Postseismic global positioning system (GPS) time series are of fundamental importance for investigating the physical mechanisms of postseismic deformations, as well as the construction and maintenance of terrestrial reference frames. Particularly, methods for constructing accurate fitting models for such time series are critical. Based on the physical features of postseismic deformation models, we propose a new algorithm that combines the strengths of the Levenberg–Marquardt (LM) and differential evolution (DE) algorithms, that is, the LM + DE algorithm. In this algorithm, the parameters are initialised by the constrained DE algorithm; the final parameters of the postseismic model are then solved by the LM algorithm. To validate the proposed method, DE, LM, and LM + DE were compared using synthetic and observational data from the 2011 Tohoku Earthquake. For all tests based on synthetic data, the LM + DE algorithm consistently converged to the global solution and the residual is small, regardless of how the independent parameter was varied. In the 2011 Tohoku earthquake, the parameters calculated by the LM + DE algorithm matched consistently for the global solution with a 100% passing rate after constraints were provided for the ratios of the initial relaxation time parameters. In contrast, the LM and DE algorithms individually achieved passing rates of only 22% and 1%, respectively. These results demonstrate that the proposed LM + DE algorithm effectively solves the initial estimate problem in the fitting of nonlinear postseismic models, and also ensures that the fits are mathematically optimal and consistent with physical reality.

地震后全球定位系统（GPS）时间序列对于研究地震后变形的物理机制以及地面参考框架的构建和维护至关重要。特别地，构造用于这种时间序列的精确拟合模型的方法至关重要。根据地震后变形模型的物理特征，我们提出了一种新算法，该算法结合了Levenberg-Marquardt（LM）和差分演化（DE）算法的优势，即LM + DE算法。在该算法中，参数是通过约束DE算法来初始化的。然后通过LM算法求解后震模型的最终参数。为了验证所提出的方法DE，LM，使用2011年东北地震的合成数据和观测数据对LM和DE和LM + DE进行了比较。对于所有基于合成数据的测试，LM + DE算法始终收敛于全局解，并且不管独立参数如何变化，残差都很小。在2011年东北地震中，在为初始弛豫时间参数的比率提供约束后，通过LM + DE算法计算出的参数始终以100％的通过率与整体解一致。相比之下，LM和DE算法分别仅达到22％和1％的通过率。这些结果表明，所提出的LM + DE算法可以有效地解决非线性后震模型拟合中的初始估计问题，