Balancing in edge detection of bodies and linear structures from potential filed anomalies

Gradient methods have been extensively used in the interpretation of near-surface potential field anomalies because they increase the resolution of the edges of geologic sources and decrease the effect of the background or ‘regional’ field. Two gradient-based methods, namely the Euler and analytic signal, have proven particularly effective in the semi-automatic interpretation of magnetic anomaly data (i.e., determination of source outline and the depths of sources). Aeromagnetic data often contain anomalies with a large range in amplitude. Processed aeromagnetic images, such as horizontal and vertical derivatives, similarly contain features with large and small amplitudes. The smaller amplitude anomalies might be of considerable geological interest, but they can be hard to delineate among those of larger amplitude. Automatic Gain Control (AGC) filters divide the data at each point by an average value computed in a window centered on that point, thus produce a balanced image where all anomalies have similar amplitude. However, their output depends strongly on the window size, (Rajagopalan and Milligan, 1995), which makes them unsuitable for applications involving aeromagnetic data sets that in most cases contain anomalies of different size. In the last few years, there has been a surge of interest in the development of filters based on the derivatives of aeromagnetic data that produce a balanced output but avoid the window-size problem of the standard AGC filter. The first filter to be introduced was the tilt angle, (Miller and Singh, 1994), which is a balanced vertical derivative. Verduzco et al. (2004) suggest using the total horizontal derivative of the tilt angle as an interpretive tool. Wijns et al. (2005) developed the theta map, a balanced total horizontal derivative, Cooper and Cowan (2006) introduced a horizontal tilt angle, which is a balanced horizontal derivative. Another approach to edge detection based on derivatives was the use of the balanced windowed standard deviation. The analytic signal, which is a complex function and makes use of the Hilbert transform, has been shown to be effective in interpretation of the subsurface magnetic contacts (e.g., Nabighian, 1972, 1974). A geologic contact or fault with significant susceptibility contrast is detected by mapping the maxima of the simple analytic signal, which is composed of the two horizontal and one vertical gradient. The analytic signal response from the larger and shallow sources is clearly visible, but it is very faint for deeper bodies. To enhance this image and bring out the detail in smaller amplitude anomalies, in this paper a balanced analytic signal was computed as followed (Cooper, 2009):
where xH and yH are the Hilbert transforms of the analytic signal in the x- and y- directions, respectively. The width of anomalies in the balanced analytic signal amplitude image has increased slightly compared with those in the original analytic signal amplitude image, which might make accurate contact mapping more difficult. The curvature of geophysical data can be a useful attribute, and in the past it has been applied to potential-field data (Phillips et al., 2007) and reflection seismic data (Blumentritt et al., 2006). In this case, the profile curvature was used, defined as (Mitasova and Jarosalav, 1993):
where,p=(∂f/∂x)2(∂f/∂y)2 andq=p. In this paper we demonstrated the application of these filters to synthetic magnetic data and as well as real magnetic data from Soork Iron mine and the aeromagnetic data from Yilgran Craton in Australia. Application of this filter to the magnetic data from Soork Iron ore lead to detection of a new hidden body which is proved by exploratory drilling.