errors (%) of the cells of the synthetic model before and after the Tikhonov regularization.
Journal Article

Numerical Inversion of the Sumudu Integral Transform in the Simulation of Electromagnetic Sounding of the Earth’s Interior Available to Purchase

M.I. Epov, О.V. Nechaev, V.N. Glinskikh
Published: 01 July 2023
Russ. Geol. Geophys. (2023) 64 (7): 860–869.
DOI: https://doi.org/10.2113/RGG20234537
... of linear algebraic equations. We apply Tikhonov’s method for regularization of this type system. The paper proposes a technique for constructing a parametrized regularizing matrix that takes into account the properties of the Sumudu images obtained by modeling the electromagnetic sounding process...
FIGURES
View PDF for article title, Numerical Inversion of the Sumudu Integral Transform in the Simulation of Electromagnetic Sounding of the Earth’s Interior
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A noise-free synthetic test: (a) true velocity model, (b) first-order Tikhonov regularization, (c) second-order Tikhonov regularization, and (d) compactness constraints.

A noise-free synthetic test: (a) true velocity model, (b) first-order Tikho... Available to Purchase

Published: 11 June 2007
Figure 2. A noise-free synthetic test: (a) true velocity model, (b) first-order Tikhonov regularization, (c) second-order Tikhonov regularization, and (d) compactness constraints.