利用微分进化法确定海洋磁场向下延拓中的最优参数

位场的解析延拓是实现不同高度海洋地磁场相互转换的主要途径，是构建海洋三维磁空间背景场模型的关键技术.针对位场向下延拓迭代法中最优正则化参数及最佳迭代次数难以确定问题，尝试引入微分进化法，以正则化参数及迭代次数为种群变量，以延拓结果的熵值为目标函数，以目标函数最小化为搜索准则，实现两种参数的并行全局寻优.采用实测数据对微分进化法在几种常用的迭代法中最优正则化参数及最佳迭代次数的确定进行了分析，与传统L-曲线准则确定的最优正则化参数及多次试验确定的最佳迭代次数进行对比，结果表明：微分进化法确定的最优参数能使三种迭代法取得最佳迭代效果，延拓结果与真实地磁场最为接近，并且该法计算稳定、自适应强，建议在海洋磁场数据向下延拓中应用.

Determination of optimum parameters using a differential evolution algorithm in downward continuation of the marine geomagnetic field

The analytic continuation of potential fields is the main approach to realize the conversion of marine geomagnetic field at different altitudes, which is a key technique to construct the 3D marine geomagnetic field model. Focusing on the determination of the optimal regularization parameters and the number of iterations, the differential evolution algorithm (DE) is adopted in iterative downward continuation. Moreover, two kinds of optimum parameters can be selected effectively according to the minimum objective function by taking the entropy value of continuation results as the objective function, and the regularization parameter and times of iteration as individual species. Furthermore, the DE method has been applied to determine optimal parameters in several commonly used iteration methods with observed data. Compared with the optimum regularization parameters determined by the L-curve rule and the best number of iterations determined through multiple experiments, the optimum parameters determined by the DE method can achieve the best effect of continuation in different iterative methods, and the continuation results are closer to the real geomagnetic field. Hence, the DE method is recommended to be applied in downward continuation of the marine geomagnetic field.