A STANDARD LINEAR SOLID MODEL REPRESENTATION OF FREQUENCY-DEPENDENT ANISOTROPY DUE TO MULTIPLE SETS OF ALIGNED MESO-SCALE FRACTURES

摘要

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.