Azimuth-dependent tuning of seismic waves reflected from fractured reservoirs

Reservoirs with thickness less than the seismic wavelength can still contai n 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 importan t role in determining fluid how 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 var ies with azimuth; hence, the tuning effect will vary with azimuth. For wave lengths much greater than typical fracture spacing, equivalent medium theor y allows such a vertically fractured layer to be modeled as a monoclinic la yer with a plane of mirror symmetry parallel to the layer. The variation in reflection and transmission coefficients with incidence and azimuthal angl e for a thin vertically fractured layer can be expressed in terms of the ho rizontal slowness, automatically accounting for the change of angle with az imuth for rays propagating through the layer and for the tuning effect whic h occurs for layers with thickness of the order of the wavelength. For low enough frequency (or equivalently, thin enough layers), approximate express ions for the reflection and transmission coefficient matrices and transmitt ed amplitudes are derived. These expressions demonstrate explicitly that al l reflected pulses and an converted transmitted pulses have the same shape as the time derivative of the incident pulse, whereas for thicker layers, d istinct reflections from the top and bottom of the layer are evident, parti cularly for small angles of incidence. When these reflections interfere, si gnificant changes in pulse shape with azimuth are found which result from d ifferences in the azimuthal variation of reflection coefficient from the ta p and bottom of the layer due to propagation effects in the layer.