基于辛-谱元方法的地球自由振荡保弥散衰减数值模拟

Dissipation-preserving simulation for Earth′s free oscillations based on symplectic spectral-element method

对大地震激发的全球自由振荡的研究是探查地球内部结构的重要研究方向之一.以地球自由振荡数值模拟高精度、长时程、全球模拟的需求为导向,本文提出了一种适用于地球自由振荡高精度模拟的辛格式-谱元保弥散数值模拟方法.真实地球介质中弹性波能量的衰减成因复杂,对于甚低频情形,地球自由振荡的弥散衰减不容忽视.本文将保结构数值方法拓展至非保守动力学系统,发展了适用于弥散-黏弹阻尼介质弹性波方程的保弥散低阶辛格式数值模拟方法,将其应用于全球尺度地球自由振荡衰减效应数值模拟.数值模拟结果表明等效弥散衰减为地球深部(地核)自由振荡衰减的重要成分,并得出地球外核的等效弥散衰减系数.本文提出的方法为通过自由振荡研究探索地核非均匀性提供了一条的新途径.

Earth′s free oscillations are three-dimensional standing waves excited by a large earthquake.The study of free oscillations of the Earth has been a vital tool in probing the Earth′s internal structure.In this paper,the structure-preserving modeling is extended into the problem of non-conservative dynamical system and a symplectic spectral-element method(SEM)for high-precision and long-time modeling of Earth′s free oscillations with attenuation is presented.A preliminary analysis of the simulation results using our method suggests that the core may have dispersive attenuation.We estimate the dispersive attenuation coefficients and provide a core model with equivalent dispersive attenuation.The results of experiments suggest that it is a practical way to view it as the main cause of the Earth′s attenuation,and this approach is suitable for treating questions on the overall perspective of the Earth′s inner equivalent heterogeneity.It provides a new choice for the geophysical studies which is related to Earth′s free oscillations and enhancing our knowledge of Earth′s free oscillations and Earth′s inhomogeneity structure.