震后GPS坐标时序中对数弛豫时间的估计

全球定位系统（global positioning system, GPS）坐标时序去除同震形变和震前稳态速度场后，采用加权非线性最小二乘估计震后对数弛豫时间，可更准确地提取震后对数弛豫项，从而可以分析震后弛豫项对测站位移的独立物理贡献，并为震后余滑和黏滞性松弛效应等现象的分析提供参考。以日本2009—2019年GPS坐标时序为例，估计2011年Mw 9.0地震震后对数弛豫时间，发现不同站点的对数弛豫时间与其震中距关系显著，且服从高斯分布。据此，构建高斯函数加常数模型，可由震中距概略估计震后对数弛豫时间。高斯分布曲线的峰值、峰值位置、半宽度信息、最低位置分别为3.5 a、0 km、262 km、0.5 a，由此得出震后对数弛豫项影响时间大于0.5 a的站点主要集中在震中距约524 km范围内。震后弛豫效应区域分布的差异性显著，对数弛豫时间越长的区域，弛豫项水平位移表征越大，其中存在两个平均弛豫时间2.5 a的中心区域，与震后余滑的中心区域及时间相吻合。

Logarithmic Relaxation Time Estimated from Post-Seismic GPS Time Series

  Objectives  In order to analyze the independent physical contribution of the post-seismic relaxation term on global positioning system (GPS) observing displacements, the regional post-seismic relaxation time and the characteristics of its spatial distribution are studied.  Methods  The logarithmic function is used to describe the post-seismic relaxation term, and the logarithmic relaxation time is estimated from post-seismic GPS coordinate time series by using nonlinear weighted least squares method. Steps are as follows: Remove the gross errors; fix the step items; remove the constant term and the steady-state velocity term; the logarithmic relaxation terms are modeled for the preprocessed GPS coordinate time series.  Results  Taking the 2009—2019 continuous coordinate time series of the global navigation satellite systems earth observation network stations in Japan as an example, the logarithmic relaxation time after 2011 Tohoku-Oki Mw 9.0 earthquake is estimated. It is found that the post-seismic relaxation time is significantly related to the epicenter distance and obeys the Gaussian distribution. Hence, a Gaussian function plus constant model is constructed to reflect the law of post-seismic relaxation time and epicentral distance. The peak value, peak position, half-width information, and minimum position of the Gaussian distribution curve of relaxation time after the earthquake are 3.5 a, 0 km, 262 km, and 0.5 a, respectively.The relaxation range with relaxation time more than 0.5 a is mainly concentrated in the region of about 524 km from the epicenter. The regional distribution of post-seismic relaxation effect is significantly different. The longer the relaxation time, the larger the average horizontal displacement of the relaxation term in the corresponding region, and there are two central regions with an average relaxation time of 2.5 years, which were consistent with the central region and time of the afterslip.  Conclusions  The proposed algorithm on estimating the post-seismic logarithmic relaxation time can help to analyze the independent physical contribution of post-seismic relaxation term, the afterslip and viscoelastic relaxation.