Enhancing the total-field magnetic anomaly using the normalized source strength

Nguyen Ngoc Long; Luan Thanh Pham; Kamal Abdelrahman; Hanbing Ai; Dat Viet Nguyen; Van-Hao Duong; Mohammed S. Fnais; Ahmed M. Eldosouky

doi:10.1515/geo-2022-0741

Artikel Open Access

Enhancing the total-field magnetic anomaly using the normalized source strength

Nguyen Ngoc Long , Luan Thanh Pham , Kamal Abdelrahman , Hanbing Ai , Dat Viet Nguyen , Van-Hao Duong , Mohammed S. Fnais und Ahmed M. Eldosouky

Veröffentlicht/Copyright: 20. Dezember 2024

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Abstract

Enhancement methods of aeromagnetic data are widely used in mapping geological features. Many methods based on field gradients have been introduced to outline the source edges. However, the disadvantage of these methods is that they require the reduction to pole (RTP) or gradients of the magnetic potential directly measured by specific sensors. This study introduces a new method to enhance magnetic anomaly data without needing the RTP. This method uses the normalized source strength (NSS) calculated from the total-field magnetic anomaly, subsequently balanced by the tilt angle filter. The new method is tested on synthetic datasets and a real dataset of the Olympic Peninsula. The findings show that the presented method is less sensitive to variations in the source depth. These findings also showed that this method is less dependent on the magnetization direction and produces more precise and sharper boundaries than other methods. Thus, the presented method appears promising in providing a valuable tool for interpreting magnetic data compared to traditional methods.

Keywords: aeromagnetic data; edge enhancement; normalized source strength

1 Introduction

The magnetic method is a geophysical technique that measures variations in the magnetic field to identify buried structures [1,2,3,4,5,6]. Aeromagnetic surveys are routinely carried out to extract geologic boundaries or are considered a tool to help the mineral potential mapping [7,8,9,10,11]. Magnetic datasets are also used in many tasks, including hydrocarbon exploration, geothermal exploration, and environmental surveys [1,12,13,14,15]. In addition, aeromagnetic surveys are carried out to assess groundwater potential [16,17], typically present in fractured, crystalline metamorphic basement rocks [18]. Many enhancement detectors have been developed to locate the body borders from the magnetic field, which are based on field gradients [19,20,21,22,23,24,25,26,27,28]. Most enhancement methods require the reduction to the pole (RTP) filter to minimize the effect of the magnetic inclination angle before computing the edges [29,30]. However, this filter does not work well when the survey area is low latitude [31,32]. Therefore, it may lead to erroneous results for the shape of the magnetic field. To overcome this problem, several authors have introduced some techniques to interpret magnetic data directly, i.e., without the RTP filter. The best-known approach is the analytic signal amplitude (AS), which is given by [33,34]

(1) AS = ∂ f ∂ x 2 + ∂ f ∂ y 2 + ∂ f ∂ z 2 ,

where f is magnetic data. The AS filter uses maximum values to present the edges of the causative body [34,35]. For 2D bodies, the shape of AS does not depend on the direction of magnetization. However, Li [36] showed that the 3D AS is not independent of the magnetization direction but has reduced sensitivity to this direction. In addition, using the simple analytic signal appears insufficient to detect geologic boundaries because of interference effects. Hsu et al. [37] suggested using high-order derivatives to increase the edge resolution. Their technique is determined by

(2) EAS = ∂ 2 f ∂ x ∂ z 2 + ∂ 2 f ∂ y ∂ z 2 + ∂ 2 f ∂ z 2 2 .

Ansari and Alamdar [38] introduced another approach, namely, the analytic signal of the tilt angle (ASTA), to improve the border resolution. This filter can outline the edges directly from magnetic data and is formulated as follows [38]:

(3) ASTA = ∂ TA ∂ x 2 + ∂ TA ∂ y 2 + ∂ TA ∂ z 2 ,

where TA is the tilt angle normalizing the vertical gradient in the inverse tangent function [39], which is given by

(4) TA = tan − 1 ∂ f ∂ z ∂ f ∂ x 2 + ∂ f ∂ y 2 .

To balance anomalies of sources having different depths and reduce the dependence of interpretation results on the magnetization vector, Ibraheem et al. [40] introduced an improved analytic signal (IAS) amplitude. It is expressed as

(5) IAS = sin − 1 ∂ AS ∂ z ∂ AS ∂ x 2 + ∂ AS ∂ y 2 + ∂ AS ∂ z 2 .

