# A Fully Automatic DEXP Method for Gravity Data and Its Application on a Potash Salt Deposit
## 1 Introduction  
The rapid imaging method aims at estimating source distribution, including depth, structural index, and density (or susceptibility). It is characterized by a simple algorithm, fast inversion processing, and stable results. One of its significant advantages is that it does not require prior information or iteration, making it a convenient and efficient approach. Several general rapid imaging methods have been developed, including the correlation (probability) method [1; 2; 3; 4; 5; 6; 7], the migration method [8], the DEXP method [9; 10; 11], the continuous wavelet transform method [12; 13; 14; 15; 16; 17; 18; 19], and others. These imaging techniques have proven to be highly effective, particularly for isolated, compact, and depth-limited sources, which make them valuable tools in the field of source distribution estimation. The depth from extreme points (DEXP) method, initially introduced by [PERSON] [9], is used to estimate the depth and structural index of potential field sources and generate images of the source distribution [20]. This method involves scaling the potential field, or its partial derivatives, with a specific power law whose exponent is related to the structural index, a quantity related to source geometry. This method has been successfully applied togravity, magnetic, and self-potential data, providing rapid imaging of the corresponding source distributions [21; 22; 23] and achieving satisfactory results. The scale function plays an important role in the DEXP method, and the construction of the scale function depends on the structure index (SI) value; however, the empirical choice of the SI limits the automatic processing capabilities of the methods. To address the limitation, a variety of papers have discussed the solution for automatically selecting the SI. [PERSON] and [PERSON] (2009) [24] proposed using the reciprocal of the depth, \"\(q=1/z\)\", to obtain the SI, but this method was found to be significantly disturbed in complex multi-source situations, and its reliability depended on judgments made based on rich experience. [PERSON] et al. (2013) [23] suggested estimating the buried depth using the maximum SI; the result demonstrated satisfactory stability and anti-noise ability. [PERSON] and [PERSON] (2014) [25] improved the local wavenumber method with the DEXP method, and it estimated the center depth without the need to offer a presupposed or empirical SI value. [PERSON] and [PERSON] (2014) [25] also proposed building the ratio of different-order derivatives, which solved the pre-SI requirement and simplified the algorithm. The potential problem of having a zero denominator in this calculation process was addressed by setting the threshold empirically. It is evident that much of the research on the DEXP method has primarily focused on determining the appropriate value for the structural index (SI). Two main solutions have been proposed to address the issue: one involves specifying the SI based on experience, while the other replaces the SI with the ratio of different-order derivatives. However, the former approach, relying on experience to determine the SI value, is limited because it requires manual intervention and cannot be easily automated. This limitation hinders the ability of the algorithm to process data automatically. The latter approach, which replaces the SI with the ratio of different-order derivatives, achieves an automatic judgment of the SI satisfactorily. However, a potential issue arises when the denominator of the ratio becomes zero, which can significantly affect the imaging results. To mitigate this problem, a threshold method has been used. Although less than satisfactory, this threshold introduces a new interference factor known as the \"trapezoid line\". Furthermore, when applying it to real data, we observed that the influence of topography cannot be ignored. The surface-to-plane method has been widely used to address this issue.