Edge detection process of Qom salt dome gravity anomalies ... · Edge detection process of Qom salt dome gravity anomalies using hyperbolic tilt angle Ahmad Alvandi 1, Rasoul Hoseini

INTERNATIONAL JOURNAL OF GEOMATICS AND GEOSCIENCES

Volume 5, No 2, 2014

© Copyright by the authors - Licensee IPA- Under Creative Commons license 3.0

Research article ISSN 0976 – 4380

Submitted on September 2014 published on October 2014 209

Edge detection process of Qom salt dome gravity anomalies using

hyperbolic tilt angle

Ahmad Alvandi1, Rasoul Hoseini Asil2

1- Young Researchers Club and Elites, Islamic Azad University, Toyserkan Branch,

Toyserkan, Iran

2- Young Researchers Club and Elites, Islamic Azad University, Sahneh Branch, Sahneh,

Iran

[email protected]

ABSTRACT

In recent decade the edge detection procedure has been of great utility in the modeling and

interpretation of self-potential, magnetic and gravity anomalies. This paper applies a precise

edge detection procedure, called hyperbolic tilt angle (HTA) technique. The sufficiency of the

HTA method is indicated using complex synthetic models and a residual gravity data set from

Iran. Compared with the formal methods, the HTA filter more detailed outcomes for buried

models and is less sensitive to noise.

Key Words: Edge Detection, Hyperbolic Tilt Angle, Theoretical and Field Gravity Anomalies,

Low-Pass Filtering, Qom Salt Dome, Iran

1. Introduction

Gravity and magnetic anomalies are essential to geophysical approaches to geologic mapping

(Pilkington and Keating, 2010). Boundaries detection of causative sources is one of the most

important stages in the modeling of gravity anomalies (Bournas and Baker, 2001; Ardestani

and Motavalli, 2007). Accurate detection of source shape coordinates is becoming the main

goal for interpretation and therefore enhanced methods are acquiring an increasing revival in

data interpretation (Bournas and Baker, 2001). There are various procedures that have been

engaged to attain edge detection, for example, Analytic signal (AS), tilt angle (TI), theta map

(TH) and etc. (Arisoy and Dikmen, 2013). Potential field derivatives are largely used to

modeling of buried sources (Arisoy and Dikmen, 2013). The analytical signal (AS) is one

known filters that is applied to interpretation and modeling gravity and magnetic data

(Pilkington and Keating, 2004; Cooper and Cowan, 2008; Cooper, 2009).

Miller and Singh (1994) introduced a tilt derivative (TA) filter to detect edge (Hoseini et al.,

2013). Verduzco et al (2004) suggested total horizontal derivative of the tilt angle (THDR) to

improve edge detection process (Pilkington and Keating, 2004; Cooper and Cowan, 2006).

Wijns et al (2005) introduced the usage of theta angle which is supported the AS to magnetic

and gravity interpretation (Nejati Kalateh and Roshandel Kahoo, 2012). In this research, we

employed a Hyperbolic Tilt Angle filter (Cooper and Cowan, 2006) for detecting gravity

source boundaries. In order to illustrate the performance of this technique, we have first given

some complex theoretical examples and compared our results with those obtained by edge

detection known methods. Then, the approach was applied to one gravity anomaly, extracted

from an Iran gravity ground survey data set. All map images applied in our research have

been generated using MATLAB 7.11 program.

Edge detection process of Qom salt dome gravity anomalies using hyperbolic tilt angle

Ahmad Alvandi, Rasoul Hoseini Asil

International Journal of Geomatics and Geosciences

Volume 5 Issue 2, 2014 210

2. Edge detection filters

The five edge detection filters used in this paper to detect the boundaries of buried sources

are showed in table 1. Parameter F is the gravity field, F/ x and F/ y are horizontal

derivatives of field and F/ z is vertical derivative of field. Main edge detection techniques

geometric description is shown in figure 1.

