The effect of mineralization on the ratio of normal to tangential compliance of fractures

The effect of a fracture on the propagation of seismic waves can be represented in terms of the normal compliance B_N and tangential compliance B_T of the fracture. If   B_N / B_T = 1  for all fractures, the effective elastic stiffness tensor of an isotropic background containing an arbitrary orientation distribution of fractures is orthotropic (i.e., has three orthogonal planes of mirror symmetry) in the long-wave limit. However, deviations from orthotropy may occur if   B_N / B_T   differs significantly from unity and this can cause the principal axes of the P -wave NMO ellipse and of the variation in the PP -reflection amplitude as a function of azimuth, to deviate from the fast and slow polarization direction of a vertically propagating S -wave. Simple models of a fracture in terms of a planar distribution of cracks suggest that   B_N / B_T ≈ 1  for dry fractures. However, naturally occurring fractures often exhibit mineralization in the form of bridges between opposing faces of the fracture. The presence of such bridges leads to significant departures of   B_N / B_T   from unity.