Analytical and Numerical Study of the Reflection/Transmission Coefficients in Slight Viscoelastic Medium

摘要

The study done in this paper brings out the effect of the viscoelasticity on the reflection/transmission coefficients. The knowledge of this effect can be useful for several applications, such as enhancing the resolution of the seismic sections, fluid and fracture detection. It can also have other applications different from the geophysical domain, as the study of the bonding between the materials in the civil engineering domain. We use the complex Lame coefficients in the continuity equations at the boundary layers to get the analytical expressions of the reflection/transmission coefficients in viscoelastic media. The coefficients can be divided into two parts, the first part is independent from the quality factor, and it corresponds to the elastic reflection/transmission coefficients. The second part is dependent on the quality factor contrast and it represents the contribution of the viscoelasticity on the reflection/transmission coefficients. From the numerical study it appears that the effect of the viscoelasticity is significant near to the critical angles. This effect is not clear and it is difficult to interpret and we do not know if it has a physical meaning or it is only a mathematical artifact that is why it is better to be far from the critical angles for seismic investigation.