Stoneley wave properties in a fracture filled with viscous fluid

The properties of a generalized Stoneley wave, a symmetric trapped mode in a fracture filled with a viscous Newtonian fluid embedded into either poroelastic or a purely elastic rock are derived. Symmetric mode is considered. Full dispersion relation corresponding to linearized Navier-Stokes equation in a fracture coupling to either Biot or elasticity equations in the rock via proper boundary conditions is rigorously written down. A cubic equation for wavenumber is found that provides analytical approximation of the exact solution. In the frequency range of 10 −2 − 10 3 Hz and for layer width less than 10 cm, the analytical approximation is verified vs. numerical solution of the full dispersion relation by comparing phase velocity and attenuation, and found to be one of high quality. Comparison to earlier results addressing viscous fluid in either porous rock with rigid matrix or in a purely elastic rock is made, and our formulae are found to better match the numerical solution.