The Echo of a Fracture

Effects of single faults, joints or fractures of large planar extent on wave propagation has been studied. The reflection and transmission coefficients for P-P, S-S and converted waves are both frequency and horizontal slowness (slowness along the fracture) dependent. The frequency dependence arises from the fact that, even though the fracture is modeled by a boundary condition and thus is assumed to be of zero width, it has attributed a characteristic width which provides the length scale necessary for wavelength dependence. An interesting feature of the reflectivity when horizontal slowness is increasing, is that the P-P and S-S reflections initially decrease to a minimum, and subsequently increase, with or without a sign change. This 'extinction' slowness (at which the minimum value occurs) yields information about the fracture compliances, and hopefully about the physical properties of the fracture.