Edge detection of gravity anomalies by enhanced mathematical morphology filter

Enhancement on the edges of the causative source is a tool in the interpretation of potential field data. There are many methods for recognizing the edges, most of which involve high pass filters based on derivatives of potential field data. In this paper, a new edge detection method is introduce, called the enhanced mathematical morphology (EMM) filter for interpretation of field data. The EMM filter uses the ratio of the erosion of the total horizontal derivative to the dilation of the total horizontal derivative to recognize the edges of the sources, and can display the edges of the bodies simultaneously. Edge detection of the potential field data has been widely used as a significant tool for geophysical exploration technologies, which can delineate the horizontal locations of causative sources. Normally, various high-pass filters are used to recognize the edges of the potential field data (Evjen 1936; Fedi and Florio 2001; Verduzco et al. 2004; Cooper and Cowan 2006; Cooper and Cowan 2011; Ma and Li 2012; Ma 2013).
The EMM filter uses the ratio of the erosion of THD to the dilation of THD to recognize the edges of the source. Mathematical morphology was developed by Matheron and Serra in 1964 (SERRA, 1983); which is an image analysis and recognition tool. The structuring element (SE) is a basic operator in mathematical morphology, used to interact with an image and to draw conclusions about how a shape fits or misses the shapes in the image. SE consists of a matrix of 0s and 1s that can have any arbitrary shape and size. The basic operations of mathematical morphology are dilation and erosion. Dilation is defined as the maximum value in the window ascertained by the SE. Erosion is defined as the minimum value in the window ascertained by the SE. The EMM filter is expressed as (Lili et al., 2013):
where imerode (F,SE) and imdilate (F,SE) represent the erosion and dilation of the THD, respectively.
In this paper, a new relationship is presented for EMM filter that is tested on synthetic data with and without noise as well as the real potential field data in Qom salt dome. The EMM method successfully delineates the edges of the causative sources, which gives better resolution of the deeper source than other filters, and can display the edges of the bodies in a more centralized way. In this article, a new relationship is defined for the EMM filter as:
The EMM filter was used to recognize the edges of the sources. It can display the edges of the shallow and deep bodies simultaneously. The EMM filter does not require the computation of vertical derivatives, which makes this method computationally stable. The EMM filter is tested on synthetic, and real potential field data in Qom salt dome and the edge detection was done with reasonable results.