Abstract
Edge detection plays a critical role in delineating subsurface source boundaries from gravity and magnetic data. This study presents a systematic comparison of the common used edge-enhancement techniques, including the total horizontal derivative (THDR), tilt angle (TDR), analytical signal amplitude (ASA), theta map (THETA), THDR_NTilt, Gompertz function (GF), improved logistic (IL), and wavelet space entropy (WSE), using both synthetic magnetic model and free air gravity data from the Laxmi Basin, Arabian Sea. A 3D synthetic nine prism magnetic model is used to evaluate boundary localization accuracy and robustness of each technique. Quantitative evaluation using RMS error analysis under Gaussian noise shows that WSE provides the lowest error and superior noise robustness compared to conventional derivative-based filters. Application to free air gravity data shows that, among all the methods considered, the WSE method reliably delineates the geological boundaries of the Laxmi Ridge, as well as the Raman and Panikkar seamounts and the Wadia Guyot, showing close agreement with the bathymetry map. These results highlight the ability of WSE to preserve structural continuity, making it a robust and effective tool for potential field data interpretation in complex geological settings.
1 Introduction
Mapping structural boundaries and lithological contacts in potential field data is fundamental to understanding crustal architecture in both continental and marine settings. Gravity and magnetic anomalies commonly exhibit lateral gradients where density or magnetization contrasts occur, providing key constraints on basin margins, rift systems, crustal structure, intrusive complexes, and fault networks (Telford et al., 1990; Blakely, 1995; Dwivedi et al., 2019; 2025). Consequently, boundary detection filter can detect the lateral location of the potential field sources (Dwivedi and Chamoli, 2022; Pham et al., 2025). Thus, numerous edge detection techniques have been developed to enhance and delineate such boundaries (Blakely and Simpson, 1986; Miller and Singh, 1994; Cooper, 2009; Nasuti and Nasuti, 2018; Sahoo et al., 2022; Pham et al., 2023; Ai et al., 2024; Alvandi et al., 2024; Alvandi et al., 2025; Deniz Toktay et al., 2025). One of the key advantages of these filters is that they do not require any prior knowledge about the source characteristics.
Derivative-based filters such as the Total Horizontal Derivative (THDR) enhance sharp lateral gradients and are widely applied to identify near-surface or steeply bounded sources (Cordell and Grauch, 1985; Cooper, 2009). The Analytic Signal Amplitude (ASA) is independent of magnetization direction and produces maxima over source edges (Nabighian, 1972; Roest et al., 1992), while the Tilt Angle (TDR) and its higher order derivatives like THDR_NTilt normalizes amplitude variations, aiding interpretation across regions of variable anomaly strength (Miller and Singh, 1994; Arisoy and Dikmen, 2013; Nasuti and Nasuti, 2018). Techniques such as the Theta map, Gompertz function (GF), improved logistic (IL) filter, TGAS and other normalized gradient operators aim to improve stability and reduce amplitude bias (Verduzco et al., 2004; Wijns et al., 2005; Alvandi and Ardestani, 2023; Pham et al., 2020; Pham et al., 2024). In addition, wavelet-based approaches address multi-scale decomposition, allowing structural information to be analyzed across depth-sensitive spatial scales (Mallat and Zhong, 1992; Daubechies, 1992; Moreau et al., 1997). Wavelet-based techniques have been successfully applied to boundary delineation in potential-field data (Dwivedi and Chamoli, 2021; Dwivedi et al., 2023), tsunami detection (Lockwood and Kanamori, 2006; Chamoli et al., 2010; Telesca et al., 2013) and different time series analysis (Chamoli et al., 2007; Yemets et al., 2025).
In this study, edge-detection filters are applied to a synthetic prismatic model to delineate subsurface structural boundaries. The results are systematically compared, and their performance is quantitatively evaluated to assess the robustness and reliability of each method under noisy conditions. The techniques are further applied to free-air gravity anomaly data from the Laxmi Basin, Arabian Sea, to test their robustness and delineate the tectonic boundaries.
2 Methodology
2.1 Total horizontal derivative (THDR)
The maximum amplitude values of the THDR highlight the edges of anomaly sources, and the method was developed by Cordell and Grauch (1985) as:where is the gravity or magnetic anomaly and are the data gradients in and directions.
2.2 Tilt angle (TDR)
In the TDR method, the peak response occurs over the center of the anomalous body, while zero values of the TDR correspond to source edges (Miller and Singh, 1994). It is defined as:where is the vertical derivative of the field .
