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

INTRODUCTION

The present work covers various issues related to fractures and anisotropy, especially in relation to some of the published work of Michael Schoenberg (Schoenberg, 1980; Schoenberg and Helbig, 1997; Schoenberg and Sayers, 1995; Schoenberg and Muir, 1989). Details of methods presented here will also make use of an approach outlined by Sayers and Kachanov (1991), and used previously by Berryman (2009,2008,2006) in a recent series of published papers. [However, it is important to recognize that in earlier work it has also been shown (Berryman, 2006) that the general results of Bakulin et al. (2000) (for example) for the Thomsen (1986,2002) weak anisotropy seismic parameters and contained in their Figure 6, are both qualitatively and even (reasonably) quantitatively consistent with each other, as well as being consistent with results from the method of Sayers and Kachanov (1991) treated explicitly here.] Thus, a high degree of consistency has been established among fracture-influence results that are based in part on the linear-slip model of fractures by Schoenberg (1980) and in part on penny-shaped (or approximately penny-shaped) cracks. [Also see Grechka et al. (2006).] This fact is important to the theme of the paper, because it shows that the details are often less important than the grand scheme of how fractures affect both the elastic system response and the wave propagation results.

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