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Modelling viscoelastic wave phenomenon by homogenisation of the poroelasticity equations
European Journal of Applied Mathematics ( IF 1.9 ) Pub Date : 2021-01-18 , DOI: 10.1017/s0956792520000467
Q. LI , F. SANTOSA , B. WHEELOCK , K. GOVIL

Poroelastic effects have been of great interest in the seismic literature as they have been identified as a major cause of wave attenuation in heterogeneous porous media. The observed attenuation in the seismic wave can be explained in part by energy loss to fluid motion in the pores. On the other hand, it is known that the attenuation is particularly pronounced in stratified structures where the scale of spatial heterogeneity is much smaller than the seismic wavelength. Understanding of poroelastic effects on seismic wave attenuation in heterogeneous porous media has largely relied on numerical experiments. In this work, we present a homogenisation technique to obtain an upscaled viscoelastic model that captures seismic wave attenuation when the sub-seismic scale heterogeneity is periodic. The upscaled viscoelastic model directly relates seismic wave attenuation to the material properties of the heterogeneous structure. We verify our upscaled viscoelastic model against a full poroelastic model in numerical experiments. Our homogenisation technique suggests a new approach for solving coupled equations of motion.

中文翻译:

通过多孔弹性方程的均匀化模拟粘弹性波现象

多孔弹性效应在地震文献中引起了极大的兴趣,因为它们已被确定为非均质多孔介质中波衰减的主要原因。观察到的地震波衰减可以部分解释为孔隙中流体运动的能量损失。另一方面,众所周知,在空间异质性尺度远小于地震波长的分层结构中,衰减尤为明显。对多孔弹性对非均质多孔介质中地震波衰减的影响的理解在很大程度上依赖于数值实验。在这项工作中,我们提出了一种均质化技术,以获得一个放大的粘弹性模型,该模型在亚地震尺度非均质性是周期性的时捕获地震波衰减。升级后的粘弹性模型直接将地震波衰减与异质结构的材料特性联系起来。我们在数值实验中针对全多孔弹性模型验证了我们的放大粘弹性模型。我们的均质化技术提出了一种求解耦合运动方程的新方法。
更新日期:2021-01-18
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