Effective elasticity of a medium with many parallel fractures
Abstract
We consider an alternative way of obtaining the effective elastic properties of a cracked medium. Similarly, to the popular linearslip model, we assume flat, parallel fractures, and long wavelengths. However, we do not treat fractures as weakness planes of displacement discontinuity. In contrast to the classical models, we represent fractures by a thin layer embedded in the background medium. In other words, we follow the SchoenbergDouma matrix formalism for Backus averaging, but we relax the assumptions of infinite weakness and marginal thickness of a layer so that it does not correspond to the linearslip plane. To represent the properties of a fracture, we need a fourthorder elasticity tensor and a thickness parameter. The effective tensor becomes more complicated, but it may describe a higher concentration of parallel cracks more accurately. Apart from the derivations of the effective elasticity tensors, we perform numerical experiments in which we compare the performance of our approach with a linearslip model in the context of highly fractured media. Our model becomes pertinent if filledin or empty cracks occupy more than one per cent of the effective medium.
 Publication:

Geophysical Journal International
 Pub Date:
 December 2021
 DOI:
 10.1093/gji/ggab306
 arXiv:
 arXiv:2006.10434
 Bibcode:
 2021GeoJI.227.1818A
 Keywords:

 Elasticity and anelasticity;
 Seismic anisotropy;
 Theoretical seismology;
 Microstructure;
 Physics  Geophysics;
 Physics  Applied Physics
 EPrint:
 23 pages, 3 figures