DIVERSITY AND UNITY FROM EXPRESSION OF KNOTT EQUATION ABOUT THE ELASTIC INTERFACE

Knott equation is the analytical indication of AVO theory. The amplitude ratios of incidents of harmonic plane waves at a plane interface between two elastic half spaces of different properties are governed by Knott equations, which are significant in the researches of elastic wave propagation and oil explorations. It is essential to learn the differences in expressions of Knott equations caused by different mathematic definitions and restrictions of a certain boundary value problem. The results show that there are totally 8 independent expressions from Knott equations for the incidences of plane harmonic P and SV waves in XOZ plane, in detail, 4 for P waves and 4 for SV waves. For those incidences of the same type in one half space with different Knott-equation expressions, their corresponding energy equilibrium equations are identical.