Abstract: We propose an equivalent first-order hyperbolic velocity-stress Biot two-phase isotropic medium elastic wave equation in order to separate pure fast and slow compress waves and pure shear wave in full wave field of two-phase medium.Feasibility of the method is demonstrated with divergence and curl theory.In a high-order staggered-grid finite-difference scheme forward simulating operator is constructed.PML absorbing boundary condition and stability condition are derived.Isotropic and heterogeneous layered two-phase medium models are tested.Full elastic wave field,completely separated pure compress wave and pure shear wave of the solid fluid phase components are obtained.Boundary absorbing effect is perfect,and numerical precision is high.It shows that the fast compress wave and slow compress wave are coupled which can't be separated.They belong to pure compress wave fields.Energy of slow compress wave in fluid phase is greater than that in solid phase which is important in understanding propagating laws and validating elastic wave theory for two-phase medium.

Key words: Biot two-phase isotropic medium, equivalent wave field separation numerical simulation equation, pure fast&low p wave and s wave, PML absorbing boundary condition, solid phase and fluid phase