基于谱-有限元法的SNERI地球模型固体潮形变计算

Deformation of the Solid Earth Tides for SNERI Earth Model Based on Spectral-Finite Element Method

基于谱-有限元法计算一个球型、非自转、完全弹性、各向同性(SNERI)的地球固体潮形变,其中地球固体部分潮汐形变的弱解用哈密顿变分原理给出,液核部分的弱解采用静态中性分层的流体近似。计算过程中把SNERI地球进行等间距球层剖分,球面上对解函数和试探函数采用球谐展开,径向上采用线性插值。比较数值计算结果与同质地球模型的解析解结果得出,1km径向等距剖分即可获得10-8精度量级的低阶Love数。基于PREM地球模型的计算结果表明,谱-有限元法计算的固体潮2~3阶Love数与Runge-Kutta法的计算值差异在10-4量级;与武汉台超导重力仪8个主潮波的实测重力潮汐因子相比,本方法计算的理论重力潮汐因子相差平均约0.15%。研究结果说明,谱-有限元法具有较好的收敛性与较高的计算精度,比传统Runge-Kutta法更适用于高精度地计算复杂地球模型的固体潮形变。

This study presents the application of the spectral-finite element method on the solid tide response calculation of SNERI Earth.The weak formulations of Earth tide deformation equations are given respectively,by means of the Hamilton’s principle in the solid Earth and the approximation of neutral stratified fluid in the liquid core.The solution space is divided into a certain number of concentric spherical layers.Hence spherical harmonic functions are used to span the 2\|D spherical shell and linear functions are used to interpolate in the radius direction.Compared with the analytical solution of a homogeneous earth,the numerical solution shows that the numerical precision of spectral-finite element method can up to 10-8 magnitude in 1 km equal radial divided interval.As respect to the PREM Earth model,the numerical solution difference of 2nd and 3rd degree tide Love numbers between spectral-finite element method and Runge-Kutta mothed is at about 10-4 magnitude;the average difference of tidal gravimetric factor between the 8 main tidal waves observational results,recorded by superconducting gravity meter in Wuhan station,and theory results,calculated from spectral-finite method,is about 0.15%.The results show spectral-finite method has good convergence and high numerical precision and is more powerful in high precision numerical calculation of complex Earth tidal Love numbers.