Potential field data balancing using the Hilbert transform

Potential field images obtained in potential field data measurements are suitable tools for mineral and hydrocarbons resources explorations. These images consist of different anomalies which in many cases are contaminated with noise. The horizontal location of the boundaries of potential field anomaly sources is of interest in potential field interpretation. However, the edge of potential field sources is not clear, because of the loss of resolution of the anomaly shape with respect to the shape of their sources. Edge enhancement is a technique, applied to potential field data to produce regions of constant field amplitude that are separated by sharp boundaries, as an aid to interpretation.
Various methods have been introduced for anomaly edge detection, such as the analytic signal, tilt angle, total horizontal gradient and profile curvature. The tilt angle is the ratio of the first vertical derivative to the horizontal gradient. Curvature of the geophysical data is one of the most important attributes with many applications in geophysical data processing and interpretation. The profile curvature at a point shows the change in slope in maximum gradient direction. We can compute the tilt angle and profile curvature by Eq. (1) and Eq. (2), respectively.
(1)
(2)
where, is potential field and
(3)
In many cases of geological interpretation of potential field data, the study of low-amplitude anomalies is more important than the high-amplitude anomalies. However, most existing methods for determining the lateral expansion of geological structure are sensitive to amplitude of the potential data. Amplitude of potential field data has a direct relationship with depth of the geological structure. So we can say that the efficiency of methods to detect geological structures severely depends on the depth of geological structures. Automatic gain control filters can construct the balanced image of all anomalies by assigning the computed gain of each window of the data to the center of it.
In this paper, we used two-dimensional Hilbert transform to balance the image of potential field data as Eq. (4).
(4)
Where, and are 2-D Hilbert transforms of image in and directions, respectively.
In order to show the efficiency of proposed method to balance the potential field images, we test the method on two usual edge detection methods entitled as profile curvature and the tilt angle filter. We used a model with three anomalies with various depths as the synthetic model. Results from synthetic data showed that the profile curvature and the tilt angle filter cannot detect the edges of the deep anomalies as well as shallow anomalies. By applying the 2-D Hilbert transform based balancing method on images of common method the resolution of detected edges of anomalies for deep and shallow anomalies are balanced. We used the gravity anomalies related to granite intrusion at Trompsburge, South Africa and salt dome at sedimentary basin, Center of Iran as real data. Balancing method improved significantly the images resulted from profile curvature and the tilt angle filter.