Figure 1: Main edge detection techniques of gravimetric anomalies: Analytic Signal (AS),

Total Horizontal Derivative (THDR), Tilt Angle (TI) and Theta Map (TH) (Bongiolo and

Ferreira, 2012)

3. Theoretical gravity modeling examples

3.1. Model 1

In this part, synthetic examples are applied to test the abilities of the presented techniques. 2-

D and 3-D theoretical Model (1), shown in figure 2(a), is generated by using finite prisms

located at various depths. The bottom and top depths of prism A were selected as 6 and 3 km,

the widths of prism A in the x and y coordinates were selected as 20 and 20 km, respectively.

Prism B is deeper than prism A. The top and bottom depths of prism B were selected as 6 and

10 km, and the widths of prism B in the x and y directions were selected as 20 and 20 km,

respectively. The synthetic map of residual anomaly is shown in Figure 2(b). The map of

THDR, AS, TI, TH and HTI are shown in figures 2(c), 2(d), 2(e), 2(f) and 2(g) respectively.

Then, 3 % Gaussian noise was added to the synthetic anomalies. Figures 3(a), 3(b), 3(c), 3(d),

3e and 3(f) show, respectively, the anomaly map with added noise, THDR map, AS map, the

TI generated from the noisy anomaly map, TH method and the outputs of the HTI technique.

In the noisy model, it is seen that the proposed method produces precise outcomes than the

THDR, AS and TI methods. The maps of HTI data filtering and frequency domain filtering

are shown in figures 3(g) and 3(h) respectively.





Table 1: Edge Detection methods for field F, having components X, Y, and Z (Hoseini et al.,

2013; Pilkington and Keating, 2004)





Figure 2: a) Buried synthetic models in subsurface; b) Theoretical model anomaly map

(mGal); c) Total horizontal derivative; d) analytic signal; e) Tilt angle; f) Theta map; g)

Hyperbolic tilt angle









Figure 3: a) Noisy anomaly map (mGal); b) Total horizontal derivative; c)

analytic signal; d) Tilt angle; e) Theta map; f) Hyperbolic tilt angle; g) HTI data filtering; h)

Frequency domain filtering

3.2 Model 2

2-D and 3-D theoretical Model (2), shown in Figure 4(a), is produced by using finite prisms

located at various depths. The bottom and top depths of prism A were selected as 5.1 and 3.1

km. the widths of prism A in the x and y coordinates were selected as 20 and 20 km,

respectively. Prism B is deeper than prism A. The top and bottom depths of prism B were

selected as 6 and 8 km, and the widths of prism B in the x and y directions were selected as

20 and 15 km, respectively. Prism C is deeper than prism B. The top and bottom depths of

prism C were selected as 9 and 11 km, and the widths of prism C in the x and y directions

were selected as 20 and 20 km, respectively. Prism D is deeper than prism C. The top and

bottom depths of prism D were selected as 12 and 14 km, and the widths of prism D in the x

and y directions were selected as 20 and 16 km, respectively.

The synthetic gravity anomaly map is shown in Figure 4(b). The results of using total

horizontal derivative, analytic signal, tilt angle, theta map, and hyperbolic tilt angle are

shown in figures 4(c), 4(d), 4(e), 4(f) and 4(g) respectively. To demonstrate how this

approach performs on contaminated with noise data, random noise with amplitude equal to

5 % of the maximum data amplitude was added to the gravity data set shown in Figure 5(a).

Figures 5(b), 5(c), 5(d), 5(e) and 5(f) show, respectively, THDR map, AS map, the TI

obtained from the noisy anomaly map, TH map and the outputs of the proposed method. In

the case of noisy data, it is seen that the HTI technique produces better results than the

THDR, AS and TI methods. The maps of HTI data filtering and frequency domain filtering

are shown in figures 5(h) and 5(g) respectively.