This approach provides results similar to those obtained from the tilt of AS [41]. Although the analytic signal amplitude-based methods do not require RTP data, the edges obtained from these methods are diffused or deformed [25,31,42,43].

Another approach is to use the magnetic gradient tensor to detect the source location [44]. Although its direct measurement can generate superior findings, such measurements are generally unavailable. The gradient tensor is calculated using Fourier processing of measured total magnetic intensity data [44,45]. Like RTP, this calculation is unstable when the geomagnetic field has a slight inclination angle [46].

In this research, we introduce a novel method for lining the edges of magnetic sources using the normalized source strength (NSS) of magnetic anomalies instead of the magnetic gradient tensor. This method does not require RTP data and produces more precise and sharper edges than traditional methods. Model examples and a real example are used to show the applicability of the presented method.

2 Method

Considering the magnetic field vector B = ( B x , B y , B z ) and the magnetic scalar potential ( U ), the complete magnetic gradient tensor Γ is defined as [47]

(6) Γ = − C m ∂ 2 U ∂ x 2 ∂ 2 U ∂ x ∂ y ∂ 2 U ∂ x ∂ z ∂ 2 U ∂ y ∂ x ∂ 2 U ∂ y 2 ∂ 2 U ∂ y ∂ z ∂ 2 U ∂ z ∂ x ∂ 2 U ∂ z ∂ x ∂ 2 U ∂ z 2 = ∂ B x ∂ x ∂ B y ∂ x ∂ B z ∂ x ∂ B x ∂ y ∂ B y ∂ y ∂ B z ∂ y ∂ B x ∂ z ∂ B y ∂ z ∂ B z ∂ z ,

where C m is the magnetic permeability and equal to 10 − 7 H/m in SI units [46,48].

The trace of the tensor is zero since the scalar potential U satisfies the Laplace equation. As Γ is Hermitian, it can be diagonalized with real eigenvalues as

(7) Γ = V T Λ V ,

where Λ = λ 1 0 0 0 λ 2 0 0 0 λ 3 and V = [ v 1 , v 2 , v 3 ] with λ i and v i (i = 1, 2, 3) are the eigenvalues and eigenvectors.

Beiki et al. [12] used NSS calculated from eigenvalues of Γ to detect source location. This technique is given by

(8) NSS = − λ 2 2 − λ 1 λ 3 .

The NSS is weakly dependent on magnetization vector direction [12]. However, the calculation of gradient tensor data in the frequency domain is unstable when the inclination angle is small [44]. To solve this issue, we introduce a new technique, called enhanced NSS (ENSS), in which NSS is computed by the second derivatives of the total-field magnetic anomaly, rather than using magnetic field components. In this case, the new matrix Γ ′ is defined as

(9) Γ ′ = ∂ 2 f ∂ x 2 ∂ 2 f ∂ x ∂ y ∂ 2 f ∂ x ∂ z ∂ 2 f ∂ y ∂ x ∂ 2 f ∂ y 2 ∂ 2 f ∂ y ∂ z ∂ 2 f ∂ z ∂ x ∂ 2 f ∂ z ∂ y ∂ 2 f ∂ z 2 ,

and ENSS can be obtained from new eigenvalues λ 1 ′ , λ 2 ′ , and λ 3 ′ of the new matrix Γ ′

(10) ENSS = − λ 2 ′ 2 − λ 1 ′ λ 3 ′ .

The eigenvalues λ 1 ′ , λ 2 ′ , and λ 3 ′ can be calculated by solving the characteristic equation det( Γ ′ − ΛI) = 0. For the 3 × 3 tensor matrix Γ ′ , this equation is expressed as follows:

(11) det ( Γ ′ − Λ I ) = ∂ 2 f ∂ x 2 − λ ′ ∂ 2 f ∂ x ∂ y ∂ 2 f ∂ x ∂ z ∂ 2 f ∂ y ∂ x ∂ 2 f ∂ y 2 − λ ′ ∂ 2 f ∂ y ∂ z ∂ 2 f ∂ z ∂ x ∂ 2 f ∂ z ∂ y ∂ 2 f ∂ z 2 − λ ′ = λ ′ 3 − I 1 λ ′ 2 + I 2 λ ′ − I 3 = 0 ,

where I₁, I₂, and I₃ are invariants that are given by [49]