2.3 Analytical signal amplitude (ASA)
The ASA is defined as the square root of the sum of the squared directional derivatives of the potential-field data, and its maximum values correspond to the source edges (Nabighian, 1972; Roest et al., 1992) as:
2.4 Theta map (THETA)
The theta map is a phase-based filter used to detect the edges of causative sources, delineating boundaries through its maximum values (Wijns et al., 2005) as:
2.5 The THDR_NnTilt method
The THDR_NnTilt method is given by Nasuti and Nasuti, (2018). The maximum value of the THDR_NnTilt shows the edges of the anomalous sources.where is potential field, is the second vertical derivative and is the analytical signal of the order vertical derivative, is positive scalar number which is estimated as the magnitude of the average value of , and is dimensional correction factor. and are sampling intervals in and directions.
2.6 Improved logistic (IL)
Pham et al. (2020) uses the IL filter which is the combination of logistic function and THDR, where edge of the source occurs at the maxima of the signal as:where and .
In this case, is chosen for all the synthetic and real data examples based on Pham et al. (2020).
2.7 Gompertz function (GF)
The GF method identifies source edges using the maximum of its amplitude response, as proposed by Alvandi and Ardestani (2023), and is defined as:where ITHDR , is a constant value, and are the Hilbert transform of the algorithm in and directions. In this study, is considered for all the synthetic and real example based on Alvandi and Ardestani (2023). All spatial derivatives (horizontal and vertical) used in this study are computed in the frequency (wavenumber) domain using Fourier transform based operators and subsequently transformed back to the spatial domain using the inverse Fourier transform (Equations 1–7).
2.8 Wavelet space entropy (WSE)
Dwivedi et al. (2023) combined wavelet decomposition with Shannon entropy to determine lateral source edges. The 2D WSE at level D is defined as:where , and are relative, mean and total wavelet energy of the window at decomposition level . The WSE method does not compute spatial derivatives and is implemented in the wavelet (spatial-scale) domain using Haar wavelet decomposition and entropy analysis (Equation 8). High entropy values indicate increased disorder in the wavelet energy distribution, which is characteristic of lateral boundaries of subsurface sources.
3 Application on synthetic case and effect of noises
A synthetic model (M) comprising multiple prismatic sources of varying dimensions and depths is constructed to replicate the key geological scenarios of interest. The model parameters are summarized in Table 1 and illustrated in Figure 1a. Magnetic data are generated on 8000 m × 8000 m grid with a sampling interval of 20 m. The extension of all the prisms vary laterally. In this configuration, prisms P2, P3 and P4 have strike azimuth of −450 and 600 and 450. The prisms P4, P6, and P7 simulate relatively shallow sources and the combined presence of prisms P4 - P5 accounts for interference effects arising from closely spaced sources. In contrast, prism P1, P3, P8, and P9 represents an isolated deep seated sources. All prisms are assigned induced magnetization with an inclination of +900 and declination of 00. The total magnetic anomaly is computed for nine prismatic sources (P1-P9) positioned at different depths with the edge correspond to upper surface of the source (red dashed line) (Figure 1b). This synthetic configuration facilitates the evaluation of the methods under realistic conditions involving depth-dependent responses and mutual interference between nearby bodies.
TABLE 1
| Model | Prismatic source | Length (m) | Width (m) | Extent (m) | Susceptibility (SI) | Z top(m) | Inclination of prism (degree) |
|---|---|---|---|---|---|---|---|
| M | P1 | 4000 | 800 | 700 | +0.05 | 600 | 0 |
| P2 | 400 | 2800 | 700 | +0.06 | 500 | −45 | |
| P3 | 400 | 2200 | 700 | +0.06 | 600 | 60 | |
| P4 | 2000 | 2000 | 700 | +0.06 | 200 | 45 | |
| P5 | 800 | 800 | 700 | +0.06 | 400 | 0 | |
| P6 | 800 | 800 | 700 | +0.07 | 250 | 0 | |
| P7 | 800 | 800 | 700 | +0.08 | 300 | 0 | |
| P8 | 4000 | 800 | 700 | +0.05 | 600 | 0 | |
| P9 | 4000 | 800 | 700 | +0.05 | 600 | 0 |
The source geometries of the synthetic case of the magnetic model (M).