3.3 Model 3

The third example shows five prisms with different geometries, inserted in to a surface of 100

km×100 km. Figure 6(a) displays the shapes built with the amounts of table2. Figure 6(b)

displays the residual anomalies generated from the prisms of figure 6(a) with the parameters

of table (2). The results of using total horizontal derivative, analytic signal, tilt angle, theta

map, and hyperbolic tilt angle are shown in figures 6(c), 6(d), 6(e), 6(f) and 6(g)

respectively .To demonstrate how this approach performs on noisy data, random noise with

amplitude equal to 9 % of the maximum data amplitude was added to the gravity data set

shown in picture 7(a). pictures 7(b), 7(c), 7(d), 7(e) and 7(f) show, respectively, the anomaly

map with added noise, THDR map, AS map, the TI obtained from the noisy anomaly map,





TH map and the outputs of the proposed method. In the case of noisy data, it is seen that the

proposed method produces better results than the THDR, AS and TI methods. The maps of

HTI data filtering and frequency domain filtering are shown in figures 7(g) and 7(h)

respectively.





Figure 4: a) Spatial distribution of the 2-D and 3-D synthetic models in subsurface; b)

theoretical model anomaly map (mGal); c) Total horizontal derivative; d) analytic signal; e)

Tilt angle; f) Theta map, g) Hyperbolic tilt angle





Figure 5: a) Noisy anomaly map (mGal); b) Total horizontal derivative; c) Analytic signal;

d) tilt angle; e) Theta map; f) Hyperbolic tilt angle; g) Frequency domain filtering; h) HTI

data low-pass filtering





Table 2: Parameters of the shapes in figure 6(a)

Anomaly Density

(g/cm3)

Width

(Km)

Length

(Km)

Thickness

(Km)

Depth of top

(Km)

A 2.75 20 22 1 10

B 2.85 21 25 1 10

C 2.75 0.5 75 0.5 10

D 3 2.5 45 0.8 10

E 2.5 20 20 3 15





Figure 6: a) 2D and 3D representation of the synthetic shapes A, B, C, D and E, with

parameters listed in Table 2; b) Theoretical model anomaly map (mGal); c) Total horizontal

derivative; d) Analytic signal; e) Tilt angle; f) Theta map, g) Hyperbolic tilt angle





Figure 7: a) Noisy anomaly map (mGal); b) Total horizontal derivative; c) Analytic signal;

d) tilt angle; e) Theta map; f) Hyperbolic tilt angle; g) HTI data filtering; h) Frequency

domain filtering





4. Field gravity example

This section considers the application and abilities of edge detection methods to field gravity

data from the Qom salt dome in the center of Iran (Motasharreie et al., 2010). The gravity

anomalies (mGal) and up-ward continuation mapping (0.5 km) are shown in figure 8 (a) and

8(b) respectively. The results of using THDR, AS, TI, and TH are shown in figures 8(c), 8(d),

8(e), and 8(f) respectively. The edge detection by the HTI procedure is more accurate and

better than the THDR, AS and TI method (figure 8g). The maps of HTI data filtering and

frequency domain filtering are shown in figures 8(h) and 8(I) respectively.





Figure 8: a) Residual anomalies map (mGal); b) up-ward continuation (0.5 km); c) THDR;

d) AS; e) TI; f) TH; g) HTI; h) HTI low-pass filtering; I) Frequency domain filtering





5. Conclusion

In this research, we tested the capabilities of hyperbolic tilt angle (HTA) procedure on

synthetic data and Qom salt dome data, center of Iran. The HTA filter show the better

efficiency on theoretical models and field model of other edge detection methods. Compared

with the analytic signal and tilt angle methods, the HTA filter more detailed outcomes for

buried models and is less sensitive to noise.

6. References

1. Pilkington, M., and Keating, P., (2010), geologic applications of magnetic data and using

enhancements for contact mapping, EGM international workshop Adding new value to

electromagnetic, gravity and Magnetic methods for exploration, Capri, Italy, pp 11-14.

2. D. Aydogan, (2011), Extraction of lineaments from gravity anomaly maps using the

gradient calculation: application to Central Anatolia, Earth Planets Space, 63, pp 903–

909.

3. Bournas, Nasreddine, and Baker, Haydar Aziz., (2001), interpretation of magnetic

anomalies using the horizontal gradient analytic signal, Annali di Geofisica, 44 (3), pp

506-526.

