A combination of the logistic function and the directional Hilbert transform for edge detection of gravity data

Authors

Tehran university

Abstract

Gravity anomalies map feature spatially overlapping fingerprints from a potentially huge number of sources, each with a different shape, depths and densities. In recent decades, geophysicists have developed a variety of image-enhancement filtering algorithms or edge detectors to accurately display the geometry and details of subterranean sources. However, in common filters, the images obtained for deeper sources are usually diffuse or fuzzy, or filters cannot equalize the edges of weak and strong amplitudes at the same time. In order to overcome these problems, in this paper, an effective filter using the combination of the logistic function, the directional Hilbert transform and the total horizontal gradient is introduced, abbreviated as "MLK". The results on the 2D and 3D data with noise and without noise show that MLK proposed filter performs better compared to the other filters. Also, we used the measured complete Bouguer anomaly (CBA) high resolution dataset in Slovakia territory. In addition to gravity map we also used the geological map to control our results as a case study. The primary goal of this research is to compare MLK edge determination filter and to assess the quality of filter and balance signals from shallow and deep geological structures.

Keywords

References

ابراهیم‌زاده اردستانی، سید وحید.، (1389)، گرانی‌سنجی کاربردی، انتشارات دانشگاه تهران.
الوندی، ا؛ توکتای, ه، د؛ فام، ل، ث. (1400)، تفسیر داده­های گرانی با استفاده از تابع لجستیک و گرادیان افقی کل، مطالعه موردی: تاقدیس چارک، پژوهش­های ژئوفیزیک کاربردی، 7 (4)، 401-412.
 
Hinze WJ, von Frese RRB, Saad AH. Gravity and magnetic Exploration—Principles, Practices, and Applications. 1st ed. Cambridge University Press; (2013). 525 p.
 
Ai, H., Huang, Q., Ekinci, Y. L., Alvandi, A., & Narayan, S. (2025). Robust edge detection for structural mapping beneath the Aristarchus Plateau on the Moon using gravity data. Earth and Space Science, 12, e2025EA004379. https://doi.org/10.1029/2025EA004379.
 
Ai, H., Ekinci Y.L., Alvandi A., Deniz Toktay H., Balkaya Ç. and Roy A. (2024). Detecting edges of geologic sources from gravity or magnetic anomalies through a novel algorithm based on hyperbolic tangent function, Turkish Journal of Earth Sciences, 33 (6). https://doi.org/10.55730/1300-0985.1936.
 
Ai, H., Alvandi, A., Ghanati, R., Pham, L., Alarifi, S., Nasui, D. and Eldosouky, A., (2023), Modified non-local means: A novel denoising approach to process gravity field data. Open Geosciences, 15(1), https://doi.org/10.1515/geo-2022-0551.
 
Alvandi, A., Su, K., Ai, H., Ardestani, V.E., and Lyu, C., (2023), Enhancement of Potential Field Source Boundaries Using the Hyperbolic Domain (Gudermannian Function). Minerals, 13, 1312. https://doi.org/10.3390/min13101312.
 
Alvandi, A., and Ardestani, V.E., (2023), Edge detection of potential field anomalies using the Gompertz function as a high-resolution edge enhancement filter. Bull. Geophys. Oceanogr, 64, 279–300. https://doi.org/10.4430/bgo00420.
 
Alvandi, A., Ardestani, V. E., & Motavalli Anbaran, S. H. (2025). Enhancement of the total horizontal gradient of potential field data using the Modified Gudermannian Function (MGTHG): application to aeromagnetic data from Georgia, USA. Bulletin of Geophysics and Oceanography, 66(1), 73-94. http://dx.doi.org/10.4430/bgo00479.
 
Alvandi, A., Ardestani, V. E., & Motavalli Anbaran, S. H. (2024). Novel Detectors Based on the Elliott Function for Mapping Potential Field Data: Application to Aeromagnetic Data from Indiana, United States. Annals of Geophysics, 67(6), GP656. https://doi.org/10.4401/ag-9146.
 
Cooper, G. R. J., and Cowan, D. R., (2006), Enhancing potential field data using filters based on the local phase. Computers and Geosciences, 32(10), 1585–1591.
 
Cooper, G.R.J., Cowan, D.R., (2009). Terracing potential field data. Geophysical Prospecting, 57, 1067–1071.
 
Deniz Toktay, H., (2022), Modeling of Archaeomagnetic Anomaly Maps, Springer, Singapore, https://doi.org/10.1007/978-981-19-4219-8.
 
Deniz Toktay, H., Ai, H., Alvandi, A., Su, K., & Li, J. (2025). MTAHG and MTBHG: Modified approaches for interpreting gravity data. Earth and Space Science, 12, e2024EA003900. https://doi.org/10.1029/2024EA003900.
 
