Dispersion of Low-frequency Waves in Fractured and Periodically Layered Media

We defined the low-frequency dispersion of the waves propagating vertically through the periodical set of fractures and layers. Different fracture distributions are analyzed. In the weak-contrast approximation, we defined the sensitivity matrix to illustrate the pure and cross-contributions of layering and fracturing effects into low-frequency dispersion. In case of a single fracture, we define the low-frequency fracture induced anisotropy parameters for small values of fracture weaknesses. Numerical simulations show the low-frequency dispersion for different fracture distributions including the layering.