Downward Continuation of Potential Field Data Based on Chebyshev–Padé Approximation Function

Zhou, Wenna; Li, Jiyan; Yuan, Yuan

doi:10.1007/s00024-017-1680-1

Cited by 14 publications

(13 citation statements)

References 21 publications

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“…Many new stable algorithms have been introduced to implement the downward continuation method (Fedi and Florio, 2002;Cooper, 2004;Ma et al, 2013;Zeng et al, 2013Zeng et al, , 2014Zhang et al, 2013;Zhou et al, 2018). Zhou et al (2018) has compared the errors between the function exp(x) and its different approximation functions, including Taylor series, Chebyshev approximation, Pade´ approximation, and Chebyshev-Pade´ approximation. Comparison of results indicate that downward continuation based on Chebyshev-Pade´ approximation can obtain a more precise result.…”

Section: Ndc Of the Largest Eigenvaluementioning

confidence: 99%

“…where the downward continuation operator e �hω γ can be approximated by the (three and two) terms of Chebyshev-Pade´ as follows (Zhou et al 2018…”

Section: Ndc Of the Largest Eigenvaluementioning

confidence: 99%

“…h is a positive number for the downward continuation distance and vice versa for the upward continuation. Zhou et al (2018) have pointed out that Chebyshev-Pade´ approximation can give a more precise approximation in…”

Section: )mentioning

confidence: 99%

“…Based on the advantages of the largest eigenvalue of the structure tensor, in this paper, we apply the NDC on the largest eigenvalue of the structure tensor of the downward continued field to estimate the depth and the horizontal edges. In order to increase the stability of the NDC process, the Chebyshev-Pade´ approximation downward continuation method developed by Zhou et al (2018) was brought to compute each downward continuation level field. The synthetic models with and without noise and the real measured potential field data are utilized to validate the effectiveness of this new method.…”

Section: Introductionmentioning

confidence: 99%

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Application of the normalized largest eigenvalue of structure tensor in the interpretation of potential field tensor data

Yuan

Zhang

Zhou

et al. 2020

Earth Planets Space

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Obtaining horizontal edges and the buried depths of geological bodies, using potential field tensor data directly is an outstanding question. The largest eigenvalue of the structure tensor is one of the commonly used edge detectors for delineating the horizontal edges without depth information of the potential field tensor data. In this study, we presented a normalized largest eigenvalue of structure tensor method based on the normalized downward continuation (NDC) to invert the source location parameters without any priori information. To improve the stability and accuracy of the NDC calculation, the Chebyshev–Pade´ approximation downward continuation method was introduced to obtain the potential field data on different depth levels. The new approach was tested on various models data with and without noise, which validated that it can simultaneously obtain the horizontal edges and the buried depths of the geological bodies. The satisfactory results demonstrated that the normalized largest eigenvalue of structure tensor can describe the locations of geological sources and decrease the noise interference magnified by the downward continuation. Finally, the method was applied to the gravity data over the Humble salt dome in USA, and the near-bottom magnetic data over the Southwest Indian Ridge. The results show a good correspondence to the results of previous work.

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Section: Ndc Of the Largest Eigenvaluementioning

confidence: 99%

“…where the downward continuation operator e �hω γ can be approximated by the (three and two) terms of Chebyshev-Pade´ as follows (Zhou et al 2018…”

Section: Ndc Of the Largest Eigenvaluementioning

confidence: 99%

Section: )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Application of the normalized largest eigenvalue of structure tensor in the interpretation of potential field tensor data

Yuan

Zhang

Zhou

et al. 2020

Earth Planets Space

Self Cite

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show abstract

“…Fedi and Florio, 2002;Trompat et al, 2003;Cooper, 2004) and during the last years there can be followed something like a "boom" in this scientific area (e.g. Ma et al, 2013;Zeng et al, 2013;Zhang H. et al, 2013;Abedi et al, 2014;Zeng et al, 2014;Zeng et al, 2015;Zhang Y. et al, 2016, Zhou et al, 2018Florio and Fedi, 2018;Zhang et al, 2018).…”

Section: Tikhonov's Regularization Approach In Stable Downward Continmentioning

confidence: 99%

Matlab tool REGCONT2: effective source depth estimation by means of Tikhonov’s regularized downwards continuation of potential fields

Pašteka

Kušnirák

Karcol

2018

Contributions to Geophysics and Geodesy

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Transformation based on downward continuation of potential fields is an important tool in their interpretation – depths of shallowest important sources can be determined by means of stable downward continuation algorithms. We analyse here selected properties of one from these algorithms (based on Tikhonov’s regularization approach) from the scope of two most important discretization parameters – dimensions of the areal coverage of the interpreted field and the sampling interval size. Estimation of the source depth is based on the analysis of computed LP-norms for various continuation depths. A typical local minimum of these norms disappears at the source depth. We show on several synthetic bodies (sphere, horizontal cylinder, vertical rod) and also real-world data-sets (results from a magnetic survey for unexploded ordnance detection) that there is a need for relatively large surroundings around the interpreted anomalies. Beside of this also the sampling step plays its important role – grids with finer sampling steps give better interpretation results, when using this downward continuation method. From this point of view, this method is more suitable for the interpretation of objects in near surface and mining geophysics (anomalies from cavities, unexploded ordnance objects and ore bodies). Anomalies should be well developed and separable, and densely sampled. When this is not valid, several algorithms of interpolation and extrapolation (grid padding methods) can improve the interpretation properties of studied downward continuation method.

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A Novel Downward Continuation Method Based on Continued Fraction in Wavenumber Domain and Its Application on Aeromagnetic Data in the Xuanhua-Huailai Area, China

Zhou

Zhang

2022

Pure Appl. Geophys.

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Downward Continuation of Potential Field Data Based on Chebyshev–Padé Approximation Function

Cited by 14 publications

References 21 publications

Application of the normalized largest eigenvalue of structure tensor in the interpretation of potential field tensor data

Application of the normalized largest eigenvalue of structure tensor in the interpretation of potential field tensor data

Matlab tool REGCONT2: effective source depth estimation by means of Tikhonov’s regularized downwards continuation of potential fields

A Novel Downward Continuation Method Based on Continued Fraction in Wavenumber Domain and Its Application on Aeromagnetic Data in the Xuanhua-Huailai Area, China

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