Reflection and transmission of seismic waves (stress waves) by a compliant fracture depends on the stress to which the fracture is subjected. Usually, an increase in wave transmission (and a decrease in reflection) can be related to an increasing normal stress on the fracture. In contrast, how shear stresses on a fracture affect the scattering of seismic waves is not well understood. Compressional (P) waves normally incident on a sheared fracture are known to generate shear (S) waves as a function of the direction and the magnitude of the stress-a phenomenon that can be used as a direct shear-stress indicator for geophysical monitoring. In this paper, the results of laboratory seismic-wave transmission experiments are presented, conducted on single fractures subjected to shear stresses. Using natural (granite) and synthetic (metal) samples, we examine the amplitudes of transmitted P waves and shear-induced, converted S waves as a function of both normal and shear stresses. The experiments indicate that the S-wave amplitude increases nonlinearly when large shear stresses are applied to a fracture. These changes are different between a well-mated fracture with high surface friction in the granite sample-exhibiting smaller S-wave amplitudes increases for larger shear stresses-and a low-friction interface in the aluminum sample-showing sudden increases in S-wave amplitudes once the surface starts to slip under high shear stresses. As we demonstrate in this paper, for relating the amplitudes of shear-induced, converted seismic waves to the shear stress on a fracture, it is critical to understand that different relationships can result depending on the behavior of a fracture during shearing.
Stress-dependent transmission and reflection of seismic waves across a fracture can be used to monitor changes in subsurface stresses. Usually, in such applications, only the stress acting normally to a fracture is considered, which results in large changes in the scattering of seismic waves. However, when a nominally planar, compliant, rough fracture is sheared while a plane elastic wave (compressional [P] or shear [S] wave) is applied normally to the surface, seemingly unusual scattering of plane elastic waves can occur. An incident P-wave generates a pair of transmitted and reflected, coherent S-waves; and an incident S-wave generates P-waves . The amplitude and the polarization (or phase) of the mode-converted waves can be related to the magnitude and the direction of the quasi-statically applied shear stress on the fracture. This phenomenon can be understood as a result of stress-induced anisotropy in the mechanical compliance of single fractures. The stress-induced anisotropy is commonly observed in the elastic compliance (and seismic properties) of rock containing compliant intergranular contacts and cracks [2, 3]. Mechanically, for wavelengths much longer than the local scale (e.g., asperity height and spacing) of a fracture surface, the effect can be explained by elastic dilation: wave-induced stresses normally applied to a fracture result in shear deformations, and shear stresses to normal deformations . At higher frequencies, i.e., the seismic wavelengths comparable to the size of the asperities and voids on the surface of a fracture, the mechanism of the converted wave generation can be understood as a superposition of the waves diffracted (and mode-converted) by these "scatterers" on the fracture.