Iterative Spherical Downward Continuation Applied to Magnetic and Gravitational Data from Satellite

Sebera, Josef; Šprlák, Michal; Novák, Pavel; Bezděk, Aleš; Vaľko, Miloš

doi:10.1007/s10712-014-9285-z

Cited by 36 publications

(20 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(1) for other quantities than the potential, whereas its value is known for a few functions [see discussion in Sebera et al (2014)]. Here, we deal with the second derivative of the anomalous gravitational potential T zz , i.e., the Cartesian derivative with respect to the spherical normal, for which rigorously holds C f ¼ ðR=rÞ 2 .…”

Section: Poisson Integral Equationmentioning

confidence: 99%

“…In this approach, the direct problem (here, the upward continuation) is solved iteratively until the input data are fitted to a possible level of agreement that is mostly corrupted by noise. Most recently, the approach was used on the plane by Xu et al (2007), Ma et al (2012), Zeng et al (2013), Zhang et al (2013) and on the sphere by Sebera et al (2014) in the case of the global downward continuation.…”

Section: Iterative Approachmentioning

confidence: 99%

“…Hence, the algorithm does not require any prior data. The term p, called the ''sensitivity parameter'' in Sebera et al (2014), is a purely optional (artificial) parameter in Eq. (4) and its value was set to 1 in the original work of Landweber (1951).…”

Section: Iterative Approachmentioning

confidence: 99%

“…However, in Xu et al (2007), it was found that the iteration can be accelerated (and stabilized) by using different values of p. In our investigations with GOCE data, we use p ¼ 2:1 since the decrease in the residuals is accelerated with this value and the iteration is still convergent. Note that higher values of p do not have to guarantee convergence of the procedure (see Figure 4 in Sebera et al 2014).…”

Section: Iterative Approachmentioning

confidence: 99%

“…For all tests, we use real data-the second vertical derivative of the anomalous potential 1 T zz obtained from data of the GOCE mission (ESA 1999). Since Sebera et al (2014) provided the approach for satellite-based grids, this study is motivated a gap in the regional continuation from the spherical surface. Originating in our previous works (Novák et al 2001;Sebera et al 2014;Janák 2014;Š prlák et al 2014), the three approaches are compared within four integration schemes, whereas the results are validated with spherical harmonic solutions TIM-r4 (Pail et al 2011) and EGM2008 (Pavlis et al 2012).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Comparative Study of the Spherical Downward Continuation

et al. 2015

Self Cite

View full text Add to dashboard Cite

Downward continuation of the potential data (gravity or magnetic) helps to interpret contributing sources by transforming the physical signal to their neighborhood. This paper applies three continuation approaches (Landweber's iteration, the direct method and the inverse-matrix approach with Tikhonov's regularization), based on the Poisson integral equation, and four integration schemes to the second vertical derivative of the anomalous potential T zz obtained from GOCE data. In the experiments, T zz was downward continued for 250 km in the area of Central Europe with special attention to edge effects. For the integration schemes, which use prior information outside the region of interest to reduce edge effects, the best agreement with TIM-r4 was achieved by the inverse-matrix approach with Tikhonov's regularization (RMS = 1.15 eotvos). On the contrary, without prior information the iterative approach performed with RMS = 1.17 eotvos.

show abstract

Section: Poisson Integral Equationmentioning

confidence: 99%

Section: Iterative Approachmentioning

confidence: 99%

Section: Iterative Approachmentioning

confidence: 99%

Section: Iterative Approachmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Comparative Study of the Spherical Downward Continuation

et al. 2015

Self Cite

View full text Add to dashboard Cite

show abstract

Numerical Solutions of the Mean‐Value Theorem: New Methods for Downward Continuation of Potential Fields

Zhang

Lü

Yan

et al. 2018

Geophysical Research Letters

View full text Add to dashboard Cite

Downward continuation can enhance small‐scale sources and improve resolution. Nevertheless, the common methods have disadvantages in obtaining optimal results because of divergence and instability. We derive the mean‐value theorem for potential fields, which could be the theoretical basis of some data processing and interpretation. Based on numerical solutions of the mean‐value theorem, we present the convergent and stable downward continuation methods by using the first‐order vertical derivatives and their upward continuation. By applying one of our methods to both the synthetic and real cases, we show that our method is stable, convergent and accurate. Meanwhile, compared with the fast Fourier transform Taylor series method and the integrated second vertical derivative Taylor series method, our process has very little boundary effect and is still stable in noise. We find that the characters of the fading anomalies emerge properly in our downward continuation with respect to the original fields at the lower heights.

show abstract