基于常Q模型的分数阶粘弹介质数值模拟方法

基于常Q模型的解耦分数阶拉普拉斯算子粘滞波动方程,可以分开模拟振幅衰减和相位错动。但该方程拉普拉斯算子的阶数是随空间变化的,因此数值求解存在一定困难。这里基于截断的泰勒展开,经过一系列近似,推导出拉普拉斯算子的阶数与空间无关的解耦分数阶粘滞弹性波动方程。采用中心差分计算时间导数,使用交错网格伪谱法计算空间导数。数值算例表明,新的方程在处理非均匀介质时具有精度高,计算简便的优点。

Fractional-order viscoelastic medium numerical simulation method based on constant Q model

Constant Q based on decoupled fractional-order Laplacian viscoelastic wave equation can be used to simulate amplitude attenuation and phase dispersion,respectively. However,the order of Laplacians is spatially variable,which introduces difficulties for its numerical simulation. In this paper,after a series Taylor expansion based approximation,we develop a constant fractional-order Laplacian viscoelastic wave equation. A staggered-grid pseudo-spectral numerical method is used for its numerical simulation. The time derivative is discretized by centered finite-difference operators. Several simulation examples are performed to verify that the numerical solution of hetergeneous model obtained by solving our constant fractional-order viscoelastic wave equation is accuracy and efficient.