(12) I 1 = ∂ 2 f ∂ x 2 + ∂ 2 f ∂ y 2 + ∂ 2 f ∂ z 2 = 0 ,

(13) I 2 = ∂ 2 f ∂ x 2 ∂ 2 f ∂ y 2 + ∂ 2 f ∂ x 2 ∂ 2 f ∂ z 2 + ∂ 2 f ∂ y 2 ∂ 2 f ∂ z 2 − ∂ 2 f ∂ x ∂ y 2 − ∂ 2 f ∂ x ∂ z 2 − ∂ 2 f ∂ y ∂ z 2 ,

(14) I 3 = ∂ 2 f ∂ x 2 ∂ 2 f ∂ y 2 ∂ 2 f ∂ z 2 − ∂ 2 f ∂ y ∂ z + ∂ 2 f ∂ x ∂ y ∂ 2 f ∂ y ∂ z ∂ 2 f ∂ x ∂ z − ∂ 2 f ∂ x ∂ y ∂ 2 f ∂ z 2 + ∂ 2 f ∂ x ∂ z ∂ 2 f ∂ x ∂ y ∂ 2 f ∂ y ∂ z − ∂ 2 f ∂ x ∂ z ∂ 2 f ∂ y 2 .

For a 2D source with ∂f/∂y = 0, the invariant I₂ can be rewritten as follows:

(15) I 2 = ∂ 2 f ∂ x 2 ∂ 2 f ∂ z 2 − ∂ 2 f ∂ x ∂ z 2 = − ∂ 2 f ∂ z 2 2 + ∂ 2 f ∂ x ∂ z 2 ,

while the invariant I 3 = 0 .

Equation (15) represents the enhanced analytic signal (EAS) that is independent of the magnetization direction [37]. For this reason, in the 2D case, ENSS only includes the invariant I₂, thus it is not dependent on the magnetization vector. Moreover, for general 3D, ENSS is less dependent on the magnetization direction than AS.

To outline both the shallow and deep sources, we enhance further ENSS using the tilt angle. The new method is written as

(16) TENSS = tan − 1 ∂ ENSS ∂ z ∂ ENSS ∂ x 2 + ∂ ENSS ∂ y 2 .

Due to using the tilt angle function, the values of the T ENSS are restricted to open interval ( − π / 2 , π / 2 ). The peaks in the T ENSS map are located over the edges of magnetic sources.

3 Model studies

We designed two magnetic models to evaluate the new filter’s effectiveness and compare it with AS and its enhanced versions, such as the EAS, ASTA, and IAS.

In the first model, we consider a prism with different magnetization vector directions, as shown in Figure 1a. Figure 1b–e present the anomalous fields generated by the prism with different inclination angles using the space method [50]. Figure 2 shows the results of AS (Figure 2a–d), EAS (Figure 2e–h), ASTA (Figure 2i–l), IAS (Figure 2m–p), ENSS (Figure 2q–t), and TENSS (Figure 2u–x). We can see that the AS and EAS methods only extract two of four borders of the body. The ASTA method can outline all the edges, but it brings some false boundaries around the east-west edges of Figure 2i and some other false peaks. The IAS method can determine all the edges, but the edges in the IAS output have a low resolution. Although the ENSS method only clearly enhances two of four edges of the body, its tilt angle (i.e., TENSS) can determine all the edges with a higher resolution than the IAS method. In addition, the TENSS method is less affected by the magnetization direction.

$Figure 1 (a) 3D view of the prism; magnetic data of the body with (b) I = 0 ° 0^\circ and D = 22 ° {22}^{^\circ } , (c) I = − 22 ° {-22}^{^\circ } and D = − 22 ° {-22}^{^\circ } , (d) I = 12 ° {12}^{^\circ } and D = 72 ° {72}^{^\circ } , and (e) I = − 5 ° {-5}^{^\circ } and D = − 65 ° {-65}^{^\circ } . The true edges are depicted by the black lines.$

Figure 1

(a) 3D view of the prism; magnetic data of the body with (b) I = 0 ° and D = 22 ° , (c) I = − 22 ° and D = − 22 ° , (d) I = 12 ° and D = 72 ° , and (e) I = − 5 ° and D = − 65 ° . The true edges are depicted by the black lines.

