Postseismic Global Navigation Satellite System (GNSS) time series followed by megathrust earthquakes can be interpreted as a result of afterslip on the plate interface, especially in its early phase. Afterslip is a stress release process accumulated by adjacent coseismic slip and can be considered a recovery process for future events during earthquake cycles. Spatio-temporal evolution of afterslip often triggers subsequent earthquakes through stress perturbation. Therefore, it is important to quantitatively capture the spatio-temporal evolution of afterslip and related postseismic crustal deformation and to predict their future evolution with a physics-based simulation. We developed an adjoint data assimilation method, which directly assimilates GNSS time series into a physics-based model to optimize the frictional parameters that control the slip behavior on the fault. The developed method was validated with synthetic data. Through the optimization of frictional parameters, the spatial distributions of afterslip could roughly (but not in detail) be reproduced if the observation noise was included. The optimization of frictional parameters reproduced not only the postseismic displacements used for the assimilation, but also improved the prediction skill of the following time series. Then, we applied the developed method to the observed GNSS time series for the first 15 days following the 2003 Tokachi-oki earthquake. The frictional parameters in the afterslip regions were optimized to A–B ~ O (10 kPa), A ~ O (100 kPa), and L ~ O (10 mm). A large afterslip is inferred on the shallower side of the coseismic slip area. The optimized frictional parameters quantitatively predicted the postseismic GNSS time series for the following 15 days. These characteristics can also be detected if the simulation variables can be simultaneously optimized. The developed data assimilation method, which can be directly applied to GNSS time series following megathrust earthquakes, is an effective quantitative evaluation method for assessing risks of subsequent earthquakes and for monitoring the recovery process of megathrust earthquakes.

中文翻译：

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用于优化摩擦参数和预测 2003 年十胜冲地震后震后变形的 GNSS 时间序列的基于伴随的直接数据同化

震后全球导航卫星系统 (GNSS) 时间序列随后发生的特大逆冲地震可以解释为板块界面后滑的结果，尤其是在其早期阶段。后滑是相邻同震滑动累积的应力释放过程，可以认为是地震周期中未来事件的恢复过程。后滑的时空演化往往通过应力扰动触发后续地震。因此，定量捕捉后滑和相关地震后地壳变形的时空演化并通过基于物理的模拟预测它们的未来演化非常重要。我们开发了一种伴随数据同化方法，它直接将 GNSS 时间序列同化为基于物理的模型，以优化控制断层滑动行为的摩擦参数。所开发的方法已通过合成数据进行验证。通过摩擦参数的优化，如果包含观测噪声，后滑的空间分布可以粗略地（但不是详细地）再现。摩擦参数的优化不仅再现了用于同化的震后位移，而且提高了后续时间序列的预测能力。然后，我们将开发的方法应用于 2003 年十胜冲地震后前 15 天观测到的 GNSS 时间序列。后滑区的摩擦参数优化为 A–B ~ O (10 kPa)、A ~ O (100 kPa) 和 L ~ O (10 mm)。在同震滑动区较浅的一侧推断出较大的后滑动。优化后的摩擦参数定量预测了接下来 15 天的震后 GNSS 时间序列。如果可以同时优化模拟变量，也可以检测到这些特征。所开发的资料同化方法可直接应用于特大地震后的GNSS时间序列，是评估后续地震风险和监测特大地震恢复过程的有效定量评价方法。如果可以同时优化模拟变量，也可以检测到这些特征。所开发的资料同化方法可直接应用于特大地震后的GNSS时间序列，是评估后续地震风险和监测特大地震恢复过程的有效定量评价方法。如果可以同时优化模拟变量，也可以检测到这些特征。所开发的资料同化方法可直接应用于特大地震后的GNSS时间序列，是评估后续地震风险和监测特大地震恢复过程的有效定量评价方法。