The echo of a fault or fracture

The seismic response of single faults, joints, or fractures of large planar extent is analyzed. These are modeled as nonwelded interfaces. In spite of the large range of scale, all are assumed to behave according to linear slip theory. Such a model has been considered theoretically and experimentally before. The aim of this paper is to give a physical interpretation to such a linear slip interface; to provide simple analytical formulae for the scattering response, even when the fracture is embedded in an anisotropic background medium; and to relate the properties of this scattering response, in the isotropic case, to the physical features of the fracture. The analysis shows that the reflectivity and transmissivity of the fracture depend on slowness along the fracture and on frequency. The frequency dependence arises from the fact that, even though the fracture is assumed to be an interface of zero thickness, it still has at least two characteristic widths that provide the length scales necessary for scattering dependence on wavelength. For isotropic media, the PP and SS reflections generally decrease in amplitude with increasing slowness along the fracture. At certain slowness values, they reach minima before starting to increase for still larger slownesses. The slowness value of these minima reveals the fracture compliances, from which inferences about the physical properties of the fracture may be drawn. Both forward modeling of the acoustic response of a fracture and the estimation of fracture properties from acoustic scattering data can benefit from the type of analysis presented here. The range of such problems extends from the scattering of earthquake-generated seismic energy by major faults in the earth, through reservoir fracture characterization from single-well sonic imaging, to the characterization of flaws or poorly bonded surfaces in ultrasonic nondestructive testing.