Edge detection of potential field anomalies using local phase filters

Potential fields are due to complex distribution of sources related to susceptibility and mass density variations for magnetic and gravity field respectively. In researching the lateral heterogeneous of different geological bodies, in particular their edge location potential field has some advantages. We mainly refer to linear features such as fault, folding axis, dyke, trend and border of the geological units as well as to circular featurs such as crates and buried voids when mentioning geological bodies.
Usually, the edge detection and edge enhancement techniques are used to distinguish between geological bodies with different depths and sizes. Edge detection methods are based on the position of the maximum or zero-crossing points associated with vertical derivative, horizontal derivative and analytic signal filters. These methods which are famed to derivative-based filters use different orders, but some instability may occur in high-order derivatives since any kind of noise or non-harmonic signal will be correspondingly enhanced with desired signals simultaneously. Another difficulty is that in the filtered image, the smaller amplitude features (which may be of considerable importance) may be hard to discern.
Other edge detection methods are local phase filters (edge enhancement methods) based on the phase variation of the derivative quantities. The advantage of these filters is their flexibility to produce new filters with most applicability just with partial variation. The edge enhancement methods mainly include Tilt angle (TA), Total Horizontal derivative of the tilt angle (THDR), theta map, Hyperbolic Tilt Angle (HTA) and normalized horizontal derivative.
The tilt angle filter did not serve as a very accurate method of locating deep sources. A much improved result came from using the second vertical derivative of the tilt angle in the space domain. Equations (1) to (4) are the local phase filters.
(1)
(2)
(3)
(4)

where, f is potential field data, T is tilt angle and x,y,z are three Cartesian components. In the above equation denote real part of function.
In this paper we applied these filters on synthetic magnetic data from a cylinder model as well as on real magnetic data from the Abadeh quadrangle. According to the obtained results the Dehshir-Baft fault in the northeast of the studied and ophiolite outcrops in the southeast are enhanced.