基于辛-谱元-FK混合方法的保结构远震波场模拟

Structure-preserving modeling of teleseismic wavefield using symplectic SEM-FK hybrid method

远震全波形层析成像能获得研究区域下方岩石圈乃至地幔过渡带高分辨率速度结构,是研究地球深部构造与动力学过程的有效工具.该类方法需以高精度及长时程远震波场正演模拟为基础,这为设计高精度长时程稳定的正演算法带来了挑战.在此背景之下,本文提出了一种适用于远震波场模拟的保结构算法.该方法采用谱元法(SEM)对研究区域进行空间离散,在不考虑耗散项情况下,将空间离散后的常微分方程变换为哈密顿系统形式,采用保辛分部龙格-库塔方法数值求解.在三级保辛分部龙格-库塔算法基础上添加额外空间离散项,得到修正辛算法.本文将该时间-空间全离散形式称为修正辛-谱元法(SSEM),并将SSEM算法与频率波数域(FK)方法结合,发展了可模拟高频远震波场在局域模型内传播的SSEM-FK混合方法.该方法结合了FK方法模拟层状介质中平面波传播的高效性和SSEM计算复杂介质中弹性波传播的精确性.数值实验表明,SSEM-FK能够准确模拟高频远震波场在研究区域内的传播,结合该方法在计算效率上的优势,可为高效、高精度的远震全波形层析成像打下基础.

Teleseismic full-waveform tomography can obtain high resolution velocity structure of upper mantle, and even the structure of mantle transition zone beneath the study area. It has been a vital tool in probing the Earth′s internal structure and dynamic process. This method is based on effective forward simulation of seismic wavefield, which requires forward-modeling methods with high accuracy and long-term stability. Under this background, we present a structure-preserving scheme based on symplectic geometric theory, which is specially tailored for teleseismic wave modeling. The spectral element method (SEM) is used to discretize the study area. Without the consideration of the dissipation term, the discretized ordinary differential equation is transformed into a Hamiltonian system, which can be solved numerically by the symplectic-preserving partitioned Runge-Kutta (PRK) method. After adding an extra spatial discretization term into the PRK scheme, we developed a new symplectic scheme with fourth-order temporal accuracy. We call the spatial-temporal discretized scheme symplectic SEM (SSEM). We combine SSEM with FK method, which calculates plane wave propagation in one-dimensional layered media. After that, we construct a hybrid method (SSEM-FK) to efficiently calculate teleseismic elastic wave propagation in regional heterogeneous model. Numerical experiments show that SSEM-FK can accurately simulate the propagation of high-frequency teleseismic wavefield in the study area. The advantage of this method in computational efficiency forms the foundation for high-efficient and high-accurate teleseismic full-waveform tomography.