REGCONT: A Matlab based program for stable downward continuation of geophysical potential fields using Tikhonov regularization

Pašteka, Roman; Karcol, Roland; Kušnirák, Dávid; Mojzeš, Andrej

doi:10.1016/j.cageo.2012.06.010

Cited by 66 publications

(4 citation statements)

References 20 publications

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“…In this case, we use the derivative Euler deconvolution (Hsu, 2002) applied to the first vertical derivative, and the smoothing is applied to this field. To determine the optimal amount of smoothing, the C-norm criterion was used (Pašteka et al, 2009(Pašteka et al, , 2012. The C-norm curve ( Figure 10) shows a clear local minimum correlating with the optimal β value to use in equation 6.…”

Section: A Synthetic Examplementioning

confidence: 99%

On the estimation of the structural index from low-pass filtered magnetic data

2014

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The estimation of the structural index and of the depth to the source is the main task of many popular methods used to analyze potential field data, such as Euler deconvolution. However, these estimates are unstable even in the presence of a weak amount of noise, and Euler deconvolution of noisy data leads to an underestimation of structural index and depth. We have studied how the structural index and depth estimates are affected by applying low-pass filtering to the data. Physically based low-pass filters, such as upward continuation and integration, have been shown to be the best choice over a range of altitudes (upward continuation) or orders (integration filters), mainly because their outputs have a well-defined physical meaning. In contrast, mathematical low-pass filters require that the filter parameters be tuned carefully by means of several trial tests to produce optimally smoothed fields. The C-norm criterion is a reliable strategy to produce a stabilized vertical derivative, and we discourage Butterworth filters because they tend to a vertical integral filter, for a high cutoff wavenumber, thus complicating the interpretation of the estimated structural index. We found that the estimated structural index and depth to source increase proportionally with the amount of smoothing, unless in the case of overfiltering. In that case, the severe distortion of the original field may cause a decrease of the estimated structural index and depth to source.

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Section: A Synthetic Examplementioning

confidence: 99%

On the estimation of the structural index from low-pass filtered magnetic data

2014

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“…Another utilizes the linear multiplicative algorithm based on the convolution in the frequency domain (Dean, 1958;Hughes, 1942;Tomoda & Aki, 1955;Tsuboi & Fuchida, 1937). However, its frequency downward continuation factor should be filtered or regularized to diminish the amplifying impact (Abedi et al, 2013;Clarke, 1969;Ferguson, 1988;Huestis & Parker, 1979;Lima et al, 2013;Pašteka et al, 2012;Pawlowski, 1995;Sebera et al, 2015;Tikhonov et al, 1977;Zhang et al, 2016), and moreover, appropriate…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

Lü

Yan

et al. 2018

Geophysical Research Letters

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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.

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Section: Derivadas Regularizadasunclassified

“…A abordagem da norma de Chebyshev, também conhecida como norma C ou norma L ∞ (Glasko et al, 1970;Pašteka et al, 2009) (Pašteka et al, 2012;Zeng et al, 2014;Pašteka et al, 2018;Karcol & Pašteka, 2020) e às derivadas direcionais no processamento da deconvolução de Euler (Pašteka & Richter, 2005;Pašteka et al, 2009). Esse critério não é eficiente em dados subamostrados (Pašteka et al, 2012(Pašteka et al, , 2018 e pode resultar em curvas com mínimos fracamente definidos (Florio et al, 2014) ou múltiplos mínimos locais (Karcol & Pašteka, 2020) próximos ao máximo global da norma C das soluções adjacentes. Nesse caso, o parâmetro de regularização pode ser selecionado a partir da análise qualitativa das soluções regularizadas (Pašteka & Richter, 2005;Pašteka et al, 2009), escolhendo a solução que seja a mais suave possível e, ao mesmo tempo, representativa das características do sinal de entrada.…”

Section: Derivadas Regularizadasunclassified

Parâmetros de regularização de operadores diferenciais no processamento de dados aeromagnéticos

Melo

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The evaluation of numerical derivatives is an essential tool in magnetic data processing, aiming to map structural lineaments and estimate the depth of the respective anomalous sources in the subsurface. Generally, directional derivatives are obtained through numerical methods based on the calculation of the Fourier transform, susceptible to noise amplification due to numerical instability. One way to improve stability in differentiation is to apply Tikhonov regularization to balance the oscillatory characteristics of the derivatives with the smoothing degree associated with the particular regularization parameter choice. This work proposes a graphical procedure to estimate regularization parameters for different potential field transformations that require first or second-order derivatives. This tool is based on normalizing the L 2 -norm of the respective transformed fields to a trial regularization parameters sequence, resulting in a characteristic function with a staircase format. This function has smooth and monotonic behavior, decreasing from 1 to 0 for increasing regularization values, in which the upper step (1) of the function is associated with non-regularized and sub-regularized transformations and the lower step (0) corresponds to over-regularized transformations. Synthetic tests simulating models with different noise levels or anomaly complexities illustrated that the well-suited regularization parameter selection for transformed fields depends on analyzing the distortions in the maps. Euler deconvolution processing applied to synthetic models showed that the appropriate regularization parameter choice is associated with the ascertaining of erroneous (overestimated) depth inferences. The applicability of the regularization procedure is evaluated on gridded aeromagnetic data covering two study areas in the Tocantins Province, central Brazil. In Area-I, covering the Anápolis-Itauçu Complex, transformations using first-order derivatives regularized with the intermediate ramp criterion were efficient in better mapping the continuity of magnetic lineaments with different directions and intersections, associated with shear zones, geological faults, and intrusive bodies. Applications in Area-II covering the Transbrasiliano tectonic corridor revealed the need for a low-dose regularization to obtain depth estimates consistent with the depths of the underlying basement of the Bananal Basin, according to available information from seismic lines and gravity models.Regularization tuned to the intermediate ramp criterion was sufficient for transformations with first-order derivatives to map the complex pattern of multiple linear structures. The results in Area-II showed that transformations based on second-order derivatives require a high degree of regularization to detect the contributions from subtle structural features.

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REGCONT: A Matlab based program for stable downward continuation of geophysical potential fields using Tikhonov regularization

Cited by 66 publications

References 20 publications

On the estimation of the structural index from low-pass filtered magnetic data

On the estimation of the structural index from low-pass filtered magnetic data

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

Parâmetros de regularização de operadores diferenciais no processamento de dados aeromagnéticos

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