Figure 2

Results of magnetic anomalies in Figure 1(b)–(e). (a)–(d) AS, (e)–(h) EAS, (i)–(l) ASTA, (m)–(p) IAS, (q)–(t) ENSS, and (u)–(x) TENSS. The black lines depict the true edges.

The second experiment uses magnetic data due to four prisms having different depths to estimate the applicability of the new method. The plan and 3D views of these prisms are shown in Figure 3a and b, respectively. The information of the four bodies is shown in Table 1. The anomalous map is obtained by using inclination I = 70° and declination D = 0° for all bodies as in the actual example (Figure 3b). Figure 4a–f present the results obtained from applying AS, EAS, ASTA, IAS, ENSS, and TENSS to data in Figure 3c. One can see that AS and EAS are dominated by the shallow structures M1, M2, and M3, while ASTA is less effective in determining the edges for the complex model. IAS can enhance all the boundaries of the sources with the same amplitude. However, the edges at the corners are distorted compared to the true edges. ENSS enhances the edges of the bodies M1, M2, and M3 better than the AS, EAS, and ASTA, but these sources also dominate it. The presented method, TENSS, effectively enhances different signals, and the edges in the TENSS map are more precise and sharper than those from other methods.

Figure 3

(a) Plan view of four sources, (b) 3D view, (c) theoretical anomaly of the sources, and (d) theoretical anomaly of the sources with noise. The black lines depict the true edges.

Table 1

Parameters of four sources

Parameters	M1	M2	M3	M4
Coordinates of the center (km, km)	100, 30	100, 110	100, 110	100, 110
Width (km)	170	70	95	25
Length (km)	15	15	95	25
Top depth (km)	5	5	10	5
Bottom depth (km)	10	10	15	10
Inclination and declination (°)	70, 0	70, 0	70, 0	70, 0
Magnetization (A/m)	1	−1	−1	1

Figure 4

Results of magnetic anomalies in Figure 3c. (a) AS, (b) EAS, (c) ASTA, (d) IAS, (e) ENSS, and (f) TENSS. The black lines depict the true edges.

Since real magnetic measurements often include noisy signals, in the third example, 10% random noise was added to magnetic data in Figure 3c. Figure 5a–f show the results of the AS, EAS, ASTA, IAS, ENSS, and TENSS methods for noisy data. The results of AS and EAS do not show any significant changes compared to the previous test. In this case, ENSS still indicates the edges of the structures M1, M2, and M3 more clearly than AS and EAS, but the signals over the edges of the body M4 are blurred. The ASTA, IAS, and TENSS methods are more noise-sensitive than other techniques, although TENSS still outlines all the edges. The reason is that these techniques are based on the normalization of data that also enhances noisy signals.

Figure 5

Results of magnetic anomalies in Figure 3d. (a) AS, (b) EAS, (c) ASTA, (d) IAS, (e) ENSS, and (f) TENSS. The black lines depict the true edges.

We recommend mitigating noise signals with upward continuing data in noisy cases. Figure 6a–f show the results obtained from applying AS, EAS, ASTA, IAS, ENSS, and TENSS to noisy data after a 2 km upward continuation, respectively. In this case, AS and IAS do not show the boundaries of the body M1, and the boundaries at the corners of other bodies are distorted. The ASTA does not outline any edges, while the ENSS still provides clear boundaries over the bodies M1, M2, and M3. TENSS is more effective in enhancing all the boundaries of the bodies than other methods. TENSS provides thinner edges than the IAS with the same amplitude.

Figure 6

Results of noisy magnetic anomalies after upward continuation. (a) AS, (b) EAS, (c) ASTA, (d) IAS, (e) ENSS, and (f) TENSS. The black lines depict the true edges.

4 Real application

The applicability of the presented detector is estimated on the aeromagnetic dataset of the Olympic Peninsula. The peninsula is located in the Pacific Northwest (Figure 7) and occupies a crucial position within the tectonic framework of the Cascadia subduction zone. This area is characterized by the Juan de Fuca plate northeastward subduction under the North [53]. Figure 7 provides an overview of the Olympic Peninsula’s geological features, distinguished by its unique geologic terranes and structural configuration. Its geology is marked by an east-plunging anticlinorium, encompassing two principal geologic terranes [54]. The primary terrane consists of a non-magnetic tertiary sedimentary core. In contrast, the peripheral terrane comprises early Eocene basalts and marine sediments, which encircle the eastern segment of the mountain range. The peripheral terrane predominantly comprises the Crescent Formation basalts of early to middle Eocene age, accompanied by associated volcanic rocks and sediments [51]. The Crescent Formation is stratified into lower and upper members, each characterized by distinct lithological features. Massive submarine basalts, indicative of volcanic activity within a marine environment, characterize the lower member. In contrast, the upper member comprises subaerial basalts interlayered with sparse sediments [55].

