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Bott's method

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Comparison of convergences of Bott’s method (gray dots, r1=r2=1) and extended Bott’s method (black dots, r1=0.9 and r2=0.1) along the iterations, stabilized with L=5. The noise in data has a standard deviation of 0.1 mGal.

Comparison of convergences of Bott’s method (gray dots, r 1 = r ... Available to Purchase

Published: 22 August 2014
Figure 8. Comparison of convergences of Bott’s method (gray dots, r 1 = r 2 = 1 ) and extended Bott’s method (black dots, r 1 = 0.9 and r 2 = 0.1 ) along the iterations, stabilized with L = 5 . The noise in data has a standard deviation
Journal Article

Modified Bott-Parker method for gravimetric Moho modeling Available to Purchase

Jinbo Li, Chuang Xu, Huiyou He, Fengshun Zhu, Yang Li, Heping Sun
Journal: Geophysics
Published: 20 February 2025
Geophysics (2025) 90 (2): G59–G72.
DOI: https://doi.org/10.1190/geo2024-0382.1
..., existing inversion methods such as the Parker-Oldenburg (P-O) and Bott-Parker (B-P) methods face challenges including nonconvergence and noise amplification. We develop a modified B-P (mB-P) method to estimate the Moho depth with variable density contrast from gravity data. Our method casts exponential...
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Journal Article

Fast gravity inversion of basement relief Available to Purchase

João B. C. Silva, Darcicléa F. Santos, Karina P. Gomes
Journal: Geophysics
Published: 22 August 2014
Geophysics (2014) 79 (5): G79–G91.
DOI: https://doi.org/10.1190/geo2014-0024.1
...Figure 8. Comparison of convergences of Bott’s method (gray dots, r 1 = r 2 = 1 ) and extended Bott’s method (black dots, r 1 = 0.9 and r 2 = 0.1 ) along the iterations, stabilized with L = 5 . The noise in data has a standard deviation...
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Journal Article

Efficient gravity inversion of discontinuous basement relief Available to Purchase

Darcicléa F. Santos, João B. C. Silva, Cristiano M. Martins, Raphael Di Carlo S. dos Santos, Laisse C. Ramos, Ana Carolina M. de Araújo
Journal: Geophysics
Published: 05 May 2015
Geophysics (2015) 80 (4): G95–G106.
DOI: https://doi.org/10.1190/geo2014-0513.1
...Darcicléa F. Santos; João B. C. Silva; Cristiano M. Martins; Raphael Di Carlo S. dos Santos; Laisse C. Ramos; Ana Carolina M. de Araújo ABSTRACT We have developed a gravity inversion method to estimate a discontinuous basement relief based on an extended version of Bott’s method that allows...
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View of the inverted basement relief of the rift basin with six different size grabens using (a) our developed method with λh=1, λm=1, and ω=10−2; its misfit is shown in (b); (c) Bott’s method. The locations of seven known depths are denoted with the red stars. (d) The NVDR-THDR of the inverted result using Bott’s method.

View of the inverted basement relief of the rift basin with six different s... Available to Purchase

Published: 29 August 2018
Figure 5. View of the inverted basement relief of the rift basin with six different size grabens using (a) our developed method with λ h = 1 , λ m = 1 , and ω = 10 − 2 ; its misfit is shown in (b); (c) Bott’s method. The locations of seven known depths
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Stabilization. (a) True (black thick line) and estimated (red line) basement topographies obtained by applying Bott’s method to a noise-corrupted anomaly after 15 iterations. (b-d) Understabilized (L=5), stabilized (L=19), and overstabilized (L=41) solutions (red lines), respectively, using the extended Bott’s method.

Stabilization. (a) True (black thick line) and estimated (red line) basemen... Available to Purchase

Published: 22 August 2014
Figure 6. Stabilization. (a) True (black thick line) and estimated (red line) basement topographies obtained by applying Bott’s method to a noise-corrupted anomaly after 15 iterations. (b-d) Understabilized ( L = 5 ), stabilized ( L = 19 ), and overstabilized ( L = 41
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Coefficient ck (given in equation 21) measuring the average proximity between the true and the estimated basements along the iterations for the Bott’s method (gray dots: r1=r2=1) and the extended Bott’s method (black dots: r1=0.9 and r2=0.1) using a step-size optimization similar to the one used in Marquardt’s method.

