Thursday, January 22, 2026
Space & Astronomy
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Generalizing β-VDR for Robust Source Edge Detection & Depth Estimation

Nature
January 18, 20264 days ago
Generalizing β-VDR-based derivative computation for robust source edge detection and depth estimation from potential field data

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This article discusses generalizing the β-VDR method for robust source edge detection and depth estimation from potential field data. It introduces stable methods for computing vertical derivatives and applying them to interpret geophysical data for mineral exploration and structural mapping. The outcome is improved accuracy in identifying geological features.

Butler, D. engineering and environmental applications of the potential field methods of geophysics. https://doi.org/10.4133/1.2924683 (2007). Falade, S. C. et al. Non-Invasive detection of structural features and potential gold mineralization zones in Northwestern Rijau environ of Zuru schist Belt, Nigeria. NIPES-JSTR ISSUE. 7, 2736–2742 (2025). Gang, Y. & Lin, Z. An improved stable downward continuation of potential fields using a truncated Taylor series and regularized vertical derivatives method. J. Geophys. Eng. https://doi.org/10.1088/1742-2140/AAC53A (2018). Liu, Y. et al. A stable method for estimating the derivatives of potential field data based on deep learning. IEEE Geosci. Remote Sens. Lett. 22, 1–5 (2025). Oliveira, S. P., Pham, L. & Pašteka, R. Regularization of vertical derivatives of potential field data using morozov’s discrepancy principle. Geophys. Prospect. 72, 2880–2892 (2024). Pašteka, R., Richter, F. P., Karcol, R., Brazda, K. & Hajach, M. Regularized derivatives of potential fields and their role in semi-automated interpretation methods. Geophys. Prospect. 57, (2009). Van Tran, K. & Nguyen, T. N. A novel method for computing the vertical gradients of the potential field: application to downward continuation. Geophys. J. Int. 220, 1316–1329 (2020). Blakely, R. J. Potential Theory in Gravity and Magnetic Applications (Cambridge University Press, 1996). Fedi, M. & Florio, G. Detection of potential fields source boundaries by enhanced horizontal derivative method. Geophys. Prospect. 49, 40–58 (2001). Florio, G., Fedi, M. & Pasteka, R. On the application of Euler Deconvolution to the analytic signal. Geophysics 71, L87–L93 (2006). Tatchum, C. N., Tabod, T. C., Koumetio, F. & Manguelle-Dicoum, E. A gravity model study for differentiating vertical and dipping geological contacts with application to a Bouguer gravity anomali over the Foumban shear Zone, Cameroon. Geophysica 47, 43–55 (2011). Oliveira, S. P. & Pham, L. T. A stable finite difference method based on upward continuation to evaluate vertical derivatives of potential field data. Pure Appl. Geophys. 179, 4555–4566 (2022). Pham, L. T. et al. Reliable Euler Deconvolution solutions of gravity data throughout the β-VDR and THGED methods: application to mineral exploration and geological structural mapping. Vietnam J. Earth Sci. https://doi.org/10.15625/2615-9783/21009 (2024). Pham, L. T. et al. Selection of Euler Deconvolution solutions using the enhanced horizontal gradient and stable vertical differentiation. Open Geosci. 16 (2024). Abdelrahman, K. et al. Reliable Tilt-depth estimates based on the stable computation of the Tilt angle using robust vertical derivatives. Sci. Rep. 14 (2024). Pham, L. T. A generalized $β$-VDR method for computing high-order vertical derivatives: application to downward continuation. Geophys. J. Int. 243, ggaf334 (2025). Alvandi, A., Ardestani, V. E. & Motavalli-Anbaran, S. Novel Detectors Based on the Elliott Function for Mapping Potential Field Data: Application to Aeromagnetic Data from Indiana, United States. Ann. Geophys. https://doi.org/10.4401/ag-9146 (2025). Pham, L. T. et al. Enhancement of the balanced total horizontal derivative of gravity data using the power law approach. Geocarto Int. 39, 2335251 (2024). Ai, H., Huang, Q., Ekinci, Y. L., Alvandi, A. & Narayan, S. Robust edge detection for structural mapping beneath the Aristarchus Plateau on the Moon using gravity data. Earth Sp. Sci. 12, eEA004379 (2025). (2025). Burg, J. P. Maximum Entropy Spectral Analysis (Stanford University, 1975). Gibert, D. & Galdeano, A. A computer program to perform transformations of gravimetric and aeromagnetic surveys. Comput. Geosci. 11, 553–588 (1985). Phillips, J. D., Hansen, R. O. & Blakely, R. J. The use of curvature in potential-field interpretation. Explor. Geophys. 38, 111–119 (2007). Cooley, J. W. & Tukey, J. W. An algorithm for the machine calculation of complex fourier series. Math. Comput. 19, 297–301 (1965). Aderoju, A. B., Ojo, S. B., Adepelumi, A. A. & Edino, F. A reassessment of hydrocarbon prospectivity of the Chad basin, Nigeria, using magnetic hydrocarbon indicators from highresolution aeromagnetic imaging. IFE J. Sci. 18, 503–520 (2016). Genik, G. J. Petroleum geology of Cretaceous-Tertiary rift basins in Niger, Chad, and central African Republic. Am. Assoc. Pet. Geol. Bull. 77, 1405–1434 (1993). Genik, G. J. Regional framework, structural and petroleum aspects of rift basins in Niger, Chad and the central African Republic (C.A.R). Tectonophysics 213, 169–185 (1992). Obaje, N. G. Geology and Mineral Resources of Nigeria. https://doi.org/10.1007/978-3-540-92685-6 (Springer, 2009). Okosun, E. A. Review of the geology of Bornu basin. J. Min. Geol. 31, 113–122 (1995). Awoyemi, M. O. et al. Investigation of basement fault propagation in Chad basin of Nigeria using high resolution aeromagnetic data. Arab. J. Geosci. 9, 453 (2016). Goni, I. B. & Zarma, A. A. Occurrence and distribution of igneous intrusions in the Nigerian sector of the Chad basin: impact on hydrocarbon. Pet. Technol. Dev. J. 5, 76–94 (2015). Awoyemi, M. O. et al. Magnetically inferred regional heat flow and geological structures in parts of Chad Basin, Nigeria and their implications for geothermal and hydrocarbon prospects. J. Pet. Sci. Eng. 213, 110388 (2022). Yulin, L. K-Ar and ~(39)Ar-~(40)Ar geochronology of basalts from the Chad Basins,Africa and its geodynamics setting. Acta Geol. Sin (2009). Pouclet, A., Vidal, M., Doumnang, J., Vicat, J. & Tchameni, R. Neoproterozoic crustal evolution in Southern chad: Pan-African ocean basin closing, Arc accretion and late- to post-orogenic granitic intrusion. J. Afr. Earth Sci. 44, 543–560 (2006).

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    Robust Source Edge Detection: β-VDR Methods