Seismic Anisotropy of Fractured Rocks

A simple method for including the effects of fracturing on the seismic propagation through fractured rocks is described. It is shown that the effective medium compliance tensor may be written as a sum of the fourth rank compliance tensor of the (unfractured) background rock and the excess fourth rank compliance tensors, one for each set of parallel fractures or aligned cracks, and each derivable from a second rank fracture compliance tensor. For a rotationally symmetric set of fractures, this fracture compliance tensor depends on only two fracture compliances, one controlling fracture compliance normal, the other, tangential, to the plane of the fractures. The stiffness tensor, which is more useful in the consideration of elastic wave propagation through rocks, is then obtained by inversion. The components of the excess fracture compliance tensor represent the maximum amount of information , that can be obtained from seismic data. The estimation of the shape and size distribution is beyond the capability of long wavelength seismic data.