Tuning effects of a thin layer with triclinic anisotropy

Tuning effects, induced by the interference between scattering waves at the top and bottom interfaces, characterize the dependence of thin-layer seismic responses on wave frequencies, thin-layer thicknesses, and medium elastic properties. The characteristics of tuning effects are frequently used to infer thin-layer properties. We analyze the tuning effects of a thin triclinic layer between two varying triclinic half-spaces. Exact thin-layer reflection and transmission (R/T) coefficients are developed to characterize the pre-stack thin-layer tuning effects of P-, S1-, and S2-waves. The thin-layer R/T coefficient approximations are proposed to build concise relationships between tuning effect characteristics and medium parameters. The relationships give insights when estimating thin-layer properties from interpreting tuning effect characteristics. As inferred from the approximations, the tuning effect of a thin triclinic layer is composed of two fundamental tuning effects making sense for two particular thin-layer models of which one has identical enclosing half-spaces and the other has identical elastic parameter discontinuities at the bottom and top interfaces. The combined influences of wave frequencies, thin-layer thicknesses, and incidence angles on the two fundamental tuning effects can be assessed by a unique factor for each wave mode. For a general thin triclinic layer, this factor characterizes the periodic variations of reflection amplitudes versus wave frequencies. The maximum and minimum thin-layer reflection amplitudes are determined by the reflectivities at the top and bottom interfaces. With wave frequencies or thin-layer thicknesses increasing from zero, thin-layer reflections have smaller or larger amplitudes when the two single-interface reflectivities have equal or opposite polarities, respectively. We develop a method to evaluate the sensitivity of thin-layer reflection amplitudes to thin-layer elastic parameters. The sensitivity is higher when the two single-interface reflectivities have opposite polarities compared to the equal-polarity case. Numerical tests are used to demonstrate the proposed approximation accuracy and the characteristics of tuning effects.