Terracing in interpretation of the potential field data

Terracing is an operator that is applied to potential field data to produce regions of constant field amplitude that are separated by sharp boundaries. Magnetic data are usually transformed into pseudo-gravity data (Baranov, 1957) prior to the application of terracing. The objective of terracing is ‘to recast potential field maps into a geologic map like format’ (Cordell and McCafferty 1989). Terracing is performed by moving a window through the data and computing the curvature at each point. The curvature of the field f is calculated using a three coefficient numerical approximation to the Laplacian derivative operator, which for profile data is given by:

(Scaling factors relating to the data sampling interval are unimportant here and have been ignored). The output value (located at the centre of the window) takes on one of three possible values. It becomes the value at the centre of the window, if this is greater than or lower than the rest of the data values in the window. If the curvature is positive, then the output value is set to the minimum of the data values in the window, while if it is negative then the output value is set to the maximum of the data values in the window. Terracing is performed in an iterative manner, with the data being sharpened progressively.
Cordell and McCafferty (1989) found that the terracing algorithm tended to square off the corners of anomalies, resulting in ragged domain boundaries. To compensate for this they computed the total horizontal derivative of the data and then tracked its local maxima using the algorithm of Blakely and Simpson (1986). These ridges were then overlain on the terraced data. The problem of the square boundaries is due to the fact that the calculation of the Laplacian function is only numerically approximated.
We propose that the problem of square domain boundaries was due to the curvature of the data being computed using a directionally biased approximation to the Laplacian and that it can be solved by using instead the profile curvature, which is the curvature computed in the direction of steepest ascent at each point of the data. Note that because both the Laplacian derivative operator and the profile curvature use the second horizontal derivatives of the data they are prone to noise problems and data may benefit from smoothing prior to their computation.
The objective of this work was to improve the output of the terracing filter and it was shown (by using both synthetic and real gravity data sets) that this can be achieved if the filter is based on the sign of the profile curvature of the data rather than on the sign of the Laplacian derivative operator. Although both the original and the modified algorithms are sensitive to noise because they use the second horizontal derivatives of the data, the modified algorithm appears to be more robust in this respect.
In this paper this method is applied on synthetic gravity data from adjacent prisms in different depths. Results show that this operator enhances subsurface boundary more accurately than other filters. Also we applied the proposed methods on real gravity data from southwest England. in this region, location of faults and Granite bodies enhanced.