Low-frequency scattering on a half-space filled with periodic fluid-solid medium with dipped layers

A low-frequency effective model has been developed for a medium with periodical liquid and solid layers with the slip between layers. It is shown that for an effective periodically n-layered medium with solid dipped layers with slip there exist n +1 plane waves with a fixed horizontal slowness that propagate downward. The boundary conditions are determined for low-frequency scattering at the boundary between a solid half-space and a half-space filled with an effective medium. These conditions depend on the dip angle of the layers and their filling. Based on the boundary conditions, linear systems of equations for the reflection and refraction coefficients are derived. Low-frequency scattering on a half-space with dipped solid layers with the slip is described by a system of n +3 equations with n +3 unknowns. In the presence of liquid layer, the number of equations and unknowns is equal to n +2. If the lower half-space consists of horizontal layers, the number of equations and unknowns is equal to 3. Explicit formulas for the roots of this system of equations are obtained for the case when the layers are horizontal. The theory is demonstrated on various examples of calculating the reflection and refraction coefficients.