Acoustic Nonlinearities Produced by a Single Macroscopic Fracture in Granite

Mathematical Fundamentals of a Diagnostic Method by Long Nonlinear Waves for the Structured Media

“…Now we represent the theoretical fundamentals for new method of diagnostics of medium by means of the long nonlinear waves. Let us prove the principal relation which enables us to obtain the inverse function ζ ¼ ζ V=c 2 ðÞ for the desired function…”

“…Indeed, for the monotonic one-valued function V=c 2 ¼ V=c 2 ζ ðÞ , we find the integral in (59) by integrating the inverse function ζ ¼ ζ V=c 2 ðÞ , since the transformation Jacobian is not equal to zero. We have the chain of identifies…”

“…Natural media, in the general case, should not be treated as structureless. The experiments have shown that the intrinsic structure of a medium influences the wave motions [1][2][3][4][5][6][7][8]. Existing inhomogeneities complicate the problem and, at the same time, are fully manifested under the propagation of nonlinear waves.…”

“…Existing inhomogeneities complicate the problem and, at the same time, are fully manifested under the propagation of nonlinear waves. The principal part of the problem is associated with the phenomena caused by the nonlinear behavior of natural media, in particular, more substantial increase of nonlinear effects in structured media than that in homogeneous ones [1][2][3][4][5]7].…”

Strain‐dependent partial slip on rock fractures under seismic‐frequency torsion

“…We have adapted a low‐frequency (0.1–100 Hz) subresonance apparatus, designed for shear modulus and attenuation measurements [ Bonner and Wannamaker , , ; Saltiel et al ., ] to explore the seismic signature of fractures and understand the mechanics of asperity contacts under low normal stresses and a range of shear strains. Our instrument is unique in its ability to conduct measurements at low normal stresses, simulating “open” fractures in shallow or high fluid pressure reservoirs, which often dominate the permeability of fractured systems.…”