An approximation to the reflection coefficient of plane longitudinal waves based on the diffusive-viscous wave equation

The frequency-dependent seismic anomalies related to hydrocarbon reservoirs have lately attracted wide interests. The diffusive-viscous model was proposed to explain these anomalies. When an incident diffusive-viscous wave strikes a boundary between two different media, it is reflected and transmitted. The equation of the reflection coefficient is quite complex and laborious, so it does not provide an intuitive understanding of how different amplitude relates to the parameters of the media and how variation of a particular parameter affects the reflection coefficient. In this abstract, we first derive the two-term (intercept-gradient) and three-term (intercept-gradient-curvature) approximations to the reflection coefficient of the plane diffusive-viscous wave without any assumptions. Then, we give the limitations of the obtained approximations by comparing the approximate value of the reflection coefficient with its exact value. Finally, we analyze the impacts of parameters of the media on the intercept, gradient and curvature terms in the approximations. The results show that the diffusive parameter in the diffusive-viscous wave equation has a big impact on the them, while the viscous parameter is insensitive to them.