Incidence of plane waves upon a fracture

Abstract

This paper investigates the details of reflection, transmission, and conversion of plane waves incident upon a fracture at arbitrary angles. The elastic compliance of fractures that is produced by the presence of a planar collection of void spaces and asperities of contact is modeled as a displacement‐discontinuity boundary condition between two elastic half‐spaces. Closed‐form expressions for the transmission and reflection coefficients on a fracture are derived by replacing the boundary conditions for a welded interface by those for a fracture into the standard procedure for plane wave analysis. The closed‐form expressions reveal that a single fracture can produce a variety of potentially diagnostic waves such as transmitted waves, reflected waves, converted waves, head waves, and P interface waves and introduce a finite group time delay to all these waves with respect to the incident wave. The amplitude and group time delay of the fracture‐induced waves are controlled by the fracture stiffness, wave frequency, and the Poisson's ratio of the medium. The head wave and inhomogeneous P interface waves are generated when an SV wave is incident upon a fracture, at and beyond a critical angle, respectively, which is determined by Snell's law. For some combinations of the fracture stiffness and the Poisson's ratio of the half‐spaces, no reflection or transmission of a P wave or an SV wave occurs.

Critical analysis of theoretical basics of displacement discontinuity model for media with oriented fractures.

“…Модели разрыва смещений были представлены и другими авторами [Kitsunezaki, 1983;Pyrak-Nolte, Cook, 1987;Pyrak-Nolte et al, 1990a, 1990bPyrak-Nolte et al, 1996;Gu et al, 1996;Pyrak-Nolte, 2007;Shao, PyrakNolte, 2013] под названием "displacement discontinuity". В них рассматриваются различные аспекты этой моде-ли.…”

Sensitivity analysis of fracture scattering

“…When fractures are much larger than the seismic wavelength, then we can take fracture interfaces as infinite planes and apply plane wave theory to calculate their reflection and transmission coefficients and interface waves (Schoenberg, 1980;Pyrak-Nolte and Cook, 1987;Gu et al, 1996). In field reservoirs, fractures always have finite length, and fractures with characteristic lengths on the order of seismic wavelength are one of the important scattering sources that generate seismic codas.…”

Micromechanical model of rough contact between rock blocks with application to wave propagation

“…The micromechanical model described above is applied to investigate wave propagation through rock joints based upon the imperfectly bonded interface methodology, also known as linear slip or displacement discontinuity approach (Schoenberg 1980, Pyrak-Nolte et al 1990, Gu et al 1996, Pecorari 2003. In the subsequent description we focus upon incident P waves only; however, we note that incident SV and SH waves may be treated in a similar manner.…”

“…Brought to you by | University of Kansas Libraries Authenticated Download Date | 11/16/15 5:01 PM normalized reflected and transmitted wave amplitudes for oblique incidence are given in Gu et al 1996). …”