Modelling viscoelastic wave phenomenon by homogenisation of the poroelasticity equations. (18th October 2021)

• Record Type: Journal Article
• Authors: LI, Q.; SANTOSA, F.; WHEELOCK, B.; GOVIL, K.
• Is Part Of: European journal of applied mathematics. Volume 32:Number 5(2021)
• Page Start: 846
• Page End: 864
• Publication Date: 2021-10-18
• Subjects: Homogenisation -- multiscale methods -- periodic structure -- viscoelastic material -- porous media; 35B27 -- 74Qxx; Mathematics -- Periodicals; 519
• DOI: 10.1017/S0956792520000467
• Languages: English
• ISSNs: 0956-7925

Abstract

Abstract : 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.