Calculation And Application Of The Normal Mode Of The Earth

A normal mode of an oscillating system is a pattern of motion in which all parts of the system move with the same frequency and with a fixed phase relation.The free motion described by the normal modes takes place at the fixed frequencies.These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies.A physical object,such as a building,bridge or molecule,has a set of normal modes and their natural frequencies that depend on its structure,materials.The phenomenon of free oscillation caused by earthquakes can be understood as the superposition of long-period standing waves,which ranges from ten seconds to one hour,but essentially a normal modular superposition of the earth.In other words,the Earth's normal modes are objectively present and do not depend on whether or not an earthquake occurs.It is mainly related to the internal structure of the Earth.The geostrophic changes caused by dynamic phenomena such as earthquakes,tide,and loads can all be expressed by the Earth's normal modes.The main research contents and innovations are as follows:(1)The earth's normal mode theory and computation.In this paper,the free vibration of the string with both ends fixed is taken as an example.The basic theorem of the normal mode is introduced.According to the tiny elastic motion equation of the spherical symmetric earth,the ordinary differential equations of the free oscillation of the earth are derived,and the detailed solution derivation is given.This paper gives an example of a three-component synthetic seismic seismogram.However,the surface deformation caused by the earthquake contains not only three translational components,but also three rotational components.(2)Changes in the Earth's rotation induced by large earthquakes.In this paper,we used the PREM earth model to calculate changes in the Stokes coefficients,the total inertial tensor and in the Earth's oblateness caused by ten large earthquakes with Mw?8.3 since 2000 based on the theory of normal mode and the point dislocation methods.Besides,we discussed the convergence problem of normal mode superposition,also the effect of the earthquake magnitude and the influence of the focal depth change on the polar motion excitation and the length of day.(3)Computation of Love numbers by the normal mode method.By making use of the normal mode theory of the Earth,this paper studies the variations of the displacement field in the Earth's interior and of the gravity field in the Earth's exterior due to deformation caused by different external forces,including body and surface ones for a spherically symmetric,non-rotating,elastic and isotropic(SNREI)Earth.The operational formulas,indicating the intrinsic relation between normal modes and Love numbers,are derived to compute the Love numbers of various deformation problems of the Earth such as tide,surface loading,earthqukedislocation,as well as those due to press and shear forces.