## 1 Introduction  
The magnetic method is widely used in mineral resource exploration and structure investigation. To determine the depth, position, and shape of the magnetic anomaly body, the magnetic data inversion is usually needed, which mainly includes parameter inversion [1, 2], imaging inversion [3, 4, 5], and physical property inversion [6]. Physical property inversion can recover the shape and depth of complex sources without depending on a specific model. Therefore, the inversion of physical properties has become one of the most important and commonly used methods. Linear iterative methods, such as the steepest descent method, [PERSON]'s method, and conjugate gradient method, are usually used in physical property inversion [7, 8, 9]. However, the gradient-based algorithms are independent of the initial guess to start the optimization process and are easy to trap into local minima for nonlinear problems [10]. Contrary to the conventional approaches, the metaheuristic methods like differential evolution (DE) do not require good initial solutions when searching the global minimum. DE [11] is a population-based metaheuristic global optimization algorithm. Because of its fast convergence and easy implementation, it has been widely used to solve the optimization of practical problems, such as electromagnetic optimization [12, 13], pattern recognition [14], signal processing [15, 16, 17, 18, 19, 20], engineering application [21, 22, 23], and other inversion problems [24, 25, 26, 27]. Considering the dependency of control parameters [28], some scholars tried to adjust them by using adaptive or self-adaptive manners. [PERSON] and [PERSON] proposed an adaptive DE based on fuzzy logic (FADE) [29]. [PERSON] optimized the scaling factor (F) and crossover rate (CR) by encoding them into individuals as parameters [30]. [PERSON] and [PERSON] automatically adjust F and CR based on historical experience information, then proposed an adaptive DE with an optional external archive (JADE) [31]. In JADE, F, and CR are generated based on Cauchy distribution and Gaussian distribution, respectively. Besides, JADE introduces a new mutation strategy named \"current-to-pbest\", which can balance the global exploration and local exploitation capability of the algorithm better than the traditional ones. Then, researchers have proposed success-history based DE (SHADE) by improving the technique of the parameter adjustment in JADE [32]. In recent years, a series of DE algorithms with superior performance have been presented based on SHADE, such as using linear population size reduction to improve the search performance of SHADE (LSHADE) [33], improved LSHADE algorithm (iLSHADE) [34], ensemble sinusoidal differential covariance matrix adaptation with Euclidean neighborhood (LSHADE-EpSin) [35], LSHADE with semi-parameter adaptation hybrid with CMA-ES (LSHADESPACMA) [36], single objective real-parameter optimization algorithm (\(\mathfrak{g}\)SO) [37], etc. DE has few applications in magnetic data inversion. For example, some scholars first applied DE into 3D inversion of the magnetic anomaly to estimate the source parameters such as the horizontal extension, the depth of top and bottom interface, the magnetic dip, and declination [38]. Other scholars have applied DE to analytic signal amplitude (ASA) inversion of two-dimensional (2D) magnetic data [39]. As far as magnetic inversion is concerned, there is a huge difference between the observed data and the inverted parameters, which means that one needs to recover a large number of model parameters by using a small amount of physical field information. Hence, the magnetic inversion is ill-conditioned and exists in multiple solutions. To address the mentioned issues, it is necessary to add the prior information as a constraint to reduce non-uniqueness and make the calculated model as close to the real one as possible. In addition, since the forward modeling calculation in this paper is based on the finite volume method, the relation of magnetic source parameters and magnetic data is nonlinear.