Deniz Toktay, H., Alvandi, A., Ai, H. (2026). A bi-hyperbolic tilt method for robust edge detection in gravity and magnetic data. Eur. Phys. J. Plus, 141:398. https://doi.org/10.1140/epjp/s13360-026-07646-0.
 
Everett, M.E. (2013). Near-surface applied geophysics. Cambridge University Press.
 
Eldosouky, A.M.; Mohamed, H. Edge detection of aeromagnetic data as effective tools for structural imaging at Shilman area, South Eastern Desert, Egypt. Arab. J. Geosci. 2021, 14, 1–10.
 
Eldosouky A. M., L. T. Pham, A. Henaish. (2022). High precision structural mapping using edge filters of potential field and remote sensing data: a case study from Wadi Umm Ghalqa area, South Eastern Desert, Egypt, Egypt J Remote Sens Space Sci, 25, 2, 501–513.
 
Florio, G., Fedi, M., and Pasteka, R., (2006), On the application of Euler deconvolution to the analytic signal. Geophysics, 71(6), L87–L93.
 
Hók, J., Kahan, Š. & Aubrecht, R., (2001): Geológia Slovenska. Bratislava, Univerzita Komenského, 1 – 47. (In Slovak.).
 
Melouah. O., and Pham, L.T. Improved ILTHG method for edge enhancement of geological structures: application to gravity data from the Oued Righ valley, J. Afr. Earth Sci., 177 (2021), Article 104162
 
Nabighian, M. N., (1972), The analytic signal of two-dimensional magnetic bodies with polygonal cross-section – Its properties and use of automated anomaly interpretation. Geophysics, 37, 507-517.
 
Nabighian, M. N., (1984), Toward a three-dimensional automatic interpretation of potential field data via generalized Hilbert transforms – Fundamental relations. Geophysics, 49, 780-786.
 
Oksum E, Le DV, Vu MD, Nguyen THT, Pham LT. (2021). A novel approach based on the fast sigmoid function for interpretation of potential field data. Bull Geophys Oceanogr. 62(3):543–556.
 
Prasad, K.N.D., Pham, L.T., Singh, A.P., (2022). Structural mapping of potential field sources using BHG filter. Geocarto International, 37, 1-22, DOI: 10.1080/10106049.2022.2048903.
 
Pham, L.T., Oksum, E., Do, T. D., Le-Huy, M., (2018). New method for edges detection of magnetic sources using logistic function. Geofizicheskiy Zhurnal, 40(6), 127-135.
 
Pham, L.T., Oksum, E. & Do, T.D. Edge enhancement of potential field data using the logistic function and the total horizontal gradient. Acta Geod Geophys 54, 143–155 (2019). https://doi.org/10.1007/s40328-019-00248-6
 
Pham, L.T., Van Vu, T., Le Thi, S. et al. Enhancement of Potential Field Source Boundaries Using an Improved Logistic Filter. Pure Appl. Geophys. 177, 5237–5249 (2020). https://doi.org/10.1007/s00024-020-02542-9
 
Pham, L. T., (2021), A high resolution edge detector for interpreting potential field data: A case study from the Witwatersrand basin, South Africa. Journal of African Earth Science, 178(104), 190.
 
Roest, W. R., J. Verhoef, and M. Pilkington, (1992), magnetic interpretation using the 3-D analytic signal. Geophysics, 57, 116-125.
 
Salem, A., Ravat, D., Gamey, T.J., and Ushijima, K. (2002). Analytic signal approach and its applicability in environmental investigations. Appl. Geophys., 49, 231–244.
 
Su, K., Ai, H., Alvandi, A., Lyu, C., Wei, X., Qin, Z., Tu, Y., Yan, Y. & Nie, T. (2024). Hunger Games Search for the elucidation of gravity anomalies with application to geothermal energy investigations and volcanic activity studies. Open Geosciences, 16(1),20220641.https://doi.org/10.1515/geo-2022-0641
 
Staškovanová, Veronika and Minár, Jozef. "Modelling the geomorphic history of the Tribeč Mountains and the Pohronský Inovec Mountains (Western Carpathians) with the CHILD model" Open Geosciences, vol. 8, no. 1, (2016), pp. 371-389. https://doi.org/10.1515/geo-2016-0038.
 
Zahorec P., Pašteka R., Mikuška J., Szalaiová V., Papčo J., Kušnirák D., Pánisová J., Krajňák M., Vajda P., Bielik M., Marušiak I., (2017): Chapter 7 – National Gravimetric Database of the Slovak Republic. In: Paˇsteka R., Mikuˇska J., Meurers B. (Eds.): Understanding the Bouguer Anomaly: A Gravimetry Puzzle. Elsevier, Amsterdam, 113–125, doi: 10.1016/B978-0-12-812913-5.00006-3.
Volume 12, Issue 2
September 2026
Pages 141-150

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