New method for edges detection of magnetic sources using logistic function

L. T. Pham, E. Oksum, T. D. Do, M. L. Huy


The tilt angle of the analytic signal amplitude (TA) is defined as the arctangent of the ratio of the first vertical derivative to the total horizontal derivative of the analytic signal amplitude. It is commonly used as a useful tool to estimate edges of magnetic sources because its value is slightly dependence on the direction of magnetization vector, and it is more effective in estimating the edges of the bodies than the analytic signal amplitude and the standard tilt angle. Based on logistic function (L) that has the same shape with the shape of arctangent function, and the derivatives of the analytic signal amplitude, we introduce some new filters which also can reduce the effect of the magnetization direction. Other notable features of these filters are that they produce amplitude maxima over the edges of sources and that they balance anomalies from shallow and deep sources. The feasibility of the proposed filters is demonstrated on noise-free and noisy synthetic magnetic data from two 3D models where the obtained results coincide well with the actual edges. The effectiveness of the filters is also evaluated by comparing it with other edge detection methods. The results also show that our filters are less sensitive to variations in the depth of the source bodies and that a modified logistic function (Lk) can achieve better edge detection results than the analytic signal amplitude (AS), the analytic signal amplitude of the tilt angle (AT), the TA and L filters. The filters are also applied to real magnetic data from an area in south-central Vietnam, and the results demonstrate that the proposed filters is a useful tool for the qualitative interpretation of magnetic data.


logistic function; tilt angle; analytic signal amplitude; edge detection; interpretation of magnetic data

Full Text:



Ansari, A. H., & Alamdar, K. (2011). A new edge detection method based on the analytic signal of tilt angle (ASTA) for magnetic and gravity anomalies. Iranian Journal of Science and Technology, 35(2), 81―88. doi: 10.22099/ijsts.2011.2131.

Cooper, G. R. J. (2014). Reducing the dependence of the analytic signal amplitude of aeromagnetic data on the source vector direction. Geophysics, 79(4), J55―J60.

Cooper, G. R. J., & Cowan, D. R. (2008). Edge enhancement of potential-field data using normalized statistics. Geophysics, 73(3), H1―H4.

Cooper, G. R. J., & Cowan, D. R. (2006). Enhancing Potential Field Data Using Filters Based on the Local Phase. Computers & Geosciences, 32(10), 1585―1591.

Cordell, L. (1979). Gravimetric Expression of graben faulting in Santa Fe Country and the Espanola Basin, New Mexico. In R. V. Ingersoll (Ed.), Guidebook to Santa Fe Country (pp. 59―64). New Mexico Geological Society, Socorro.

Cordell, L., & Grauch, V. J. S. (1985). Mapping Basement Magnetization Zones from Aeromagnetic Data in the San Juan Basin, New Mexico. In The Utility of Regional Gravity and Magnetic Anomaly Maps (pp. 181―197). Society of Exploration Geophysicists, Tulsa.

Geological Survey of Japan and Coordinating Committee for Coastal and Offshore Geoscience Programs in East and Southeast Asia (CCOP). (1996). Magnetic anomaly map of East Asia 1:4 000 000. CD-ROM.

Hsu, S. K., Coppense, D., & Shyu, C. T. (1996). High- resolution detection of geologic boundaries from potential field anomalies: An enhanced analytic signal technique. Geophysics, 61(2), 1947―1957.

Li, X., (2006). Understanding 3D analytic signal amplitude. Geophysics, 71(2), L13―L16.

Miller, H. G., & Sing, V. (1994). Potential field tilt a new concept for location of potential field sources. Journal of Applied Geophysics, 32(2-3), 213―217.

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(3), 507―517. 1.1440276.

Pilkington, M., & Tschirhart, V. (2017). Practical considerations in the use of edge detectors for geologic mapping using magnetic data. Geophysics, 82(3), J1―J8.

Roest, W. R., Verhoef, J., & Pilkington, M. (1992). Magnetic interpretation using the 3-D analytic signal. Geophysics, 57(1), 116―125.

Verduzco, B., Fairhead, J. D., Green, C. M., & MacKenzie, C. (2004). New insights to magnetic derivatives for structural mapping. The Leading Edge, 23(2), 116―119. 10.1190/1.1651454.

Wijns, C, Perez, C., & Kowalczyk, P. (2005). Theta map: Edge detection in magnetic data. Geophysics, 70(4), L39―L43. 1.1988184.

Creative Commons License
Licensed under a Creative Commons Attribution 4.0 International License.