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正则化反演通过引入模型约束和正则化因子求解病态的地球物理反演问题,但该方法存在正则化因子选取困难和初始模型依赖的问题。针对该问题,本文提出多目标粒子群反演算法。该算法反演中不需要目标函数梯度信息和正则化因子,先同时求数据拟合和模型约束的多目标反演解集,再权衡两者的相对重要程度,最后从反演解集中优选出最终反演结果,从而起到正则化因子的作用。以二维磁测数据反演为例,进行理论模型反演试验,试验结果表明,多目标粒子群反演算法能尽可能多地保留可行解,得到反演解集;通过分析反演解集,既能深入的理解反演过程,又能灵活地从数据拟合和模型约束两方面进行权衡与选择,得到比正则化反演更合理的反演结果;该算法能同时解决正则化因子选取困难和初始模型依赖问题。
Regularized inversion solves ill-posed geophysical inversion problems by introducing model constraints and regularization factors. However, this method has the problem of difficulty in selecting regularization factors and dependence on initial model. To solve this problem, this paper proposes a multi-objective particle swarm inversion algorithm. The algorithm does not require gradient information and regularization factor in the inversion of the objective function. First, the multi-objective inversion solution set of the data fitting and the model constraint is obtained simultaneously, and the relative importance of the two solutions is weighed again. Finally, The final inversion results, which play the role of regularization factor. Taking the two-dimensional magnetic data inversion as an example, the theoretical model inversion experiment is carried out. The experimental results show that the multi-objective particle swarm inversion algorithm can reserve feasible solutions as much as possible and obtain the solution set. By analyzing the inversion solution set , Which not only can deeply understand the inversion process, but also flexibly weigh and select from the data fitting and model constraints to obtain a more reasonable inversion result than the regularization inversion. This algorithm can simultaneously solve the problem of regularization factor selection Difficulties and initial model dependencies.