ARTICLE

A standard linear solid model representation of frequency-dependent anisotropy due to multiple sets of aligned meso-scale fractures

QI HAO1* QIAODENG HE2
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1 China University of Petroleum, Qingdao, P.R. China.,
2 Jilin University, Changchun, P.R. China. Heqiaodeng@gmail.com,
JSE 2013, 22(2), 169–182;
Submitted: 9 October 2012 | Accepted: 2 March 2013 | Published: 1 May 2013
© 2013 by the Authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract

Hao, Q. and He, Q., 2013. A standard linear solid model representation of frequency-dependent anisotropy due to multiple sets of aligned meso-scale fractures. Journal of Seismic Exploration, 22: 169-182. The effective medium theory developed by Chapman (2003) has been used to interpret the phenomena of frequency-dependent anisotropy in porous media with meso-scale fractures. However, until recently, no research has attempted to study the propagation of seismic waves in media with meso-scale fractures. Considering a large amount of expensive numerical computation using frequency-domain modelling approaches, the key is to obtain the time-domain explicit constitutive relationships for this model. In this paper, a standard linear solid (SLS) model is used to represent frequency-dependent anisotropy in media with two sets of aligned mesoscapic fractures. Meanwhile, we find that the order of the SLS model used to represent Chapman’s model is no more than four. Consequently, two types of time-domain constitutive relationship are obtained by introducing auxiliary differential equations. Furthermore, based on the first-order velocity-stress wave equations, the time-domain numerical modelling can be applied to simulate the wave propagation in such media.

Keywords
frequency-dependent anisotropy
numerical modeling
standard linear solid
fracture
finite-difference
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Journal of Seismic Exploration, Electronic ISSN: 0963-0651 Print ISSN: 0963-0651, Published by AccScience Publishing