Analysis for reflection and transmission of P-SV waves based on dual variables system

Dual variables system is a new systematic methodology for analysis of dynamic systems, and regarding displacement variables and the corresponding stress variables as dual variables, plane P-SV wave problems can be steered to Hamiltonian dual variables system. Based on eigenvector expansion solution of the dual variables equation, the unified analyzing and solving methods for reflection and transmission problems of P-SV waves are presented, and the methods are fit for uniform waves, inhomogeneous waves and Stoneley wave problems. As the typical applications, Zeoppritz equation for reflection coefficients and transmission coefficients of uniform waves, the equation for propagation coefficients of inhomogeneous waves, and the frequency equation of Stoneley wave are obtained by the unified methods. In dual variables system, the solving process is intuitional and simple, physical meanings are concise, and these show the validity and versatility of the analysis methods of dual variables systems for elastic waves problems.