适用于大尺度速度场建模的MQ-B新模型

基于MQ-B方法的基本数学原理提出沿大地线度量距离构造核函数,得到一种适于大尺度范围速度场建模的MQ-B新模型,该速度场在参考椭球面上建立。将适于标量场的MQ-B方法推广到适于矢量场,拓宽了多面函数拟合方法的应用领域。实际算例表明,提出的基于大地线核函数的多面函数拟合模型与传统的通过经纬度坐标差构造核函数的多面函数拟合模型在中国区域内精度相当,但理论上更完善,可用于大尺度速度场建模。

A New MQ-B Method Suitable for Large Scale Velocity Field Modeling

The MQ-B(multiquadric-Biharmonic method) proposed by Hardy as a geometry fitting method was widely used in geodesy,geophysics,etc.In this paper,we firstly expanded a MQ-B method that suitable for large scale velocity field establishment on the Reference ellipsoid.The method we expanded use the geodesicto establish the kernel function,the way we establish theKernel Functionis more reasonable than the traditional B and L differential kernel function as to Hardy's theory.Secondly,we find that this method can be extended in vector fieldas if we can calculate the projection matrix,andthe form of projection matrix is shown in this paper.Finally,this new geodesic Kernel Function MQ-B method was tested through an experiment.It shows that this new method has a same precisionasthe traditional B and L differentialkernel function method in the region of china.However,this new method has a more rational theoretical accountthanthe traditional B and L differentialkernel function method,It can be used to establish the large scale velocity field.