FIGURE 1
I assess the robustness of THDR, TDR, ASA, THETA, THDR_NTilt, GF, IL, and WSE using a synthetic magnetic anomaly generated from the prismatic model shown in Figure 1a. The edges identified by these methods are presented in Figure 2. The comparison begins with a qualitative visual assessment, consistent with a standard practice in geological interpretation. Most edge filters perform well in delineating the shallow sources (P4, P6, and P7) and have limitations in resolving the edges due to oblique prisms P2 and P3. These methods show restrictions in resolving the edge of P5 due to interference with P4, except for THDR, TDR, THDR_NTilt, IL, and WSE. The boundary estimated for P4 using TDR appears significantly broader than the actual model boundary, indicating reduced spatial localization accuracy (Figure 2b). The ASA demonstrates limited capability in resolving the deeper sources (P1, P8, and P9) due to the decrease in anomaly amplitude with depth (Figure 2c). The edges of all sources identified from the THETA map appear broader compared to the actual boundaries (Figure 2d). The THDR_NTilt estimates edges (black dashed lines) that coincide with the actual boundaries for P4, P6, and P7 but also produces numerous spurious edges near the map boundaries (Figure 2e). The GF method shows limitations in delineating the edges of P5, P6, and P7 (Figure 2f). The IL method does not perform well in delineating the edges of P2 and P3 and generates additional false edges similar to THDR_NTilt (Figure 2g). The WSE method employs the Daubechies wavelet of order one (db1) at decomposition level 1. After calculating the mean, total and relative wavelet energy, it clearly delineates the boundaries of the prismatic sources, except for P2 and P3 (Figure 2h). The source boundaries are clearly identified by relatively high entropy values, reflecting behaviour similar to disorder in physical systems (Dwivedi et al., 2023).
FIGURE 2
To quantitatively assess performance, root mean square (RMS) error is computed along selected profiles (L1, and L2) that intersect the model source boundaries. In Figure 3, the true edges (vertical dashed lines) are compared with the edge signatures produced by these techniques. A noticeable lateral shift in the detected signatures is observed for the oblique prisms P2 and P3 across all methods along L1 (Figure 3a), and a similar shift is evident for P4 along L2 (Figure 3b). The RMS error for all the methods are shown in Figure 4. Among these methods, WSE and IL perform better for edge enhancement than other techniques.
FIGURE 3
FIGURE 4
In general, noise from various sources affects data quality during acquisition and influences the reliability of interpretation. Thus, the noise robustness of these techniques are evaluated by adding Gaussian noise with zero mean and a standard deviation of 2 nT to the total magnetic anomaly of the 3D synthetic model, following procedures commonly adopted in previous edge-detection studies (Arisoy and Dikmen, 2013; Dwivedi et al., 2023). Figure 5 illustrates the delineation of edges obtained using these methods after the addition of noise. The Theta map, THDR_NTilt, and IL filters perform poorly in detecting edges of lateral sources. In contrast, the THDR, TDR and ASA methods effectively identify the edges of sources P4, P6, and P7, but they are less successful in delineating the boundaries of deeper sources such as P1, P8, and P9. The GF filter also shows limitations, struggling to resolve the boundaries of P6 and P7, as well as those of the deeper sources. Visual inspection indicates that the WSE peaks clearly demarcates the upper surface edge of the P4, P6, and P7 and vice versa for deep sources P1, P8, P9. Overall, these results indicate that the sensitivity of edge-detection methods decreases with increasing source depth.
FIGURE 5
For further comparison among these methods, two profiles (L1 and L2) are extracted from the edge characterization shown in Figure 5. It is evident that the THETA and THDR_NTilt produce false edge peaks for P2, P3, P6, and P7 along profile L1. In contrast, the THDR, TDR, ASA, GF, IL, and WSE methods accurately delineate the edges of P6 and P7, although they generate multiple false peaks for the oblique prisms P2 and P3. Along profile L2, none of the methods are able to resolve the edges of P1, P5, and P8, with the exception of P4, whose boundaries are identified by THDR, TDR, ASA, GF, IL, and WSE (Figure 6). These observations highlight that while some methods are effective for certain sources, their performance is strongly dependent on source geometry and orientation. The calculated RMS errors for the edge detection methods, excluding THETA and THDR_NTilt are ∼75 m (THDR), ∼64 m (TDR), ∼46 m (ASA), ∼92 m (GF), ∼112 m (IL), and ∼41 m (WSE), with WSE exhibiting the lowest error.
