## Reflection and Transmission coefficient for VTI media

### Ritesh Kumar Sharma, Robert James Ferguson

Presently, we obtain the reflection (R) and transmission (T) coefficients of plane waves at boundary between two transverse anisotropic media with t he vertical axis of symmetry (VTI) in behalf of its importance for numerical computations. Additionally, these coefficients are valuable for the full elastic wave modelling in anisotropic media. Classical R and T coefficients have been obtained in terms of phase angle and can be computed by using the effective ray parameter. To do this, we compute a normal for e ach individual plane wave based on local velocity, that is function of Thomson's parameter of the medium, and a vector cross-product of this normal with the normal to the reflec tor yields a ray parameter that is used here to compute the corresponding R and T coefficients for a given plane wave. Further, the importance of the Thomson's parameters in order to understand the seismic waves signatures in anisotropic media make it necessary to obtain R and T coefficients in Thomson's parameters. For doing so, we build a relationship betw een Vigot elastic constants and Thomson's parameters by following Graebner's approach . Using this relationship, the corresponding R and T coefficients are obtained in terms of Th omson's parameters. Another importance of this approach is the automatic adaption of R and T coefficients for the transverse anisotropic media with the horizontal axis of sy mmetry (HTI). Moreover, amplitude versus offset (AVO) is a variation in seismic reflection amplitude with offset and it's also referred as AVA (amplitude versus angle). Typically, a mplitude decreases with offset because of geometric spreading, attenuation and other fact ors while an AVO anomaly is characterized by the increasing AVO in a sedimentary sectio n and indicates the probability of the presence of hydrocarbons. As opposed to the isotropic case where the velocity remains constant for all incident angles, the velocity is the function of the angle of incidence for anisotropic media and motivates author to analyze the effect of rock anisotropy on the R and T coefficients of seismic waves. To achieve this purpose, first SH wave is considered, due to its simplicity for VTI media. The effect of Thomson parameter on the R coefficients is delineated presently. In continuing of this, the three models characterized by the Class 1, 2 and 3 type of Gas-sand anomaly are considered for obs erving the influence of anisotropy on P-wave reflectivity and to test the accuracy of the plane wave R coefficients. A test of accuracy of the popular Ruger's approximation is also delineated here.