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Type: Journal article
Title: 2.5-D poroelastic wave modelling in double porosity media
Author: Liu, X.
Greenhalgh, S.
Wang, Y.
Citation: Geophysical Journal International, 2011; 186(3):1285-1294
Publisher: Blackwell Publishing Ltd
Issue Date: 2011
ISSN: 0956-540X
Statement of
Xu Liu, Stewart Greenhalgh, and Yanghua Wang
Abstract: To approximate seismic wave propagation in double porosity media, the 2.5-D governing equations of poroelastic waves are developed and numerically solved. The equations are obtained by taking a Fourier transform in the strike or medium-invariant direction over all of the field quantities in the 3-D governing equations. The new memory variables from the Zener model are suggested as a way to represent the sum of the convolution integrals for both the solid particle velocity and the macroscopic fluid flux in the governing equations. By application of the memory equations, the field quantities at every time step need not be stored. However, this approximation allows just two Zener relaxation times to represent the very complex double porosity and dual permeability attenuation mechanism, and thus reduce the difficulty. The 2.5-D governing equations are numerically solved by a time-splitting method for the non-stiff parts and an explicit fourth-order Runge-Kutta method for the time integration and a Fourier pseudospectral staggered-grid for handling the spatial derivative terms. The 2.5-D solution has the advantage of producing a 3-D wavefield (point source) for a 2-D model but is much more computationally efficient than the full 3-D solution. As an illustrative example, we firstly show the computed 2.5-D wavefields in a homogeneous single porosity model for which we reformulated an analytic solution. Results for a two-layer, water-saturated double porosity model and a laterally heterogeneous double porosity structure are also presented.
Keywords: Numerical solutions
elasticity and anelasticity
seismic attenuation
wave propagation.
Rights: © 2011 The Authors Geophysical Journal International © 2011 RAS
DOI: 10.1111/j.1365-246X.2011.05106.x
Grant ID: ARC
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