FIGURE 6
4 Application to Laxmi basin and associated oceanic features
The Arabian Sea records the breakup of India from the Seychelles microcontinent and the early stages of ocean basin formation during the Late Cretaceous-Paleogene (Krishna et al., 2006; Bhattacharya and Yatheesh, 2015). Within this region, the Laxmi Basin forms a deep seafloor depression bordered by the Laxmi Ridge (LR) to the west and the Indian continental margin to the east. This Basin contains the chain of the Raman (R), Panikkar (P) Seamount, and Wadia (W) Guyot in its axial region. These morphotectonic elements are clearly visible in the bathymetry map as prominent structural highs (Figure 7a), reflecting a history of rifting, extinct seafloor spreading, and later hotspot-influenced volcanism (Yatheesh, 2020; Savio et al., 2022). The bathymetry data is obtained from the GEBCO (General Bathymetric Chart of the Oceans) database using the GEBCO 2025 global grid (https://download.gebco.net/, last accessed: 09 November 2025). Likewise, the Free-Air Anomaly (FAA) data is extracted from the Bureau Gravimétrique International (BGI) using the WGM-2012 global gravity model (https://bgi.obs-mip.fr/data-products/outils/wgm2012 visualizationextraction/#/form-wgm2012-model, last accessed: 09 November 2025) to generate the FAA map of the study region (Figure 7b). The bathymetry patterns of the basin and surrounding highs correlate strongly with signatures in FAA data. Smooth deep basin regions correspond to lower gravity, while seamounts and volcanic ridges produce positive anomaly highs.
FIGURE 7
The edge detection methods are applied to evaluate their ability to delineate the structural boundaries of major seafloor features. The THDR, TDR, and ASA methods successfully delineate the boundaries of the Laxmi Ridge and other geological features (R, P, and W), showing good agreement with the trends observed in the bathymetry map. However, these methods also produce numerous spurious boundaries due to their sensitivity to high-amplitude responses (Figures 8a–c). In contrast, THETA and THDR_NTilt provide unsatisfactory results for delineating geological boundaries (Figures 8d,e). The GF filter identifies the boundary of the Laxmi Ridge, but the resulting boundary appears relatively broad compared to the bathymetry map and fails to resolve the R, P, and W structures (Figure 8f). The IL filter produces prominent structural edges accompanied by several artifacts, which hinder the reliable interpretation of structural boundaries (Figure 8g). The zones of maximum entropy response correspond closely to the boundaries of Laxmi Ridge, Raman and Panikkar Seamounts, Wadia Guyot, and other geological structures, as indicated by the black lines (Figure 8h). The identified boundaries by WSE method matches with the bathymetry map of the study region. This demonstrates that the WSE based edge extraction preserves the spatial continuity of geological structures, allowing sharp transitions to be mapped more reliably. The WSE approach produces a more coherent and geologically meaningful characterization of crustal boundaries and enhancing our ability to interpret basin architecture.
FIGURE 8
5 Conclusion
This study presents a comprehensive evaluation of several edge enhancement methods applied to gravity and magnetic data, using both a synthetic model and a real marine case study from the Laxmi Basin, Arabian Sea. The synthetic results show that most of the methods effectively highlight shallow sources but suffer from reduced localization accuracy, and sensitivity to interference. Quantitative RMS error analysis under noisy conditions indicates that WSE outperforms other methods, particularly for shallow prismatic sources, yielding significantly lower RMS errors and cleaner edge responses. Application to free air gravity data further demonstrates that the THDR, TDR, and ASA methods produce multiple geological edges owing to their sensitivity to high-amplitude responses; however, the THETA and THDR_NTilt methods fail to delineate boundaries effectively. The GF method identifies the boundary of the Laxmi Ridge, but the resulting boundary appears relatively broad when compared with the bathymetry map. The IL filter produces prominent edges accompanied by artifacts, which complicates reliable interpretation. In contrast, WSE reliably delineates major geological features, including the Laxmi Ridge, and seamount boundaries that correlate well with bathymetry map. The comparative framework presented here provides practical guidance for selecting an appropriate edge enhancement method in both synthetic studies and realistic scenarios.
Statements
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
Author contributions
DD: Conceptualization, Data curation, Formal Analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review and editing.
Funding
The author(s) declared that financial support was not received for this work and/or its publication.
Acknowledgments
I thank the Director, NGRI, for supporting the work; reference no NGRI/Lib/2026/Pub-13.
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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The author(s) declared that generative AI was not used in the creation of this manuscript.
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Summary
Keywords
edge detection, gravity and magnetic data, Laxmi Basin, source boundary, wavelet space entropy
Citation
Dwivedi D (2026) Comparison of edge enhancement methods for potential field data: applications to a synthetic model and the Laxmi Basin, Arabian Sea. Front. Earth Sci. 14:1771807. doi: 10.3389/feart.2026.1771807
Received
19 December 2025
Revised
06 February 2026
Accepted
09 February 2026
Published
23 February 2026
Volume
14 - 2026
Edited by
Sanjit Kumar Pal, IIT(ISM) Dhanbad, India
Reviewed by
Luan Thanh Pham, VNU University of Science, Vietnam
Ahmad Alvandi, University of Tehran, Iran
Tamer Farag, Nuclear Materials Authority, Egypt
Updates
Copyright
© 2026 Dwivedi.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Divyanshu Dwivedi, ddwivedigp@gmail.com
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.