粘声波传播建模的时域方法
A time domain method for modeling viscoacoustic wave propagation
AI总结：
本文提出一种时域方法，通过低阶有理函数近似粘声模量，结合虚拟域法和完美匹配层，采用混合有限元与二阶中心差分离散，有效模拟粘声波传播。
摘要：
在许多应用中，尤其是在地震学中，真实传播介质会使波发生频散和衰减。这种耗散行为可以通过使用粘声传播模型来考虑，该模型在本构关系中引入了一个复数的、频率依赖的粘声模量。主要困难在于找到一种有效的方式来离散化本构方程，因为它在时域中变成了一个卷积积分。为了克服这一困难，通常的方法是用频率的低阶有理函数来近似粘声模量。我们在此使用这种近似，并展示如何将其纳入粘声波的速度-压力公式中。该公式与虚拟域方法相结合，使我们能够有效地模拟复杂几何物体的衍射，并与完美匹配层模型相结合，使我们能够模拟无界域中的波传播。问题的空间离散化基于混合有限元方法，时间离散化采用二阶中心有限差分格式。几个数值例子说明了该方法的效率。
英文摘要：
In many applications, and in particular in seismology, realistic propagation media disperse and attenuate waves. This dissipative behavior can be taken into account by using a viscoacoustic propagation model, which incorporates a complex and frequency-dependent viscoacoustic modulus in the constitutive relation. The main difficulty then lies in finding an efficient way to discretize the constitutive equation as it becomes a convolution integral in the time domain. To overcome this difficulty the usual approach consists in approximating the viscoacoustic modulus by a low-order rational function of frequency. We use here such an approximation and show how it can be incorporated in the velocity-pressure formulation for viscoacoustic waves. This formulation is coupled with the fictitious domain method which permit us to model efficiently diffraction by objects of complicated geometry and with the Perfectly Matched Layer Model which allows us to model wave propagation in unbounded domains. The space discretization of the problem is based on a mixed finite element method and for the discretization in time a 2nd order centered finite difference scheme is employed. Several numerical examples illustrate the efficiency of the method.
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