Figure 7

Geology map of the Olympic Peninsula [51].

The aeromagnetic dataset of the Olympic Peninsula was acquired by the US Geological Survey in 1997 at an average flight altitude of 300 m using a stinger-mounted magnetometer [52]. A 1,000 m upward continuation was applied to the aeromagnetic dataset to reduce the noise. The aeromagnetic anomaly and its upward continuation are shown in Figure 8a and b, respectively. Here we used the AS, EAS, ASTA, IAS, ENSS, and TENSS methods to aeromagnetic anomalies in Figure 8b without the RTP. Figure 9a–f show the results of AS, EAS, ASTA, IAS, ENSS, and TENSS, respectively. High amplitude anomalies due to Eocene Crescent Formation basalts dominate the AS and EAS maps. ASTA is less effective in real applications and does not provide clear magnetic structures. The ENSS filter is also dominated by the significant anomalies related to the Eocene Crescent Formation. However, it allows for more apparent responses than AS and EAS in the northeastern region. IAS and TENSS effectively enhance magnetic data in the Olympic Peninsula. However, there is a slight difference in the results of IAS and TENSS, which may relate to the distortion of the edges determined by the IAS, as shown in the synthetic models. In addition, TENSS brings more information on magnetic structures in the area than IAS. This performance is because the TENSS better balances anomalies responding to sources located at different depths, as seen in the white box in Figure 9. Although the magnetic structures in the white box are obscured by nonmagnetic sediment, they are enhanced by the presented method, TENSS. Note that these structures are not outlined by the AS, EAS, ASTA, IAS, and ENSS techniques (white boxes in Figure 9). In addition, the TENSS map also showed the presence of high magnetically susceptible rocks, which are responsible for the almost round anomaly at the area’s eastern boundary. These rocks are not depicted on the geologic map, but according to reports from some studies, they can be emphasized by magnetic interpretation [56,57,58].

Figure 8

(a) Aeromagnetic data of the area [52] and (b) upward continuation of data in Figure 8a.

Figure 9

Results of real data in Figure 8b. (a) AS, (b) EAS, (c) ASTA, (d) IAS, (e) ENSS, and (f) TENSS.

5 Conclusion

A novel technique based on the normalized source strength calculated from magnetic anomalies has been presented to enhance aeromagnetic anomalies. The applicability of the new technique is considered on synthetic examples, as well as a real aeromagnetic dataset of the Olympic Peninsula. The results from model studies demonstrated that our method can increase performance and lessen the dependence of outputs on the magnetization direction compared to well-known methods, including the AS, EAS, ASTA, and IAS. In addition, the results of the real application showed that the new technique reveals more details on magnetization structures in the study region than other techniques. The limitation of the presented method is that it is more sensitive to noise than some first and second-order filters. However, using the upward continuation can solve this issue.

Acknowledgements

This research was supported by Researchers Supporting Project number (RSP2025R351), King Saud University, Riyadh, Saudi Arabia. The authors sincerely thank Saulo Pomponet Oliveira from the Federal University of Parana, Brazil, for his suggestions for improving the article. The three anonymous reviewers are thanked for their constructive comments and helpful suggestion. This research was funded by the research project QG.23.64 of Vietnam National University, Hanoi.

Author contributions: N.N.L. and L.T.P. contributed to the conceptualization, preparation of the manuscript, and revision process. K.A., H.A., D.V.N, V-H.D. M.S.F., and A.M.E. contributed to the preparation of the manuscript and discussion. The authors applied the SDC approach for the sequence of authors.
Conflict of interest: The authors declare no conflict of interest.
Data availability statement: Magnetic data are available from the corresponding author upon reasonable request.

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Received: 2024-09-06

Revised: 2024-11-05

Accepted: 2024-11-15

Published Online: 2024-12-20

This work is licensed under the Creative Commons Attribution 4.0 International License.

Artikel in diesem Heft

https://doi.org/10.1515/geo-2022-0741

Schlagwörter für diesen Artikel

aeromagnetic data; edge enhancement; normalized source strength

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