GPS变形场的多面函数插值方法研究

Research on spatial interpolation method of GPS deformation field based on multi-surface function

本文首先以青藏高原东北缘密集分布的GPS形变场数据为例,利用多面函数对东向分量速度和北向分量速度整体构建模型,以验后单位权中误差和检核数据残差均方根为标准获取了多面函数的最优参数,并与其他方法进行比对,结果表明多面函数优于径向基本函数,与反距离加权和最小曲率方法相当,劣于克里金方法;本文对克里金方法和多面函数方法进行组合,即先利用克里金方法对GPS数据离散化,然后利用多面函数建模,检核数据的插值残差均方根较单一方法分别降低了3%和18%,克服了克里金方法空间不连续和多面函数边缘效应的缺点.最后以2011年3月11日日本9.0级地震对中国东北地区的影响为例,获取了缺少震前观测的4个GPS站的震间速度,充分展现了测站在震前、同震和震后的动态变化.在缺少震前观测的条件下,本文为研究震后变形提供了一种获取震前运动的方法.

Taking the northeastern margin of the Qinghai-Tibet Plateau with the densely distributed GPS deformation field data as an example,this paper constructs a monolithic model of the east component velocity and the north component velocity using multisurface function,the optimal parameters are obtained according to the posterior unit weight error and the root mean square error of the checking data.Compared with other methods,the results show that the multi-surface function is superior to the radial basic function,and is comparable to the inverse distance weighting method and the minimum curvature method,but inferior to the Kriging method.Global Positioning System(GPS)data are discretized by Kriging method,and then modeled by multi-surface,the residual Root-Mean-Square(RMS)of interpolation data is reduced by 3%and 18%,respectively,the method overcomes the disadvantages,such as space discontinuity of Kriging and edge effect of multi-surface function.Finally,taking the impact of 2011 Tohoku earthquake and tsunami on northeast China on March 11,2011 as an example,the inter-seismic velocities of four GPS stations lacking pre-earthquake observation are obtained,which fully show the dynamic changes of the stations before,coseismic and post-earthquake.In the absence of pre-seismic observation,this method provides a method to obtain pre-seismic motion for studying post-seismic deformation.