Particle swarm optimization, one of the modern global optimization methods, is attracting widespread interest because it overcomes the difficulties of conventional inversion techniques, such as trapping at a local minimum and/or initial model dependence. The main characteristic of particle swarm optimization is the large search space of parameters, which in a sense allows the exploration of the entire objective function space if the input parameters are properly chosen. However, in the case of a high-dimensional model space, the numerical instability of the solution may increase and lead to unrealistic models and misinterpretations due to the sampling problem of particle swarm optimization. Therefore, smoothness-constrained regularization techniques used for the objective function or model reduction techniques are required to stabilize the solution. However, weighting and combining objective function terms is partly a subjective process, as the regularization parameter is generally chosen based on some kind of criteria of how the smoothing constraints affect the data misfits. This means that it cannot be completely predefined but needs to be adjusted during the inversion process, which begins with the response of an initial model. In this paper, a new modelling approach is proposed to obtain a smoothness-constrained model from magnetotelluric data utilizing multi-objective particle swarm optimization based on the Pareto optimality approach without using a regularization parameter and combining several objective function terms. The presented approach was verified on synthetic models and an application with field data set from the Çanakkale–Tuzla geothermal field in Turkey. Findings from these analyses confirm the usefulness of the method as a new approach for all constrained inversions of geophysical data without the need to combine the objective function terms weighted by a regularization parameter.

中文翻译：

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一种利用帕累托最优多目标粒子群优化的光滑约束大地电磁建模新方法

粒子群优化是现代全局优化方法之一，因其克服了传统反演技术的困难（例如陷入局部最小值和/或初始模型依赖性）而引起了广泛的兴趣。粒子群优化的主要特点是参数搜索空间大，从某种意义上说，如果输入参数选择得当，就可以探索整个目标函数空间。然而，在高维模型空间的情况下，由于粒子群优化的采样问题，解的数值不稳定性可能会增加，并导致模型不切实际和误解。因此，需要用于目标函数的平滑约束正则化技术或模型简化技术来稳定解。然而，加权和组合目标函数项在一定程度上是一个主观过程，因为正则化参数通常是基于平滑约束如何影响数据失配的某种标准来选择的。这意味着它不能完全预定义，而是需要在反演过程中进行调整，反演过程从初始模型的响应开始。本文提出了一种新的建模方法，利用基于帕累托最优方法的多目标粒子群优化从大地电磁数据中获得平滑约束模型，而不使用正则化参数并组合多个目标函数项。所提出的方法在合成模型和土耳其恰纳卡莱-图兹拉地热田现场数据集的应用上得到了验证。这些分析的结果证实了该方法作为地球物理数据所有约束反演的新方法的有用性，而无需组合由正则化参数加权的目标函数项。