Horizontal boundary identification of causative sources is an essential tool in potential field data interpretation due to the feasibility of automatically retrieving the boundary information of subsurface gravity or geomagnetic structures. Although many approaches have been proposed to address these issues, it is still a hot research topic for many researchers to derive novel methods or enhance existing techniques. We present two high-resolution edge detectors based on the Gudermannian function and the modifications of the second-order derivative of the field. The effectiveness of the newly proposed filters was initially tested on synthetic gravity anomalies and geomagnetic responses with different assumptions (2-D and 3-D; imposed and superimposed; noise-free and noise-contaminated). The obtained results verified that the two novel methods yield the capability of producing high-resolution, balanced amplitudes and accurate results for better imaging causative sources with different geometrical and geophysical properties, compared with the other nine representative edge enhancement techniques. Furthermore, the yielded results from the application of the two strategies to a real-world aeromagnetic data set measured from the Central Puget Lowland (C.P.L) of the United States and a gravity data set surveyed from the Jalal Abad area of Kerman province, Iran, with detailed comparative studies validated that the edges identified via the two methods are in good agreement with the major geological structures within the study areas and the determined lateral information using the tilt-depth, top-depth estimation method. These features make them valuable tools for solving edge detection problems.

A fast algorithm for solving the under-determined 3-D linear gravity inverse problem based on the randomized singular value decomposition (RSVD) is developed. The algorithm combines an iteratively reweighted approach for L₁-norm regularization with the RSVD methodology in which the large scale linear system at each iteration is replaced with a much smaller linear system. Although the optimal choice for the low rank approximation of the system matrix with m rows is q = m, acceptable results are achievable with q ≪ m. In contrast to the use of the iterative LSQR algorithm for the solution of the linear systems at each iteration, the singular values generated using the RSVD yield a good approximation of the dominant singular values of the large scale system matrix. The regularization parameter found for the small system at each iteration is thus dependent on the dominant singular values of the large scale system matrix and appropriately regularizes the dominant singular space of the large scale problem. The results achieved are comparable with those obtained using the LSQR algorithm for solving each linear system, but are obtained at reduced computational cost. The method has been tested on synthetic models along with the real gravity data from the Morro do Engenho complex from central Brazil.