Reservoirs with thickness less than the seismic wavelength can still contain significant amounts of hydrocarbons. Such layers exhibit a tuning effect which involves the interference of reflected waves from the top and bottom of the reservoir. Natural fractures in such reservoirs can play an important role in determining fluid flow, which makes the density and orientation of fractures of great interest. In the presence of one or more sets of aligned vertical fractures, the amplitude of reflected waves at nonzero offset varies with azimuth; hence, the tuning effect will vary with azimuth. For wavelengths much greater than typical fracture spacing, equivalent medium theory allows such a vertically fractured layer to be modeled as a monoclinic layer with a plane of mirror symmetry parallel to the layer. The variation in reflection and transmission coefficients with incidence and azimuthal angle for a thin vertically fractured layer can be expressed in terms of the horizontal slowness, automatically accounting for the change of angle with azimuth for rays propagating through the layer and for the tuning effect which occurs for layers with thickness of the order of the wavelength. For low enough frequency (or equivalently, thin enough layers), approximate expressions for the reflection and transmission coefficient matrices and transmitted amplitudes are derived. These expressions demonstrate explicitly that all reflected pulses and all converted transmitted pulses have the same shape as the time derivative of the incident pulse, whereas for thicker layers, distinct reflections from the top and bottom of the layer are evident, particularly for small angles of incidence. When these reflections interfere, significant changes in pulse shape with azimuth are found which result from differences in the azimuthal variation of reflection coefficient from the top and bottom of the layer due to propagation effects in the layer.
Reflection and transmission of seismic waves under initial stress at the earth's core-mantle boundary