Coefficient c k (given in equation  21 ) measuring the average p... Available to Purchase

Published: 22 August 2014
Figure 3. Coefficient c k (given in equation  21 ) measuring the average proximity between the true and the estimated basements along the iterations for the Bott’s method (gray dots: r 1 = r 2 = 1 ) and the extended Bott’s method (black dots: r 1 = 0.9
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The inverted basement relief of the Xi’an depression in the Weihe Basin using (a) Bott’s method and (b) the modified method. The yellow stars denote the three known depth points. The red solid line is the location of the profile shown in Figure 10.

The inverted basement relief of the Xi’an depression in the Weihe Basin usi... Available to Purchase

Published: 29 August 2018
Figure 9. The inverted basement relief of the Xi’an depression in the Weihe Basin using (a) Bott’s method and (b) the modified method. The yellow stars denote the three known depth points. The red solid line is the location of the profile shown in Figure  10 .
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Computer time against the number of parameters of the interpretation model required by the Gauss-Newton method with the Gauss-Jordan (dashed line) and conjugate gradient (dotted line) implementations for solving the linear system of equations at each iteration. The computer time required by the proposed extension of Bott’s method is shown in continuous black line.

Computer time against the number of parameters of the interpretation model ... Available to Purchase

Published: 22 August 2014
required by the proposed extension of Bott’s method is shown in continuous black line.
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Real data inversion. (a) Gravity anomaly over the Chintalapudi Basin, India. (b and c) The estimated relief through the extended Bott’s method using, respectively, the proposed modeling and Chakravarthi and Sundararajan’s (2004) functional, the latter reported by Silva et al. (2014). (d and e) The estimated basement topographies through the method of Santos et al. (2015) using, respectively, the proposed modeling and Chakravarthi and Sundararajan’s (2004) functional, the latter reported by Santos et al. (2015).

Real data inversion. (a) Gravity anomaly over the Chintalapudi Basin, India... Available to Purchase

Published: 20 December 2016
Figure 7. Real data inversion. (a) Gravity anomaly over the Chintalapudi Basin, India. (b and c) The estimated relief through the extended Bott’s method using, respectively, the proposed modeling and Chakravarthi and Sundararajan’s (2004) functional, the latter reported by Silva et al. (2014
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Chintalapudi basin. (a) Observed anomaly, (b) inverted anomaly shown in perspective view, (c) in perspective view plus superposed contour curves, (d) with highlighted interval between 2.9 and 3.1 km contour curves. (e) Residuals between the observed and the fitted anomaly produced by the solution shown in panel (b). (f) Solution produced by the extended Bott’s method. Labels A, B, and C in panel (b) refer to three subbasins located below the average basin floor.

Chintalapudi basin. (a) Observed anomaly, (b) inverted anomaly shown in per... Available to Purchase

Published: 05 May 2015
by the solution shown in panel (b). (f) Solution produced by the extended Bott’s method. Labels A, B, and C in panel (b) refer to three subbasins located below the average basin floor.
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Estimated basement relief from different inversion methods using the synthetic gravity data shown in Figure 1b; the inverted results are from using (a) our developed method, (b) Bott’s method, (c) the l1-norm-only as the model constraint, and (d) the l2-norm-only as the model constraint. The red stars locate the positions of known depths. (e-h) The misfits between the four inverted basements and the simulated model, respectively; the red color indicates that the inverted basement is shallower than the simulated one, whereas the blue indicates a deeper inverted result. (i-l) The fitted gravity anomalies (the black dotted lines) of each estimated result; the synthetic gravity anomalies are in the solid color lines.

Estimated basement relief from different inversion methods using the synthe... Available to Purchase

Published: 29 August 2018
Figure 2. Estimated basement relief from different inversion methods using the synthetic gravity data shown in Figure  1b ; the inverted results are from using (a) our developed method, (b) Bott’s method, (c) the l 1 -norm-only as the model constraint, and (d) the l 2
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(a) Computer time as a function of the number of observations, required to invert synthetic data: by the extended Bott’s method, computing at each iteration the anomaly fit by Chakravarthy and Sundararajan’s (2004) functional (dotted line), by the proposed modeling procedure using: M=31 and Mz=10 for gridded data (solid black line), and M=51 and Mz=100 for irregularly spaced observations (solid gray line), and by the proposed modeling discretizing, the whole basin with M=201 and Mz=100 for irregularly spaced observations (dashed line). (b) Detail of (a) in a larger scale, individualizing the curves of the proposed modeling for gridded (solid black line) and irregularly spaced observations (solid gray line).

