基于卷积滤波的谱元法在长时程波场模拟中的应用

Application of spectral element method based on convolution filtering in long-term wavefield modeling

地震波波场数值模拟是深入认识复杂地下介质的重要手段.谱元法兼顾了有限元方法的传统优势,并提高了数值精度和稳定性,已成为目前地震波波场数值模拟中最常用的方法之一.随着超大规模并行计算的普及和发展,高分辨模拟所需的网格尺寸越来越小,网格规模越来越大,导致长时程模拟的大步长需求越来越高,成为倍受关注的研究热点.区别于传统的保结构算法,本文采用时间频散变换对时间离散引起的误差进行补偿,并引入空间滤波用于打破CFL(Courant-Friedrichs-Lewy)条件对时间采样间隔的限制.为了克服谱元法中因为非均匀空间采样点引起的滤波频谱计算难题,本文采用空间卷积滤波替换传统频率域滤波,有效的降低了算法的计算需求.该滤波方法也适用于复杂起伏模型的波场模拟.将本文方法用于保结构算法,并针对四阶辛Nyström方法进行了测试,显著增大了四阶辛Nyström方法的时间采样步长.新方法可以有效的用于地球自由振荡的模拟以及其他需要长时程数值模拟的工作中.

With the continuous development of high-performance computing,seismic wavefield numerical modeling has increasingly become an essential means to understand complex underground media deeply.As a hybrid method,the spectral element method(SEM)considers the traditional advantages of the finite element.The method improves the numerical accuracy and stability,and is one of the most commonly used method in the numerical modeling of the seismic wavefield.With the popularization and development of ultra-large-scale parallel computing,the grid scale of seismic wavefield numerical modeling has gradually increased.The grid size has become smaller and smaller.The design of numerical scheme for the stability of SEM in long-term seismic wave modeling has been a continuous research hotspot.Unlike the traditional structure preservation algorithm,we use the time dispersion transformation method to compensate for the error caused by time-discrete and introduce a filter to break the limitation of Courant-Friedrichs-Lewy(CFL)conditions on time sampling intervals.To overcome the computational problem caused by the non-uniform spatial sampling points of the original filter method in the SEM,this paper replaces the traditional FFT(Fast Fourier Transform)filtering with spatial convolutional filtering,which is also suitable for the simulation of complex terrain.Finally,this method can also be used in the structure preservation algorithm(such as the 4th-order symplectic Nyström method).It is found that the time sampling step of the 4th-order symplectic Nyström method can be further increased.The new method can be effectively used in the simulation of the Earth’s free oscillations and other work that requires long-term numerical simulations.