4. Arisoy, Muzaffer Ozgo., and DikmenUnal., (2013), Edge Detection of Magnetic Sources

Using Enhanced Total Horizontal Derivative of the Tilt Angle, Bulletin of the Earth

Sciences Application and Research Centre of Hacettepe University, 34 (1), pp 73-82.

5. Pilkington, M., and Keating, P., (2004), contact mapping from gridded magnetic data: a

comparison of techniques, exploration geophysics, 35, pp 206-311.

6. Cooper, G.R.J., (2009), balancing images of potential field data, geophysics, 74(3), pp

17-20.

7. 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), pp 1585-1591.

8. Cooper, G.R.J., and Cowan, D.R., (2008), Edge enhancement of potential-field data using

normalized statistics, geophysics, 73(3), pp 1-4.

9. Miller, H.G., and Singh, V., (1994), Potential field tilt: a new concept for location of

potential filed sources. Journal of Applied Geophysics, 32, pp 213-217.

10. Verduzco, B., Fairhead, J.D., Green, C.M., and MacKenzie, C., (2004), new insights into

magnetic derivatives for structural mapping. The Leading Edge, 23(2), pp 116-119.

11. Wijns, C., Perez, C., and Kowalczyk, P., (2005), Theta map: edge detection in magnetic

data, Geophysics, 70(4), pp 39-43.

12. Roest, W.R., Verhoef, J., and Pilkington, M., (1992), magnetic interpretation using the 3-

D analytic signals and Geophysics, 57(1), pp 116-125.





13. Hadadian, A., (2011), Precise boundary detection of potential field anomalies using local

phase filters, M.Sc. Thesis, Shahrood University of Technology, p.102.

14. Hoseini Asil, R., (2013), Depth estimation using a tilt derivative map from gravity

gradient data, M.Sc. Thesis, Hamedan Branch, Islamic Azad University, p.70.

15. Hoseini, Ali Akbar., Doulati Ardejani, Faramarz.,Tabatabaie, Seyed Hashem.,

Hezarkhani, Ardeshir., (2013), edge detection in gravity field of the gheshm sedimentary

basin, International journal of Min & Geo-Eng (IJMGE), 47( 1), pp 41-50.

16. Sertcelik, I., Kafadar, O., (2012), application of edge detection to potential field data

using eigenvalue analysis of structure tensor. Journal of Applied Geophysics 84, 86–94.

17. Kalateh, Ali Nejati., and Kahoo, Amin Roshandel., (2012), edge detection of potential

field data using Theta maps, Iranian journal of geophysics, 7(1), pp 24-33, (Persian

version).

18. Bongiolo ABS., and Ferreira FJF., (2012), evaluation of enhancement techniques of

magnetic anomalies applied to structural interpretation of the Itaituba region, Brazil,

Revista Brasileira de Geofisica, 30(3), pp 373-388.

19. Motasharreie, A., Zomorodian, H., SiahKoohi, H. R., Mirzaei, M., (2010), Inversion of

gravity data in wavelet domain using normalized forward models, Journal of Earth &

space physics, 36(1), 29-38.

20. Ardestani V.E. and Motavalli H., (2007), constraints of analytic signal to determine the

depth of gravity anomalies. Journal of Earth & space physics, 33(2), 77-83.

21. Ardestani, V.E. (2005). Gravity interpretation via gravity gradients and analytic signal

Journal of Earth sciences, 12(54).

22. Cooper, G.R.J., and Cowan, D.R., (2011), a generalized derivative operator for potential

field data. Computers & Geosciences, Geophysical Prospecting, 59, pp 188–194.

23. Ming, W., Zhi-hong, G., and Luofen, H, (2013), edge detection of field data using inverse

hyperbolic tangent, Geophysical & Geochemical Exploration, 37(4), pp 655-663.

Documents

Edge detection process of Qom salt dome gravity anomalies ... · Edge detection process of Qom salt dome gravity anomalies using hyperbolic tilt angle Ahmad Alvandi 1, Rasoul Hoseini