Application of surface-derived attributes in determining boundaries of potential-field sources

This paper describes an edge detection method based on surface-derived attributes. The surfacederived attributes are widely used in the interpretation of seismic data in two main categories: (1) derivative attributes including the dip angle and the azimuth; (2) derivative attributes including curvature attributes. In general, the magnitude of the normal curvature of a surface (curvature attributes) can be expressed in terms of derivatives of that surface which are called the first and second fundamental forms of the surface. For a quadratic surface which fits to data, it is shown that the dip-angle equation in the interpretation of the seismic data is similar to the horizontal gradient magnitude (HGM) equation in the interpretation of potential field data. Among the infinite number of curvature attributes, a few of them which are suitable for edge detection are shown. The coefficients of a quadratic surface are calculated using the least square method. At a particular point, the attributes are obtained using these coefficients. Zero contours of most positive curvature and the determinant of the curvature matrix delineate the location of the edges of anomalies. The shape index attribute quantitatively reflects the local shape of the surface over sources in terms of cap, dome, ridge, saddle, rut, trough and cup. Here, the maximum curvature is introduced as a new technique to detect the horizontal location of anomalies. First, the introduced attributes were applied to the noise-free synthetic data. Then, the data with the noise added were used to check the stability of the method. In the presence of high level noise, this method was successful in determining boundaries of the anomalies. Zero contours of the most positive curvature, the determinant of curvature matrix and the maximum curvature properly illustrate the linear features within the mapped surface. The results of using surfacederived attributes were compared with tilt angle and HGM filters. This comparison showed that zero contours of the most positive and maximum curvature attributes are approximately matched with zero contours of the tilt angle and maximum values of HGM. Finally, this method was used for real data from Mobrun massive sulfide ore of Canada. MATLAB software was used for programming and calculating the required parameters of this method.