Schoenberg's angle on fractures and anisotropy: A study in orthotropy

Abstract:

For vertical-fracture sets at arbitrary orientation angles to each other - but not perfectly randomly oriented, I present a detailed model in which the resulting anisotropic fractured medium generally has orthorhombic symmetry overall. Analysis methods of Schoenberg are emphasized, together with their connections to other similarly motivated and conceptually related methods by Sayers and Kachanov, among others. Examples show how parallel vertical fracture sets having HTI symmetry turn into orthotropic fractured media if some subsets of the vertical fractures are misaligned with the others, and then the fractured system can have VTI symmetry if all the fractures are aligned either randomly, or half parallel and half perpendicular to a given vertical plane. Another orthotropic case of vertical fractures in an otherwise VTI earth system treated previously by Schoenberg and Helbig is compared to, and contrasted with, other examples treated here.

Schoenberg's angle on fractures and anisotropy: A study in orthotropy