Determining the edges of satellite gravity anomalies using the modified Gudermannian filter (modified hyperbolic domain), case study: Rafsanjan plain (Kerman province)

Recognizing the boundaries and edges of gravity anomalies is essential for understanding geological and tectonic features that arise from variations in density. In recent decades, a variety of filters and techniques have been developed and improved to delineate the edges of anomalous sources; however, these edge enhancement filters often present notable challenges, such as the introduction of false and spurious edges, sensitivity to depth variations, drawing fuzzy edges, and low resolution in the resulting edge detection maps. This study introduces a modified Gudermannian (MGDF) edge detection filter aimed at enhancing the clarity of output images, eliminating the occurrence of false and spurious edges in output maps, increasing the resolution of edge detection images, and effectively balancing weak and strong amplitudes from buried sources at different depths simultaneously. This technique has been crafted using the gradients of the total horizontal gradient (THG) in tandem with the modified Gudermannian function. The mathematical framework of both the Gudermannian function and its modified counterpart resembles that of the arctangent. The arctangent, when combined with the horizontal and vertical (directional) derivatives of the potential field at varying orders, plays a crucial and traditional role in the conception and refinement of edge detection filters for gravitational and magnetic data. To fulfill this goal, we first employed a range of standard and traditional edge detection methods (such as the total horizontal gradient (THG), tilt angle (TA), total horizontal gradient of the tilt angle (THG-TA), hyperbolic tilt angle (HTA), tilt angle of the total horizontal gradient (TAHG), modified total horizontal gradient (THG-STA), and Gudermannian (GDF) filter with coefficients of zero, two, four, six, and eight) alongside a modified Gudermannian (MGDF) effective method. The MGDF edge detection filter does not require any parameter or coefficient to regulate quality. The filtered synthetic gravity data were examined both in a noise-free condition and with Gaussian noise. A gravity model featuring four sources with different depths and both positive and negative densities was constructed within the MATLAB programming environment. Following the assessment and comparison of the proposed modified Gudermannian filter against other edge detection techniques (THG, TA, THG-TA, HTA, TAHG, THG-STA and GDF), we utilized satellite gravity data (Earth Gravitational Model 2008 (EGM2008)) pertaining to the Rafsanjan Plain in Kerman Province, Iran, to identify the locations of various structures and faults while evaluating the quality and practical functionality of the proposed filter. Considering the seismic activity in the region and the presence of diverse mineral resources, extensive geophysical studies and research have been conducted in this area. The Rafsanjan Plain in Kerman Province is characterized by four major faults, along with numerous hidden faults that constitute part of the Central Iranian System. Aligning with the Zagros Mountain ranges, it is a suitable location for assessing the efficacy of edge detection filters. Findings from both synthetic and field gravity data indicate the effectiveness of the proposed filter (MGDF) in clearly and accurately delineating the edges of gravity sources. Also, the false and spurious edges in the output maps are not observed. Thus, the modified Gudermannian filter can be reliably employed in the analysis and interpretation of gravity anomalies to offer a trustworthy qualitative assessment of geological, subsurface, and buried structures.