(a) Computer time as a function of the number of observations, required to ... Available to Purchase

Published: 20 December 2016
Figure 6. (a) Computer time as a function of the number of observations, required to invert synthetic data: by the extended Bott’s method, computing at each iteration the anomaly fit by Chakravarthy and Sundararajan’s (2004) functional (dotted line), by the proposed modeling procedure using
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View of reestimated basement relief of the rift basin using the NVDR-THDR of the inverted basement using Bott’s method instead of the NVDR-THDR of gravity anomaly with λh=1, λm=1, and ω=10−2, and (a) with seven known depth points denoted with the red stars, its misfit is shown in (b); (c) without known depth constraint, its misfit is shown in (d). (e) The difference between the two inverted results, the red color indicates that the inverted basement with known depth constraint is shallower than the result without a known depth constraint, whereas the blue indicates an opposite situation. The black solid line marked P1P2P3 represents the position of the profile shown in Figure 7.

View of reestimated basement relief of the rift basin using the NVDR-THDR o... Available to Purchase

Published: 29 August 2018
Figure 6. View of reestimated basement relief of the rift basin using the NVDR-THDR of the inverted basement using Bott’s method instead of the NVDR-THDR of gravity anomaly with λ h = 1 , λ m = 1 , and ω = 10 − 2 , and (a) with seven known depth points
Journal Article

3D gravity inversion of basement relief for a rift basin based on combined multinorm and normalized vertical derivative of the total horizontal derivative techniques Available to Purchase

Xuliang Feng, Wanyin Wang, Bingqiang Yuan
Journal: Geophysics
Published: 29 August 2018
Geophysics (2018) 83 (5): G107–G118.
DOI: https://doi.org/10.1190/geo2017-0678.1
...Figure 5. View of the inverted basement relief of the rift basin with six different size grabens using (a) our developed method with λ h = 1 , λ m = 1 , and ω = 10 − 2 ; its misfit is shown in (b); (c) Bott’s method. The locations of seven known depths...
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Member dimensions and steel reinforcement for the six-story building design... Available to Purchase

Published: 01 August 2021
Table 3. Member dimensions and steel reinforcement for the six-story building designed using the proposed method, corresponding to PSO Case 4 in Table 2 . Reinforcement sizes are designated in the American system Seismic System Gravity System Story Columns Beams Columns
Journal Article

Technique For Improved Convergence In Iterative Analysis Of Gravity Anomaly Profiles Available to Purchase

K. P. Fournier, S. F. Krupicka
Journal: Geophysics
Published: 01 June 1973
Geophysics (1973) 38 (3): 500–506.
DOI: https://doi.org/10.1190/1.1440355
...K. P. Fournier; S. F. Krupicka Abstract Narrow two-dimensional gravity anomalies are difficult to interpret iteratively by the relatively simple flat-plate method suggested by Bott (1960) and employed by others. In this report Bott's formula is modified empirically after a number of iterations have...
View PDF for article title, Technique For Improved Convergence In Iterative Analysis Of Gravity Anomaly Profiles
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Efficient gravity inversion of basement relief using a versatile modeling algorithm Available to Purchase

João B. C. Silva, Darcicléa F. Santos
Journal: Geophysics
Published: 20 December 2016
Geophysics (2017) 82 (2): G23–G34.
DOI: https://doi.org/10.1190/geo2015-0627.1
...Figure 7. Real data inversion. (a) Gravity anomaly over the Chintalapudi Basin, India. (b and c) The estimated relief through the extended Bott’s method using, respectively, the proposed modeling and Chakravarthi and Sundararajan’s (2004) functional, the latter reported by Silva et al. (2014...
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Comparison of convergences of Bott’s (gray dots) and Bhaskara Rao’s (1986) (black dots) methods along the iterations. The noise in data has a standard deviation of 0.1 mGal.

Comparison of convergences of Bott’s (gray dots) and Bhaskara Rao’s (1986)... Available to Purchase

Published: 22 August 2014
Figure 5. Comparison of convergences of Bott’s (gray dots) and Bhaskara Rao’s (1986) (black dots) methods along the iterations. The noise in data has a standard deviation of 0.1 mGal.
Journal Article

Bayesian Inference of Seismogenic Stress for the 2016 M w 7.8 Kaikōura, New Zealand, Earthquake Available to Purchase

Olivia Leigh Walbert, Eric Andreas Hetland
Published: 26 April 2022
Bulletin of the Seismological Society of America (2022) 112 (4): 1894–1907.
DOI: https://doi.org/10.1785/0120210173
... on the Wallace–Bott assumption, which equates the direction of slip and the orientation of maximum shear stress along a fault plane, and is analogous to methods that infer stress from focal mechanisms. We infer the orientations and relative magnitudes of the principal components of tensorial stress preceding...
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