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Modelling viscoelastic wave phenomenon by homogenisation of the poroelasticity equations

Part of: Partial differential equations

Published online by Cambridge University Press:  18 January 2021

Q. LI ,
F. SANTOSA Open the ORCID record for F. SANTOSA [Opens in a new window] ,
B. WHEELOCK  and
K. GOVIL
Q. LI
Affiliation:
Corporate Strategic Research, ExxonMobil Research and Engineering, 1545 Route 22 East, Annandale, NJ08801, USA, email: [email protected]; [email protected]
F. SANTOSA
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, MN55455, USA, email: [email protected]
B. WHEELOCK
Affiliation:
Corporate Strategic Research, ExxonMobil Research and Engineering, 1545 Route 22 East, Annandale, NJ08801, USA, email: [email protected]; [email protected]
K. GOVIL
Affiliation:
ExxonMobil Technical Computing Company, 1545 Route 22 East, Annandale, NJ08801, USA, email: [email protected]
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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.

Keywords

Homogenisationmultiscale methodsperiodic structureviscoelastic materialporous media

MSC classification

Primary: 35B27: Homogenization; equations in media with periodic structure
Type
Papers
Information
European Journal of Applied Mathematics , Volume 32 , Special Issue 5: 30th Anniversary Special Issue , October 2021 , pp. 846 - 864
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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